environmental chemistry notes 2011 - class

PART ONE FUNDAMENTALS OF CHEMISTRY

Fundamentals of Chemistry

Environmental Chemistry-2011 of 43

1 INTRODUCTION

For many years the attention of environmental engineering was devoted largely to the development of safe water supplies and the sanitary disposal of human wastes. Expanding populations with resultant increased industrial operations, power production, and use of motor-driven vehicles, plus new industries based upon new technology have intensified old problems and created new ones in the fields of water supply, waste disposal, air pollution, and global environmental change. Currently if one were to develop a list of the most important problems facing the world today, it would include, but not limited to, water and wastewater treatment, groundwater contamination, hazardous waste management, radioactive waste management, acid rain, air toxins emission, ozone depletion, and global climate change. Understanding these problems and development of processes to minimise or eliminate them requires a fundamental understanding of chemistry. 1.1 Water Water is one of the materials required to sustain life and has been suspect of being the source of much illness to human beings. Surface and groundwater sources have become increasingly contaminated due to increased industrial and agricultural activity though water supplies free of colour, turbidity, taste, odour, nitrate, harmful metal ions, and a wide variety of organic chemicals such as pesticides and chlorinated solvents is increasingly on demand. As populations increase, the demand for water grows accordingly especially when this is accompanied by improved standards of living. In many situations in water short areas, purposeful recycling of treated wastewater will be required in some degree to avoid serious curtailing of per-capita usage and industrial development. To achieve this goal, water chemistry will play a vital role in finding solutions for the increased demand in areas where water is a scarce resource. 1.2 Wastewater and water pollution control The disposal of human wastes has always constituted a serious problem. Both storm water and sewage are normally carried away from the area near human habitats into the nearby watercourse. It soon became apparent that rivers and other receiving bodies of water had a limited ability to handle waste materials without creating nuisance conditions. This led to the development of purification or treatment facilities in which the knowledge of chemistry is a major tool used by chemists, engineers and biologists who have played important roles in this kind of field. 1.3 Industrial and hazardous wastes Perhaps the most challenging field as far the well being of the environment is concerned at the present is the treatment and disposal of industrial and hazardous wastes. Because of the great variety of wastes produced from established industries and the introduction of wastes from new processes, a knowledge of chemistry is essential to a solution of most of the problems. Some may be solved with a knowledge of inorganic chemistry; others may require a knowledge of organic, physical, or colloidal chemistry, biochemistry, or even radiochemistry. It is to be



expected that, as further technological advances are made and industrial wastes of even greater variety appear, chemistry will serve as the basis for the development and selection of treatment methods. Definition of Environmental chemistry Environmental chemistry is essentially the science of identifying and measuring the amount of chemicals species in the environment, natural or manmade. It also includes the study of the fate and effects of these chemical species in the environment. It includes such tasks as defining the intended use of analytical data, preparing sampling plans to satisfy the intended use, selecting appropriate analytical methods, advising on the collection of samples in the field, interpreting laboratory analytical results, and assuring the validity and legal defensibility of analytical results. In determining fate and effects, it often involves an evaluation of organic and inorganic chemical reactions as well as physical processes such as volatilisation, cosolvency effects, and soil adsorption. The broad area of environmental chemistry encompasses a number of related fields, including analytical chemistry, chemical engineering, organic chemistry, data quality assurance, radiation chemistry, and inorganic chemistry. 1.5 Environmental Monitoring There are four phases of the Data Life Cycle: planning, implementation, assessment, and reporting. The Data Life Cycle illustrates how data are generated and used

In the planning stage, prospective data users decide what type, quantity, and quality of data will be needed to serve their needs. The planning stage begins with the Data Quality Objectives (DQO) Process, a systematic planning process based on the scientific method that helps investigators define the problem to be investigated; the constraints and limitations of the investigation; and the type, quantity, and quality of the data needed. Investigators also use the DQO Process to develop a sampling design for collecting the data. The outputs of the DQO Process and the resulting sampling design are documented in the Quality Assurance Project Plan (QAPP). The QAPP also



details the management authorities, personnel, schedule, policies, and procedures for the data collection event. Where possible, the QAPP incorporates Standard Operating Procedures (SOPs), which ensure that data are collected using approved protocols and quality measures. Some sample QA materials are provided. It is useful to include random spiked samples with field samples as a form of routine testing of laboratory QA/QC; you want to know how well the laboratory performs when you haven't told it you are doing a QA check! In the implementation stage, data are collected according to the methods and procedures documented in the QAPP. During the data collection event, technical assessments (TAs) are conducted to assess whether or not data are being collected as stated in the QAPP; these assessments also generate QA/QC data that accompany the results during the assessment phase. In the assessment stage, analysts use technical knowledge and statistical methods to determine whether or not the collected data meet the user's needs. The data are verified and validated to ensure that the measured values are free of gross errors due to procedural or technical problems. Investigators may then analyse the data using the Data Quality Assessment (DQA) Process, which determines whether or not the data meet the user's performance criteria as stated in the outputs of the DQO Process. Next, investigators examine the results of the DQA Process and develop scientific conclusions to the problem. In the reporting phase, the data collected by the study are reported with all the relevant quality assurance and quality control (QA/QC) data so that decision makers can judge the quality of scientific information available to support their decisions. Reporting also helps the future users of the data determine whether and how these data might be applied to additional studies or in different contexts. Data Quality Objectives (DQOs) Environmental chemistry includes such tasks as definition of intended use of analytical data, preparation of sampling plans to satisfy intended use, selection of appropriate analytical methods, sample collection in the field, interpretation of laboratory results, and the fate and effects of chemicals in the environment. Intended use of data can include such purposes as site characterisation, compliance monitoring, determination of extent of contamination, toxicological risk assessment, personnel monitoring, remediation alternative studies, and remediation verification. The selection of appropriate sampling and analysis methods must satisfy the applicable state and federal regulations. The appropriate sampling and analytical methods are determined during the Data Quality Objective (DQO) process. DQOs are qualitative and quantitative statements derived from the outputs of the first six steps of the DQO process. DQOs clarify the study objective, define the most appropriate type of data to collect, determine the most appropriate conditions from which to collect the data, and specify tolerance limits on the data used to make decision. DQOs are not restatements of laboratory limits for precision and accuracy, but statements that result from the DQO process.



The seven steps of the DQO process are: 1. State the problem – concisely describe the problem to be studied. 2. Identify the decision – identify what the study will resolve. 3. Identify the inputs to the decision – identify the information needed. 4. Define the boundaries of the study – specify time periods and spatial areas. 5. Develop a decision rule – define the statistical parameter of interest. 6. Specify tolerable limits on decision errors – define the decision-maker’s error limits. 7. Optimise the design for obtaining data – generate alternative data collection designs. By following the DQO process, one can improve the effectiveness, efficiency, and defensibility of decisions in a resource-effective manner. Sample collection must be carried out in a manner that will not compromise the intended use. Interpretation of laboratory data will involve working with the users of the data (geologists, hydrogeologists, toxicologists, and environmental engineers) to determine the suitability of the data for their intended use. Fate and effects studies address those reactions that may occur due to physical and chemical processes in the environment and often involve evaluation of the role of organic and inorganic chemical reaction mechanisms as well as physical processes such volatilisation, water transport, and soil adsorption. Data Quality Assessment Data Quality Assessment (DQA) is a formal, rigorous scientific and statistical evaluation to determine if environmental data are the right type, quality, and quantity to support their intended use. The process involves review of data quality objectives (DQOs), sampling purpose, sampling design, sampling methods, documentation, analytical procedures, validation procedures, data reduction procedures, review of data base procedures, and review of statistical methods used for decision making. The five steps in the DQA process are: 1. Review the DQOs and sampling design. 2. Conduct a preliminary data review. 3. Select the statistical test. 4. Verify the assumptions of the statistical test. 5. Draw conclusions from the data. DQA frequently requires data validation. Data validation is a process to verify that the laboratory has complied with all the requirements (Quality Control Checks) of the specified analytical method. Data qualification is the process of qualifying (flagging) data to reflect any failures to meet the requirements according to the sets of pre-established functional guidelines. The USEPA has published generic functional guidelines for flagging environmental analytical data, much of which is applicable to forensic data. The qualifications of the data are considered with respect to the intended use of the data to determine the suitability (or technical validity), which can range from complete acceptance to partial restriction to complete rejection. Often, data that has been rejected during the validation process can be “rescued.” Data rescue involves techniques to salvage data that appears to be unsuitable upon completion of qualification.



Quality Assurance (QA) QA is the total integrated process for assuring the defensibility and reliability of decisions based on chemical analysis data. The principal goal of the QA process is to provide the necessary documentation for a comprehensive user Data Quality Assessment. The DQA determines if the data quality is adequate for its intended use and involves a four-step process: 1) data validation, 2) data qualification, 3) data rescue, and 4) data suitability determination. The qualifications of the data are considered with respect to the intended use of the data to determine the suitability (or technical validity), which can range from complete acceptance to partial restriction to complete rejection. Sampling Program Design The design of a sampling scheme and selection of sampling methods is a multidisciplinary process that often requires input from environmental chemistry, environmental geology, environmental microbiology, and risk assessment. The purpose of sampling is to obtain a fraction of some lot of material that accurately represents the characteristics of the entire lot. The “lot” is what we are sampling. It may be a landfill, a tank car, a drum, sediments under a pond, or a jar in the analytical laboratory. In practice, it is not possible to obtain a perfectly representative sample of soils or sediments. Sampling procedures should be designed to minimise the sampling error and to document an estimate of the overall error, which includes sampling error, sample handling error, and analytical error. Some sources of sampling error cannot be eliminated, however, with proper understanding of sampling theory and with clear understanding of the purpose of the sampling, error can be minimised and documented. Incorrect sampling design or incorrect sampling procedures are just as damaging to the defensibility of data as are incorrect analytical methods. Planning for sampling and assessment of sampling methods should be given the same consideration as analytical data validation.



2 BASIC CONCEPTS FROM GENERAL CHEMISTRY

2.1 Introduction Applications of chemistry range throughout most manufacturing activities but even in daily life we are confronted with chemistry. In water supply and sanitation, chemistry and microbiology both play an important role especially in water supply they are tightly related to water quality. Agriculture, medicine Engineering, electronics

Mining, geology

Mining, Geology Fig 1.1 The central role of chemistry in Science

2.2 Structure and Properties of Matter 2.2.2 Properties of substances Physical properties A basic physical property is the "state of matter" which includes the solid, liquid, and gaseous form. The state of a particular kind of matter depends on conditions such as temperature and pressure. For example, water in an open vessel exists in the liquid state at 25°C but below 0°C it is a solid (ice) and above 100°C it becomes a gas (steam). Changes in physical state are due to physical phenomena or processes. It is always possible to get the original situation back, after which the substance has not been changed and shows the same properties as before. Other physical properties are density, melting point, colour and electrical conductivity. Some of these properties depend only on what the substance is; they are called intensive properties. Others depend on how much of the substance is present; they are called extensive properties.

Biology

Physics

Chemistry

Geology



Colour, density, melting point, and boiling point are intensive properties; no matter how much of the substance is present. Mass, volume, and size, on the other hand are extensive properties. Chemical properties These relate to how substances change into other substances, usually by interacting (reacting) with other substances. Examples: An iron nail, when exposed to moisture and, undergoes a chemical change, or chemical reaction, as it slowly forms a new substance called iron oxide or rust. This chemical change, oxidation, distinguishes iron from another metal like gold which is unaffected by water and oxygen. 2.3 Traditional classification of matter 2.3.1 Pure substances A pure substance is matter that has the same fixed composition and the same chemical properties throughout; it contains only one component. Distilled water is a pure substance containing only water. 2.3.2 Elements These cannot be decomposed through chemical changes. Elements are classified into metals and non-metals (metalloids). 2.3.3 Compounds These are pure substances that are a combination of elements. Therefore, all compounds can be decomposed through chemical change to elements. When elements combine to form compounds, the compounds usually have properties that are very different from those of the elements. Consider the case of sodium and chlorine. Sodium is a soft, grey, highly reactive metal that reacts very vigorously with water and air. Chlorine is a pale, green, gaseous substance; it is toxic in large doses and it is highly reactive. Sodium and chlorine react vigorously with each other to form sodium chloride (table salt). The sodium chloride is a solid white substance. Although it dissolves in water, it does not react with water. It is not generally toxic and is stable in air. 2.3.4 Mixtures Most matter does not exist in nature as pure substances but as mixtures of chemical substances. A mixture contains two or more pure substances in variable amounts; each of the substances retains its own identity. For example air is a mixture of nitrogen, oxygen, argon, and several other substances; seawater is a mixture of water, salt, and many other minerals; soil is a very complex mixture of many materials. Some mixtures are called heterogeneous mixtures. Their components are present in more than one phase. A phase is a physically distinct and mechanically separable portion of matter. Other mixtures, however, have all their components present in the same phase. These are called



homogeneous mixtures. Their components are dispersed uniformly throughout the mixture. Examples include air, coffee with sugar in it, and salt water. Homogeneous mixtures are the easiest to separate. On other hand, homogeneous mixtures are usually more difficult to separate than heterogeneous mixtures. One way to separate them is by distillation.

Figure: Elements, compounds and mixtures 2.4 Dalton's Atomic Theory and consequences To understand the way matter behaves, it is necessary to study its composition and structure. In 1803, Dalton set forth the following basic postulates: � Matter is made up of small particles called atoms. � All atoms of an element are identical in their physical and chemical properties. � Atoms of one element differ in physical and chemical properties from atoms of other

elements. � Atoms of an element cannot be subdivided and cannot be changed into atoms of another

element. � Atoms are not destroyed nor created in ordinary chemical reactions. � Compound substances consist of a combination of atoms of different elements in constant

whole-number ratios and are called molecules. Scientists eventually accepted Dalton's theory because it explained observations that led to the statement of two fundamental laws of chemistry: (i) Law of conservation of matter Matter is neither created nor destroyed in any ordinary chemical reaction. Atoms cannot be destroyed or created, but are just rearranged in chemical reactions. This implies that matter is conserved in chemical reactions (ii) Law of constant composition A compound, regardless of how it is prepared, always contains the same elements in the same proportion by mass. This is accounted for by Dalton's last postulate: If a compound is formed

Elements cannot be decomposed into a simpler substance

Compounds 1. more than one element 2. compound is definite

Mixtures 1. More than one substance

(compoundss and/ or elements) 2. Composition is variable



by a definite, constant, whole-number ratio of atoms, then it follows that it will always contain the same proportions by mass. In addition, Dalton used his postulates to predict a third fundamental law of chemistry: (iii) Law of multiple proportions If two elements combine to form more than one compound, the masses of one element that combine with a fixed mass of the second element will be in a ratio of small whole numbers. 2.4.1 Structure of molecules and properties Pure substances consist of building blocks called atoms and molecules. Elements contain only one kind of atom. Compounds, on the other hand, contain more than one element so they must contain more than one kind of atom. An atom is usually presented as a sphere and a molecule as a cluster of spheres. The next table gives an impression of the possible stable combinations in relation to the type of matter: 2.4.2 Objections to Dalton's model Note that the atomic theory of Dalton gives no explanation of or does any forecasting about: � the nature of the interaction between particles � the number of atoms that will be combined � the arrangement of the different atoms in the molecule, and � the shape of the polyatomic molecules At the present, it is known that the atom can be subdivided into smaller, more fundamental particles and that an atom of one element can be changed into an atom of another element in the course of nuclear reactions. It is known that atoms of an element can have different masses (isotopes) but do not differ significantly in chemical properties. However, still the basic principles of Dalton's atomic theory serve as the basis for understanding properties of matter. Gram atomic weights, Gram molecular weights and Equivalent weights Atomic weights of the elements refer to the relative weights of the atoms as compared with the atomic weight of Carbon 12 isotope with a value of exactly 12. Elements do not have atomic weights that are whole numbers because they consist of a mixture of isotopes. The Gram atomic weight of an element refers to a quantity of the element in grams corresponding to its atomic weight. It has principal significance in the solution of problems involving weight relationships. Gram molecular weight refers to the molecular weight in grams of any particular compound sometimes called a mole. It is important in preparation of molar or molal solutions. The term equivalent weight can be defined as follows:

Where Z can be the absolute value of the ion charge or the number of H+ or OH- ions a species can react with or yield in an acid-base reaction or the absolute value of the change in the valence occurring in an oxidation-reduction reaction.

Z

MWEW =

EW

compoundaofmoleoneeq=1



Therefore the equivalent weight of a compound is that weight of the compound which contains one gram atom of available hydrogen or its chemical equivalent. For acids, the value Z is equal to the number of moles of H+ obtainable from one mole of the acid. for HCl, Z = 1, and for H2SO4, Z = 2. For acetic acid (CH3COOH), Z = 1 since only one of the hydrogen atoms in the acetic acid molecule will ionise to yield available H+ ions in solution. CH3COOH → CH3COO- + H+ For bases, the value Z is equal to the number of H+ with which one mole of the base will react. For NaOH, Z = 1; for Ca(OH)2, Z = 2. Example: (a) What is the equivalent weight of the calcium ion (Ca2+)?

EW = MW Z = 40 g/mole 2 = 20 g per equivqlent (b) What is the equivalent weight of Calcium carbonate (CaCO3)? Consider CaCO3 + 2H+ → Ca2+ + H2CO3

Alternatively, CaCO3 is made up of Ca2+ and CO32-, the absolute value of the ion charge of each being 2. This implies that

(c) What concentration is 40 mg/L of Ca2+ when expressed as CaCO3? (Note that hardness of water is often expressed as mg/L of CaCO3)

2.5 Symbols, Formulas and Nomenclature 2.5.1 Elements and their symbols Each of the elements has been assigned its own unique symbol as a shorthand notation, which is very useful in writing chemical formulas and equations. In most cases the symbols are derived from the English name for the element. For example the symbol for Carbon is C; for chlorine is Cl, etc. In some instances, the symbols are derived from the Latin names given to

eqg

moleg

Z

MWEW

/502

/1002

)1631240(

=

=

×++=

=

eqg

EW

/502

100

=

=



those elements that were discovered long ago by alchemists. Regardless of the origin, the first letter is always capitalised and the second letter is always written in lowercase. For example, the symbol for copper is Cu, not CU. Be very careful to follow this rule to avoid confusion, for example between such symbols as Co for cobalt and CO for carbon monoxide. 2.5.2 Formulas of some compounds and structures Chemical formulas convey several kinds of information. The most important characteristic of a formula, however, is that it specifies the composition of a complex chemical substance. In a chemical formula for a compound, the constituent elements are identified by their chemical symbols. In addition, the subscripts in the formula tell how many atoms of each of the elements are present. 2.5.3 Nomenclature of some compounds Each chemical compound has its unique name, and these names are normally assigned in a systematic way. Often names such as sodium chloride - the chemical name for common table salt, are seen. This substance, NaCl, is composed of two elements, sodium and chlorine. Calcium chloride is the name for the compound CaCl2, which contains the elements calcium and chlorine. In both these cases the -ine for chlorine has been replaced by -ide. The ending -ide is a clue that nearly always indicates that two different elements are present. Not every compound is named in such a logical fashion. Many substances were discovered long before a systematic method of naming them had been put in place, and they acquired common names that are so well known that no attempt has been made to rename them. For example, following the scheme described above we might expect water would have a name such as dihydrogen oxide. Although this is not wrong, the common name water is so well known that it is always used. Another example of a compound known by its common name is ammonia, NH3.



Table 1.1 Nomenclature of oxygen-bearing acids and their salts On the basis of oxidation state

Name of acid Formula Name of salt

Sulphurous H2SO3 Sulphite Sulphuric H2SO4 Sulphate Hypochlorous HClO Hypochlorite Chlorous HClO2 Chlorite Chloric HClO3 Chlorate Perchloric HClO4 Perchlorate

On the basis of hydration

Orthosulfuric H2SO4 Orthosulfate Orthophosphoric H3PO4 Orthophosphate Orthophosphorous H3PO3 Orthophosphite

2.6 Chemical reactions in general 2.6.1 The Chemical Reaction and the Reaction Equations The chemical nature of matter means that substances can be transformed to new substances with totally different properties. Taking the structure of matter into consideration a chemical reaction is a rearrangement of atoms. To perform chemical reactions each substance is made as fine as possible before bringing into contact with each other. During the reaction, the moving particles may exist in the same or different physical states. In a homogeneous mixture or solution all the submicroscopic particles are in the same physical state (phase) and equally distributed. In heterogeneous mixtures, the particles are not fully mixed in the system. The transformation is represented by a chemical equation like:

A + B → C The arrow means "reacts to yield" or "to form". If we call the participated starting substances "reactants" (or "reagents") and the result of the transformation "products" we can rewrite the equation as:

Reactants → products A fundamental rule that must be observed at all times is that expressions of chemical reactions become equations only when they are balanced. In order to balance a chemical equation, it is essential that it represents a reaction in the true manner, and all formulas used must be correct. Unless these conditions are complied with, weight relationships are meaningless. Weight relationships serve as the basis for the sizing of chemical feeding equipment, necessary storage space for chemicals, structural design, and cost estimates in engineering considerations. For example; NaOH + HCl → NaCl + H2O Weight (23 +16+1) (1+35.5) (23+35.5) (2x1) + 16 Relationships 40 36.5 58.5 18 Thus 40g of NaOH combines with 36.5g of HCl to form 58.5g of NaCl and 18g of H2O



Oxidation - Reduction Equations An atom, molecule or ion is said to undergo oxidation when it loses an electron, and to undergo reduction when it gains an electron. When oxidation-reduction reactions occur between atoms to form molecules or ions with polar covalent bonds, certain assumptions are required in order to maintain a consistent concept, for example; H 2H:H + : O : O : → 2 : O : H H2 and O2 are homonuclear covalent molecules. We adopt the convention that the electrons are shared equally by the homonuclear cores, no atom gains or loses electrons in the formation of the molecule from its atoms; thus the oxidation number (or valence) is zero. Water is a heteronuclear polar covalent molecule. In H2O, the electrons are shared unequally by H2 and O2, oxygen having a greater holding power on the electrons, and is said to be more electronegative than hydrogen. In the formation of water molecules, each hydrogen atom takes on an oxidation number of +1 (becomes oxidized) and the oxygen an oxidation number of -2 (becomes reduced). Hydrogen and oxygen when part of essentially all heteronuclear molecules and ions of interest in environmental engineering, take on these oxidation numbers. Many oxidation-reduction reactions require the presence of a third compound usually an acid or water to progress, for example; 2KMnO4 + 10FeSO4 + 8H2SO4 → 5 Fe2 (SO4) 3 + K2SO4 + 2MnSO4 + 8H2O Or MnO4

- + 5Fe2+ + 8H+ → 5Fe3+ + Mn2+ + 4H2O K2Cr2O7 + 6KI + 7H2SO4 → Cr2(SO4)3 + 4K2SO4 + 3I2 + 7H2O Or Cr2O7

2- + 6I- + 14H+ → 2Cr3+ + 3I2 + 7H2O ⇒ Water is usually a constituent or product of chemical reactions further emphasizing the role

of chemistry in water and wastewater engineering. 2.6.2 Balancing equations In equations, there are numbers, in front of each of the formulas, called coefficients. These are present to balance the equation. An equation is balanced if the same number of atoms of each element appears on both sides of the arrow. This is a direct consequence of the law of conservation of matter. For example, the burning of butane, C4H10, the fluid used in disposable cigarette lighters, the equation for this chemical reaction is

2C4H10 (s) + 13O2 (g)→ 8CO2(g) + 10H2O

The 2 before the C4H10 means that two molecules of butane react. This involves a total of 8 carbon atoms and 20 hydrogen atoms. On the right, there are 8 molecules of CO2, which



contain a total of 8 carbon atoms. Similarly, 10 water molecules contain 20 hydrogen atoms. Finally, 26 oxygen atoms exist on both sides of the equation. 2.6.3 Subscripts, etc. In a chemical equation, it is sometimes necessary to specify the physical states of the reactants and products - that is, whether they are solids, liquids, or gases. This is done by writing the letters s (= solids), l (=liquids), or g (=gases) in parentheses following the chemical formulas. At times, it is useful to indicate that a particular substance is dissolved in water. This is done by writing the letters aq, instance, the equation for the reaction for the reaction of HCl and NaOH described earlier in this section can be written as:

HCl (aq) + NaOH (aq) → NaCl (aq) + H2O (aq) Sometimes a reaction must be helped in order to proceed. In these cases heat is supplied, or a catalyst or light is used. In the equation then we may place additional signs over the arrows:

CBACBA catT →+→+ ,

Sometimes the product will leave the reaction mixture as a precipitate or as a gaseous product. A vertical arrow is used: Precipitate: A + B → C↓ Gas: P + Q → R↑ 2.6.4 Heat effects In principle, all chemical reactions are accompanied by heat effects. If heat is released, the reaction is called exothermic reaction. If heat is absorbed, the reaction is endothermic reaction. The heat effect is denoted by the symbol ∆H and expressed in kJ/mol. In case of an exothermic reaction the values of ∆H is given a negative sign, for endothermic reactions a positive sign is used.



2.7 Chemical Calculations The masses of molecules can be determined on the atomic mass scale. Since molecules are made up of atoms, the mass of a molecule is the sum of the masses of the atoms making up the molecule. The mass of a molecule on the atomic weight scale is called the molecular mass (molecular weight or formula weight). For example, the molecular weight of nitrogen monoxide, NO, is the sum of the atomic masses of nitrogen and oxygen:

MWNO = AWN + AWO

2.7.1 Stoichiometry The calculation of quantities of material involved in chemical reactions is called stoichiometry. A chemical equation appears simple, but contains a great deal of information. Consider the reaction between hydrogen and oxygen to form water:

2H2 (g) + O2 (g) → 2H2O (l) This equation means: 2 H2 - molecules react with 1 O2 - molecule to form 2 H2O - molecules or 2 mol H2 ≡ 1 mol O2 ≡ 2 mol H2O or if:

22

=HMW and 321622

=×=OMW 1816122

=+×=OHMW

or: OHgOgHg 222 4

36

4

321 ≡≡

This kind of expression is the basis for calculating the theoretical yield of a product or the theoretical amount reactant (reagent) involved. 2.7.2 Limiting reagents and actual yields It has been assumed that all reactants are present in exactly the correct amounts to react according to the balanced equation. In practice, when a reaction between two substances is carried out, there is sometimes a large excess of one of the reactants. The reacting substance whose quantity determines the amount of product formed is called the limiting reagent. If it is not obvious from the statement of the reaction conditions which substance is the limiting reagent, then we must determine the limiting reagent by calculation. There are several ways to do this, but the most versatile is to compare the number of moles of each reactant using the balanced equation. In actual experiment, it is not always possible to recover the amount of product calculated. Losses of product sometimes occur because of physical difficulties in collecting the product. These difficulties can be minimised by careful design of the experiment and by excellent laboratory technique, but they cannot always be eliminated. Further more the incompleteness of reaction may arise because the reactants are not given enough time to react or because side reactions take place. The amount of product obtained in an actual experiment is the actual yield. When compared to the theoretical yield on a percentage basis, it is called the percentage yield:

%100×=yieldltheoretica

yieldactualyieldpercentage



2.7.3 Molar concentrations If the reaction occurs in a solution, we don't calculate with absolute quantities like mg, but in concentration units. The best units are moles of solute per litre of solution. The special name for this ratio is molar concentration or molarity, in formula:

V

NC =

In which N = number of moles and V = volume Percentage composition Percentages by weight are the forms usually used to report the ratios by mass of the elements in a compound, and a list of these percentages is called the compound's percentage composition. The percentage by weight of an element in a compound is equivalent to the number of grams of the element present in 100g of the compound. Example: Calculate the weight % Fe and water in iron sulphate (FeSO4.7H2O) Calculate first the molecular weight of the iron sulphate

278)162(71643256.7. 24=+×+×++=OHFeSOM

1 mol Fe within 1 mol iron sulphate, or: 56 g Fe in 278 g iron sulphate, so:

% Fe = %1.20%100278

56 =×

and analogous:

% Water = %3.45%100278

126 =×

2.8 THE GAS LAWS 2.8.1 Henry's Law Henry's law states: The weight of any gas that will dissolve in a given volume of a liquid, at constant temperature, is directly proportional to the pressure that the gas exerts above the liquid. In equation form,

Cequil = αPgas

Where Cequil is the concentration of gas dissolved in the liquid at equilibrium, pgas is the partial pressure of the gas above the liquid, and α is the Henry's law constant for the gas at the given temperature. Henry's law is undoubtedly the most important of all the gas laws in problems involving liquids. With a firm knowledge of Dalton's and Henry's laws, one should be capable of coping with all problems involving gas transfer into and out of liquids. Most of the problems related to the transfer of gases into liquids involve addition of oxygen by aeration to maintain aerobic conditions. The removal of gases from liquids is also accomplished by aeration devices of one sort or another. Although Henry's law is an



equilibrium law and is not directly concerned with the kinetics of gas transfer, it serves to indicate how far a liquid-gas system is from equilibrium, which in turn is a factor in the rate of gas transfer. Thus, the rate of solution of oxygen is proportional to the difference between the equilibrium concentration as given by Henry's law and the actual concentration in the liquid:

( )actualequil CCdt

dC −α (2.1)

This concept serves as the basis for engineering calculations in aerobic methods of waste treatment, such as the activated sludge process, and in the evaluation of reaeration capacity of lakes and streams. The removal of undesirable gases, such as carbon dioxide, hydrogen sulphide, and hydrogen cyanide, from liquids is also commonly accomplished by some form of aeration. The general principles involved are the same as in the transfer of gases into the liquid. However, in this case the normal partial pressure of the gas in air is very low, so that based on Henry's law, Cequil is also low and much less than Cactual. Thus the rate of transfer given by the preceding equation is negative, and the gas leaves rather than enters the solution. 2.8.2 Graham’s Law Graham’s law is concerned with the diffusion of gases, and it states: the rates of diffusion of gases is inversely proportional to the square roots of their densities. This law can be illustrated by a comparison of the rates of diffusion of hydrogen, oxygen, chlorine, and bromine, which have atomic weights of approximately 1, 16, 36, and 80, respectively. On the basis of Graham’s law, oxygen diffuses about one-fourth, chlorine about one-sixth, and bromine about one-ninth as fast as hydrogen. This law finds its great application in the field of industrial hygiene and air pollution control. 2.9 SOLUTIONS Three major categories of solutions exist: molal solutions, molar solutions and normal solutions. Molal solutions are normally used when the physical properties of solutions, such as vapour pressure, freezing point, etc. are involved. Molar solutions or concentrations are generally of interest for equilibrium calculations of various kinds. Normal solutions are commonly used for making analytical measurements. Methods of Expressing Concentration The two methods of expressing the concentration of a constituent of a liquid or gas are: Mass/volume: The mass of solute per unit volume of solution (in water chemistry). This is annalogous to weight per unit volume; typically, mg/L = ppm (parts per million). Mass/mass or weight/weight: The mass of a solute in a given mass of solution; typically mg/kg or ppm.

If the density of a solution = ρ = Lkgsolutionofvolume

solutionofmass/(

And concentration of a constituent in mg/L = CA1 )/( Lmgsolutionofvolume

tconstituenofmass=



And concentration of a constituent in ppm = CA2 )/( kgmgsolutionofmass

tconstituenofmass=

Then rearranging,

2

1

A

A

C

C=ρ

if ρ = 1 kg/L, then CA1 = CA2 that is the concentration in ppm mg/kg = concentration of a constituent in mg/L. For most applications in water and wastewater environments, ρ = 1 kg/L. For applications in air environment, Eq. (2.1) does not hold. Example 1 Express the concentration of a 3 percent by weight CaSO4 solution in water in terms of mg/L and ppm. Solution

3% by weight = ppm000300001000

00030

100

3 ==

Since the solution is water, then C = 30 000 mg/L.

Example 2 If a litre of solution contains 190 mg of +4NH and 950 mg of NO3

-, express these

constituents in terms of nitrogen (N). Solution Vapor Pressure The presence of a non-volatile solute in a liquid always lowers the vapor pressure of the solution. Thus, when sugar, sodium chloride, or a similar substance is dissolved in water, the vapor pressure is decreased. This phenomenon is believed to be due to a physical blocking effect at the surface of the liquid where particles (ions or molecules) of the solute happen to be. Raoult's Law The extent of the physical blocking effect or depression of the vapour pressure is directly proportional to the concentration of the particles in solution. For solutions that do not ionise, the effect is directly proportional to the molal concentration. For solutes that do ionise, the effect is proportional to the molal concentration times the number of ions formed per molecule of solute modified by the degree of ionization. Application of Raoult’s has shown that molal solutions of nonelectrolytes in water, such as sugar containing 6.02 x 1023 molecules or particles, have their vapour pressures decreased to the same degree, and boiling point is raised 0.52°C while the freezing point is depressed 1.86°C. A molal solution of an electrolyte such as NaCl, which yields two ions, produces nearly twice as great an effect because, after solution and ioniosation occur, the molal solution contains nearly two times Avogadro’s number of particles. Equilibrium and Le Chatelier's principle Nearly all chemical reactions are reversible to some degree. When a reaction proceeds to a point where the combination of reactants to form products is just balanced by the reverse



reaction of products combining to form reactants, then the reaction is said to have reached equilibrium. Le Chatelier's principle states that a reaction at equilibrium will adjust itself in such a way as to relieve any force, or stress, that disturbs the equilibrium. A system in equilibrium can be expressed as; KK ++↔++ zDyCxBwA

An increase in either A or B shifts the equilibrium further to the right. Conversely, an increase of either C or D will shift the equilibrium to the left. A chemical reaction in true equilibrium can be expressed as

KBA

DCxw

zy

=K

K

][][

][][ (2.2)

where K = equilibrium constant for a given temperature [ ] signifies concentrations of the reacting substances The expression is widely used and a clear understanding of its applications is necessary in all phases of science and applied sciences. If the reactants and products of a reaction are dissolved in a solvent such as water, then the concentrations in equilibrium relationships are ordinarily expressed in moles per litre. Equation 2.2 is useful in helping to understand the various ways in which substances may be distributed in aqueous solutions, and the methods for their control. Homogeneous chemical equilibria are characterised by all reactants and products of the reaction occurring in the same physical state or phase, such as reactions between gases or between materials dissolved in water. Examples of homogeneous equilibria in water are the ionisation of weak acids and bases, and complex formation. Heterogeneous chemical equilibria are characterised by substances occurring in two or more physical states. Examples are equilibria for solubility of gas in liquid, the solubility of solids in water, the distribution of a material between two different solvents, the equilibrium of a substance between its liquid phase and gaseous phase. Ionization In dealing with aqueous solutions, the equilibria of concern is the ionisation of the water molecule into a hydrogen ion, or proton, and hydroxyl ion.

H2O ⇔ H+ + OH- A proton is a very small particle and as such would have an extremely large charge-to-volume ratio. As a result it will attach itself to almost anything that does not have a large positive charge. That is;

2H2O ⇔ H3O+ + OH-

where H3O+ is called the hydronium ion.



Ionization of Acids and Bases All strong acids and bases are considered to approach 100 percent ionisation in dilute solutions, that is, they completely 2.9.1 Solubility Product A fundamental concept is that all solids, no matter how insoluble, are soluble to some degree. For example silver chloride and barium sulphate are considered to be very insoluble. However, in contact with water they do dissolve slightly and form the following equilibria; AgCl (S) = Ag+ (aq) + Cl-(aq) BaSO4(S) = Ba2+ (aq) + SO4

2-(aq) (2.3)

KAgCl

ClAg =−+

][

]][[

But the concentration of AgCl is constant, thus

KK

ClAg

s

=−+ ]][[

[Ag+][Cl-] = KSK [Ag+][Cl-] = KSP (Solubility Product) For more complex substances Ca3(PO4

3-)2 = 3Ca2+ (aq) + 2PO43-

(aq) [Ca2+]

3 [PO43-]2 = KSP

Table Typical solubility-product constants

Equilibrium equation Ksp at 25°°°°C Significance in environmental engineering

MgCO3 ↔ Mg2+ + CO32- 4 x 10-5 Hardness removal, scaling

Mg(OH)2↔ Mg2+ + 2OH- 9 x 10-12 Hardness removal, scaling

CaCO3 ↔ Ca2+ + CO32- 5 x 10-9 Hardness removal, scaling

Ca(OH)2↔ Ca2+ + 2OH- 8 x 10-6 Hardness removal

CaSO4↔ Ca2+ + SO4 2 x 10-5 Flue gas desulfurisation

Cu(OH)2↔ Cu2+ + 2OH- 2 x 10-19 Heavy metal removal

Zn(OH)2↔ Zn2+ + 2OH- 3 x 10-17 Heavy metal removal

Ni(OH)2↔ Ni2+ + 2OH- 2 x 10-16 Heavy metal removal

Cr(OH)3 ↔ Cr3+ + 3OH- 6 x 10-31 Heavy metal removal

Al(OH)3 ↔ Al3+ + 3OH- 1 x 10-32 Coagulation

Fe(OH)3 ↔ Fe3+ + 3OH- 6 x 10-38 Coagulation, iron removal, corrosion

Fe(OH)2 ↔ Fe2+ + 2OH- 5 x 10-15 Coagulation, iron removal, corrosion

Mn(OH)3 ↔ Mn3+ + 3OH- 1 x 10-36 Manganese removal

Mn(OH)2 ↔ Mn2+ + 2OH- 8 x 10-14 Manganese removal



Ca3(PO4)2 ↔ 3Ca2+ + 2PO43- 1 x 10-27 Phosphate removal

CaHPO4 ↔ 3Ca2+ + HPO42- 3 x 10-7 Phosphate removal

CaF2 ↔ Ca2+ + 2F- 3 x 10-11 Fluoridation

AgCl ↔ Ag+ + Cl- 3 x 10-10 Chloride analysis

BaSO4 ↔ Ba2+ + SO42- 1 x 10-10 Sulphate analysis

A prediction of relative solubilities of compounds cannot be made by a simple comparison of solubility product values because of the squares and cubes that enter the calculation when more than two ions are derived from the one molecule. Barium sulphate, which yields two ions, and calcium fluoride, which yields three ions, may be used to illustrate the point. The solubility of these compounds at 20°C is BaSO4 = 1.1 x 10-5 M CaF2 = 2.05 x 10-4 M It will be noted that calcium fluoride is about twenty times more soluble than barium sulphate. In saturated solutions of poorly soluble substances, it is assumed that ionisation of the dissolved material is complete. Therefore in a saturated solution of barium sulphate, both the [Ba2+] and the [SO4

2-] are equal to 1.1 x 10-5, and in a saturated solution of calcium fluoride the [Ca2+] is equal to 2.05 x 10-4 and the [F-] is twice as great, or 4.1 x 10-4. When these values are substituted into the solubility-product equation. [Ba2+][SO4

2-] = [1.1 x 10-5][1.1 x 10-5] = 1.2 x 10-10 (2.3) [Ca2+][F-] 2 = [2.05 x 10-4][4.1 x 10-4] 2 = 3.4 x 10-11 From this, it is obvious that the most soluble material (CaF2) has the smallest solubility product because of the squaring of the fluoride concentration. The case of compounds that yield more than three ions is even more exaggerated. 2.9.2 Common Ion Effect Consider a solution that has been saturated with barium sulphate. As indicated in equation 2.3, both [Ba2+] and [SO4

2-] would equal 1.1 x 10-5. If the barium ion concentration should be increased by addition from an outside source, such as BaCl2, the concentration of sulphate ion must decrease and the amount of precipitated BaSO4 must increase in order for Ksp to remain the same. To illustrate, assume that 10 x 10-5 mol/l of BaCl2 is added to the above solution. This will result in the formation of an additional x moles of precipitated BaSO4. The following changes in [Ba2+] and [SO4

2-] must then take place: Ba2+ + SO4

2- BaSO4 (1.1x10-5 + (1.1x10-5-x) x 10x10-5 -x) According to the solubility-product principle,

( )( ) 1055 102.1101.1101.11 −−− ×==−×−× spKxx

By solving for x, it is found that an additional lmol /1098.0 5−× of precipitated BaSO4 is formed and that the new equilibrium concentrations of barium and sulphate ions are



[ ] ( ) ( ) 5552 101.101098.0101.11 −−−+ ×=×−×=Ba

( ) ( ) 55524 1012.01098.0101.1][ −−−− ×=×−×=SO

The sulphate ion is reduced considerably as indicated above. The above is an application of the common ion effect, which is used extensively to accomplish essentially complete precipitation of desired or undesired ions from their solutions or wastewaters.



2.9.3 Diverse Ion Effect The diverse ion effect describes the adverse effect that unrelated ions often have upon the solubility of some relatively insoluble substances. Such ions, theoretically, play no part in the chemical equilibrium involved but often increase the solubility of the desired precipitates to such an extent that quantitative results cannot be obtained. Sometimes a common ion may serve very well up to certain concentrations, but when used at higher concentrations appears to have a diverse ion effect. In this case, the usual explanation is that complex ion formation is taking place. For example when hydrochloric acid acts in such a manner when it is used as the agent to precipitate silver ion. When hydrochloric acid is added in excess, the soluble AgCl2

- complex is formed. AgCl + Cl- → AgCl2

- Therefore, the amount of HCl acid used should be carefully controlled. The solubility of metal ions is also increased by the presence of "chelating agents". These substances have the ability to seize or sequester metal ions and hold them in a clawlike grip. The chelating agents have ligand atoms, each of which donates two electrons to form a "coordinate" bond with the ion. There are many natural chelates such as haemoglobin (containing iron), vitamin B-12 (containing cobalt) and chlorophyll (containing magnesium). EDTA is a chelating agent which has a remarkable affinity for calcium and is used for the determination of water hardness.



3 BASIC CONCEPTS FROM PHYSICAL CHEMISTRY 3.1 THERMODYNAMICS 3.1.1 Heat and Work Heat and work are related forms of energy. Heat energy can be converted into work, and work can be converted into heat energy. Heat is that form of energy which passes from one body to another solely as a result of a difference in temperature. On the molecular scale, the temperature of a substance is related to the average translational energy of the molecules, and the flow of heat results from transfer of this molecular energy. The basic unit of heat is the calorie, the heat required to raise the temperature of one gram of water one degree Celcius. Definitions Specific heat – heat required to raise 1 gram of the material 1 degree Celcius given by

TM

qC

∆= where C is the specific heat, q is the heat added in cal or J, M is the weight of the

material in grams, and ∆T is the rise in temperature of the material in degrees Celcius. Heat of fusion – heat required to melt a substance at its normal melting point. Heat of vaporisation – heat required to evaporate the substance at its normal boiling point. Work in chemical systems usually involves work of expansion. The system may either do work on its surroundings or have work done on itself depending on whether the volume of the system is expanding or contracting. Work, for closed systems, is equivalent to pressure, P times the change in volume, dV:

dw = PdV Work is measured in joules (J). 3.1.2 Energy Laws of Thermodynamics Energy exists in many forms, such as heat, light, chemical energy, and electrical energy. Energy is the ability to bring about change or to do work. Thermodynamics is the study of energy. First Law of Thermodynamics: Energy can be changed from one form to another, but it cannot be created or destroyed. The total amount of energy and matter in the Universe remains constant, merely changing from one form to another. The First Law of Thermodynamics (Conservation) states that energy is always conserved, it cannot be created or destroyed. In essence, energy can be converted from one form into another. The Second Law of Thermodynamics states that "in all energy exchanges, if no energy enters or leaves the system, the potential energy of the state will always be less than that of the initial state." This is also commonly referred to as entropy. A watchspring-driven watch will run until the potential energy in the spring is converted, and not again until energy is reapplied to the spring to rewind it. A car that has run out of gas will not run again until you walk 10 miles to a gas station and refuel the car. Once the potential energy locked in carbohydrates is converted



into kinetic energy (energy in use or motion), the organism will get no more until energy is input again. In the process of energy transfer, some energy will dissipate as heat. Entropy is a measure of disorder: cells are NOT disordered and so have low entropy. The flow of energy maintains order and life. Entropy wins when organisms cease to take in energy and die. 3.1.3 Enthalpy 3.1.4 Entropy The laws of thermodynamics are amongst the simplest, most elegant, and most impressive products of modern science. Most physical laws are designed to explain processes which humans experience in nature. The laws of thermodynamics on the other hand, were developed to explain the absence of perpetual motion (a human concept) in nature. The first law of thermodynamics states that "energy can never be created or destroyed, but it can be transformed from one form into another." An automobile engine can be used to illustrate the first law. Energy stored in gasoline is transformed into useful work used to move the car, heat the car, create frictional energy, and produce waste energy in the exhaust products. The sum of the energy of these four is exactly equal to the energy of the gasoline. The first law of thermodynamics thus seems to indicate that we could never run out of energy. Unfortunately, things are not quite so simple, and this is outlined by the second law of thermodynamics. The second law of thermodynamics says that: "Every time energy is transformed from one state to another, a penalty is exacted. The penalty is a reduction in the amount of energy available to perform useful work in the future." The term for this penalty is "entropy". The two laws of thermodynamics can be stated together in one simple sentence: "The total energy content of the universe is constant, and the total entropy is continually increasing." In other words, "there is no such thing as a free lunch; and there are always crumbs under the table." Entropy is thus a measure of the amount of energy which is no longer capable of performing work. An increase in entropy means the reduction of energy available to do work in the future. Increasing entropy can also be considered as a change from an ordered state to a disordered state. Every event in the natural world results in an increase in entropy. Time is not symmetrical, it only moves in one direction, therefore entropy will always increase. One example of increasing entropy is water falling over a dam. When the water is above the dam it has some potential energy due to gravity, which can be used to generate electricity or turn a wheel to perform some useful task. Once the water has fallen to the level below the dam, its total energy is the same - as the fall warms the water increasing its thermal energy - but it no longer has the same capacity to do work. The water has moved from what is referred to as an "available" or "free" energy state (high grade energy) to an "unavailable" or "bound" energy state (low grade energy). This change in the energy state of the water as it falls over the dam is an increase in entropy. Unavailable energy is most often in the form of thermal energy. Thermal energy is the result of random and disorderly motions of huge numbers of individual atoms and molecules. Whereas kinetic energy, such as that of a moving object is the result of the orderly motion of all the atoms in the object. Conversion of other forms of energy (kinetic, electric etc.) into thermal



energy is simple but converting thermal energy into other forms is difficult and can never be performed completely.

The concept of entropy is based on the second law of thermodynamics, which states that all systems tend to approach a state of equilibrium. The significance of the equilibrium state is realised from the fact that work can only be obtained from a system not yet in equilibrium. When a system is already at equilibrium, no chemical or physical changes can take place since no process tends to occur spontaneously. Entropy S, is defined by:

T

dqdS rev=

where qrev = the amount of heat that a system absorbs if a chemical change is brought about in an infinitely slow reversible manner. T = absolute temperature Like enthalpy, it is the change in entropy that is of major interest thus

∫=−=∆T

dqSSS rev

12

Basing on the third law of thermodynamics, entropy of a substance at 0K is zero, the absolute entropy of elements and compounds at some standard state can be determined by integration of the above equation. Significance of entropy All spontaneous changes in an isolated system occur with an increase of entropy. To determine whether a chemical or physical change from state a to b will occur in a system, a calculation of entropy can provide the information. If: ∆S > 0; the change would occur spontaneously i.e. change from a to b ∆S = 0; no change occurs ∆S < 0; the change occurs but in the reverse direction i.e. b to a. 3.1.5 Free Energy In an isolated system where energy cannot be gained or lost, both energy and entropy factors must be considered thus the free-energy concept. Free energy, TSHG −= Where H = enthalpy in Joules T = absolute temperature S = entropy in Joules/ Kelvin At constant temperature and pressure, the change in free energy, ∆G for a given reaction is:

STHG ∆−∆=∆



But recall

VPE

PVEPVEHHH

∆+∆=+−+=−=∆ )()( 112212

but ∆E = q – w ∴∆H = q – w + P∆V

From T

dqdS rev=

T∆S = qrev (at constant temperature) Therefore revqVPwqG −∆+−=∆

If a reaction is allowed to take place slowly with minimum energy losses, q ≈ qrev and w = wmax

VPwG

VPwG

qVPwqG revrev

∆−=∆−

∆+−=∆

−∆+−=∆

max

max

max

where P∆V gives the wasted work in expanding and wmax the maximum work obtainable from a system. Therefore -∆G gives the difference between the maximum work and the wasted work or the useful work that can be obtained from a system change.

usefulwG =∆−

Consider a change from A to B. If ∆G < 0; the changes occurs ∆G = 0; the system is in equilibrium and no change occurs ∆G > 0; the change can proceed but in the reverse direction. NOTE: Standard free energy of a stable element at 25°C and 1 atm is zero The hydrogen ion at unit activity (≈ 1 N solution) is assigned a standard free energy of zero.

The standard free energy of a compound (0298G∆ ) is the free energy of formation of that

compound from its elements, considering reactants and products all to be in the standard state at 25°C and 1 atm. Free energy changes accompanying chemical reactions ∆G can be used to determine the equilibrium state to which the reaction carries the system. Coinsider a reaction aA + bB ⇔ cC + dD, the free energy of such a system is given by



ba

dc

BA

DCRTGG

}{}{

}{}{ln0 +∆=∆

where ∆G = reaction free energy change (Joules) ∆G0= standard free energy change (Joules) R = universal gas constant = 8.314 J/K-mol T = absolute temperature (K) 3.2 OSMOSIS Osmosis is the movement of a solvent through a membrane that is impermeable to a solute. The direction of flow is from the more dilute to the more concentrated solution. For example, if a salt solution is separated from water by means of a semipermeable membrane, water will pass through the membrane in both directions, but it will pass more rapidly in the direction of the salt solution. As a result, a difference in hydrostatic pressure develops. The tendency for the solvent to flow can be opposed by applying pressure to that salt solution. The excess pressure that must be applied to the solution to produce equilibrium is known as the osmotic pressure and is donated by π. The net flow of solvent across the membrane results in response to a driving force which can be estimated by the difference in vapour pressure of the solvent on either side of the membrane. The transfer of the solvent across the membrane from the less concentrated to the more concentrated solution will continue until the effect of hydrostatic pressure overcomes the driving force of the vapour pressure differential. For an incompressible solvent, the osmotic pressure at equilibrium can be estimated from the following:

A

oA

A P

P

V

RTln=π (3.1)

Where π is expressed in atmospheres, R is 0.08821-atm/mol.K, T is in kelvins, and PoA and PA are the vapour pressure of solvent in the dilute and concentrated solutions, respectively. For dilute solutions in which Raoult's law (the extent of the physical blocking effect or depression of the vapour pressure is directly proportional to the concentration of the particles in solution) holds true

cRT=π (3.2) Where c is the molar concentration of particles 3.3 REVERSE OSMOSIS An application of osmotic pressure principles is in the demineralisation of salt-laden (brackish) water by reverse osmosis process. In the process, water is caused to flow in a reverse manner through a semipermeable membrane from brackish to dilute fresh water. This accomplished by exerting a pressure on the brackish water in excess of the osmotic pressure. The semipermeable



membrane acts like a filter to retain the ions and particles in solution on the brackish waterside, while permitting water alone to pass through the membrane. Example The molar concentration of the major ions in a brackish ground water supply are as follows: Na+, 0.02; Mg2+, 0.005; Ca2+, 0.01; K+, 0.001; Cl-, 0.025; HCO3

-, 0.001; NO3-, 0.002; and

SO42-, 0.012.

(a) What would be the approximate osmotic pressure difference across a semipermeable membrane which had brackish water on one side and mineral-free water on the other, assuming the temperature is 25°C? The molar concentration of particles in the brackish water is

Mc 075.0012.0002.0001.0025.0001.001.0015.002.0 =+++++++= From equation (3.2)

KmoleK

atm

litre

molecRT )25273(

1082.0075.0 +×−

−×==π

atm83.1=

(b) If in the above example, a yield of 75 percent fresh water were desired, what minimum pressure would be required to balance the osmotic pressure difference that will develop? For a 75 percent yield, the salts originally present in 4 volumes of brackish water would be concentrated in one volume of brackish water left behind the membrane after three volumes of fresh water have passed through the membrane. Thus, the particle concentration in the remaining brackish water would be four times that of the original brackish water or 0.30 M. Then, atm33.7298082.030.0 =××=π

At this time the pressure required to push the fresh water through the membrane would be in excess of 7.33 atm.

3.4 DIALYSIS By choice of a membrane of a particular permeability, which is wetted by the solvent, it is possible to cause ions to pass through the membrane while large molecules of organic substances or colloidal particles are unable to pass. Thus a separation of solutes can be accomplished and the term dialysis is justified. Dialysis is used extensively to remove electrolytes from colloidal suspensions to render the latter more stable. Dialysis can be used to recover sodium hydroxide from certain industrial wastes that have become contaminated with organic substances as shown below.



A simple dialysis cell for recovery of sodium hydroxide from industrial waste In the process, the waste material is placed in the cells with permeable membrane and the cells surrounded with water. The sodium and hydroxide ions pass through the cell wall into the surrounding water. The water is evaporated to recover sodium hydroxide, and the organic waste remaining in the cells is disposed of separately. Waste caustic solutions must be quite concentrated before recovery by dialysis can be justified economically. 3.5 PRINCIPLES OF SOLVENT EXTRACTION Industrial wastes often contain valuable constituents which can be recovered most efficiently and economically by means of extraction with an immiscible solvent, such as petroleum ether, diethyl ether, benzene, chloroform or some other organic solvent. In addition, many methods for water analysis involve extraction of a constituent or complex from the water sample as one step in the determination e.g.; of heavy metals. When an aqueous solution is intimately mixed with an immiscible solvent, the solutes contained in the water distribute themselves in relation to their solubilities in the two solvents. For low to moderate concentrations of solute, the ratio of distribution is always the same. That is

KC

C

C

C

w

s

water

solvent == (3.3)

The question in industrial waste treatment that usually requires answering is how much remains in the aqueous phase after “n” extractions. The equation defining the distribution coefficient may be written in terms of the amounts of the substance extracted and the volumes of the liquids involved.

w

so

w

s

VW

VWW

C

CK

/

/)(

1

1−==

Where W0 = weight of the substance originally present in the aqueous phase W1 = weight remaining in water after one extraction VS = volume of solvent VW = volume of water Simplifying;

ws

wo VKV

VWW

+=1

In the second step of the extraction;

ws

w

VKV

VWW

+= 12



wS

w

ws

wo VKV

V

VKV

VW

++=

2

+=

ws

wo VKV

VW

After n extractions the weight of substance remaining in the water is

n

ws

won VKV

VWW

+= (3.4)

Equation has general application and may be used to calculate the volume of a solvent needed to reduce the concentration of a material in the aqueous phase to definite levels with a fixed number of extractions, or the number of extractions needed with a fixed volume of a solvent, provided that the distribution coefficient is known. 3.6 CHEMICAL REACTION RATES AND EQUILIBRIA 3.6.1 Reaction Rates The rate or velocity of a chemical reaction is defined as the quantity of a reactant changed in one unit of volume per unit of time. Mathematically expressed as:

[ ]dt

treacdratereaction ttan−

=

Between the brackets is written the concentration at time t, usually expressed in moles/l. When the rate is expressed in terms of disappearance of a reactant, a minus sign is included because the concentration is decreasing. Factors affecting rates As stated before, a chemical reaction occurs after the particles involved collide with each other. The number of effective collisions determines the reaction rate and depends on many factors. The reaction rate depends not only on the nature of the reactants, but also on their physical state and particle size, their concentrations, the temperature and the pressure, the action of radiation and the presence of catalysts. Catalysts are substances that remain unchanged during the reaction but affect its rate. Concentration It is evident that the rate of reaction depends on the number of collisions per minute between a molecule of A and one of B. the chances for such collision to occur will increase proportionally when the concentration of either kind of molecule is increased, hence: Reaction rate = k.[A].[B] This relationship is called the law of massaction (Guldberg and Waage). After combining the rate expressions the rate law will be:



]].[.[][][][

BAkdt

Cd

dt

Bd

dt

Adratereaction =+=−==

in which k the rate constant depending on temperature, and [A], [B] and [C] represent the concentrations of A, B and C. In general we can say that the rate of homogeneous reactions in dilute solutions and in gases under low pressure can be represented as follows: Reaction: productscCbBaA →++

Reaction rate: cba CBAkdt

Ad].[].[].[

][ =−

The exponents in the rate equation are called reaction orders, the overall order is the sum of the powers of the concentrations. Temperature Accumulated experimental evidence has shown that the rate of most chemical reactions is approximately doubled for every 10°C increase in temperature (Arrhenius). This is caused by an increase in the number of collisions. Catalysts Various substances that retain their identity during a given reaction between other substances may profoundly affect the rate of the latter when also present in the reaction mixture. This influence may be positive: the reaction is accelerated by the catalyst; or negative: the reaction is slowed down (inhibitor). Except for a few cases, the mechanism of catalysts is not known; it certainly is not the same in all cases. Sometimes increased concentration of reactants at the surface of a solid catalyst is responsible for the acceleration. Most reactions performed by living organisms are mediated by catalysts (enzymes). Overall expressions and reaction mechanisms The law of mass action holds only if the mechanism of the reaction aA + bB + cC --- products occurs in such a way that the molecules of A collide simultaneously with b molecules of B and c molecules of C. In practice this hardly happens. Often these collisions occur step by step, in a so called reaction mechanism. For instance:

Mechanism: QP

stepingerratePBArapid

slow

→→+ )mindet(

Some reaction mechanisms and their corresponding reaction rate equation Chemical kinetics is concerned with the speed or velocity of reactions. Many reaction have rates which at a given temperature are proportional to the concentration of one, two, or more of the reactants raised to a small integral power. For example, if a reaction is considered in which



A, B, and C are possible reactants, then the rate equations which express the concentration dependence of the reaction rate may take one of the following forms. Rate = kCa 1st order Rate = kCa

2 or kCaCb 2nd order Rate = kCa

3 or kCa2Cb or kCaCbCc 3rd order

Where Ca, Cb, and Cc represent the concentrations of reactants A, B, and C, respectively. Reactions that proceed according to such simple expressions are said to be reactions of the first, second, or third order as indicated, with the order of the reaction being defined as the sum of the exponents of the concentration terms in the reaction equation. Many reactions proceed slowly and require rate expressins so that the reactions can be dealt with on a practical basis. This is true for BOD removal, aeration, biological growth, radioactive decay, and disinfection. In general, first order reactions are the most common, although reactions of other orders or of a more complex nature are sometimes involved. 3.6.2 Zero-Order Reactions Many biological induced reactions, particularly those involving soluble substrate, appear to occur in a linear manner over fairly large ranges of concentrations. Thus, the rate of substrate change is dependent of substrate concentration. Such reactions are referred to as being zero order. For example, oxidation of ammonia to nitrite. However, such reactions, become slower as the substrate concentration approaches zero. 3.6.3 First-Order Reactions The decomposition of a radioactive element is the simplest example of a true first-order reaction. In such a reaction the rate of decomposition is directly proportional to the amount of undecayed material and may be expressed mathematically as

kCdt

dC =−

where the minus sign indicates a loss of material with time, C is its concentration, and k is the constant for the reaction and has units of reciprocal. If the initial concentration, at time t = 0, is Co, and if at some later time t the concentration has fallen to C, the integration of Eq.----gives

∫ ∫=−c

c

t

o

dtkC

dC

0

and ktC

C

C

C o

o

==− lnln

or ktoeCC −= (3.5)

3.6.4 Consecutive Reactions Consecutive reactions are complex reactions of great importance, and so equations describing the kinetics of such reactions are of real interest. In consecutive reactions, the products of one reaction become the reactants of a following reaction:

A→ B → C



k1 k2 . Here reactant A is converted to product B at a rate determined by rate constant k1. Product B in turn becomes the reactant for the second step and is converted to product C as determined by rate constant k2

( ) tkob

tktkoa

b eCeekk

CkC 221

12

1 −−− +−−

=

( ) oc

tkob

tktkoac CeC

kk

ekekCC +−+

−+

−= −−−

2

21

1112

12 (3.6)

Equation 3.6 is widely used to describe the oxygen deficit in a stream caused by organic pollution. In this case Cb can be considered the oxygen deficit being created in the first step by the biological oxidation of organic matter with concentration Ca. At the same time, the oxygen deficit is being decreased by atmospheric reaeration to give the second step in the consecutive reactions. A consecutive reaction can also be used to describe the bacterial nitrification of ammonia. Here ammonia is oxidised by Nitrosomonas bacteria to nitrite, which is then oxidised in the second step by Nitrobacter bacteria to nitrate as indicated by the following sequence:

−− → → 323 NONONHrNitrobacteasNitrosomon

3.7 CATALYSIS Catalysts have the power to change the rate of chemical reactions. They may be positive or negative in effect. Regardless of their role in a chemical reaction, they can be recovered in their original form. They simply alter the speed with which equilibrium is attained by changing the energy of activation. Positive catalysts can initiate and maintain reactions at concentration levels below those at which ordinary reactions would occur. For example, hydrogen sulphide is catalytically oxidised to sulphur dioxide at concentrations normally incapable of supporting combustion. Enzymes produced by bacteria and other microorganisms are organic catalysts, which permit the occurrence at room temperature of a great many reactions of importance to environmental engineers such as hydrolysis, oxidation, and reduction of both inorganic and organic pollutants. 3.8 ADSORPTION Adsorption is the process by which ions or molecules present in one phase tend to condense and concentrate on the surface of another phase. Adsorption of contaminants present in air or water onto activated carbon is frequently used for purification of the air or water. The material being concentrated is the adsorbate, and the adsorbing solid is termed the adsorbent. There are 3 major types of adsorption; 3.8.1 Physical adsorption This is relatively non-specific and is due to the operation of weak forces of attraction or van der Waals’ forces between molecules. The adsorbed molecule is not affixed to a particular site on the solid surface, but is free to move about over the surface.



3.8.2 Chemical adsorption This is a result of much stronger forces, comparable with those leading to the formation of chemical compounds. Normally the adsorbed material forms a layer over the surface and the molecules are not considered free to move from one surface site to another. 3.8.3 Exchange adsorption This is used to describe adsorption characterised by electrical attraction between the adsorbate and the surface. Ion exchange is included in this class. Ions of a substance concentrate at the surface as a result of electrostatic attraction to sites of opposite charge on the surface. Ions with greater charge such as trivalent ions, are attracted more strongly toward a site of opposite charge than are molecules with lesser charge, such monovalent ions.



4 COLLOIDAL CHEMISTRY 4.1 DESCRIPTION OF COLLOIDAL SYSTEMS Colloidal chemistry is concerned with dispersions. Colloid dispersions consist of discrete, fine particles that are separated by the dispersion medium. The particles may be aggregates of atoms, molecules, or mixed materials that are considered larger than individual atoms or molecules, but are small enough to possess properties greatly different from coarse dispersions or suspensions. The state of matter of both the dispersed phase and the dispersion medium can be solid, liquid or gas. The system forms a heterogeneous system of which eight classes are known, see table 1.2 Table 1.2 Classes of colloidal systems

Class Dispersed phase Dispersion medium Common name

1 Solid Solid 2 Liquid Solid 3 Gas Solid 4 Solid Liquid 5 Liquid Liquid Emulsions 6 Gas Liquid Foams 7 Solid Gas Smokes 8 Liquid Gas Fogs

Colloidal particles normally range in size from 1 to 100 nm and are not visible even with the aid of the ordinary high-powered microscope. Their relation to other dispersions is as follows; Fine molecular 1000nm 100nm 1 nm coarse colloidal Colloidal dispersions may be considered as ultrafine dispersions and occupy a size range between fine and molecular. 4.2 METHODS OF FORMATION AND APPEARANCE OF COLLOIDS Any material that is reasonably insoluble in the dispersion medium can be made to form a colloidal dispersion. Colloidal-sized particles can be produced by grinding coarse materials. Devices designed for such purposes are called colloidal mills. They can also be formed from ions that react to form insoluble compounds. Many organic substances and compounds that are considered soluble in water do not form true solutions; instead they form colloidal dispersions e.g.; soap, starch, agar-agar, etc. In natural surface water, colloids of inorganic origin (clay) and organic origin (humic acids) are found.



4.3 GENERAL PROPERTIES 4.3.1 Surface area and mass Because colloidal particles are so small, their surface area in relation to mass is very great as a result surface phenomena like absorption and ion-exchange predominate and control the behaviour of colloidal suspensions. The mass of colloidal particles is so small that gravitational effects are unimportant. 4.3.2 Electrical Properties All colloidal particles are electrically charged. This may be caused by charged functional groups which extend from the complex molecular structure, or by adsorption of ions. The charge varies considerably in its magnitude with the nature of the colloidal material and may be positive or negative, as shown in figure below

Figure: Positive and negative colloidal particles Many colloidal dispersions are dependent upon the electrical charge for their stability. Because equally charged colloidal particles repel each other they cannot come close enough to agglomerate into larger particles. So the electrokinetic properties of the colloids are of great importance. When colloidal particles are placed in an electrical field, the particles migrate toward the pole of positive charge. This phenomenon is known as electrophoresis and is used extensively to determine the nature of the charge on the colloidal particle and other properties. 4.3.3 Tyndall Effect Because colloidal particles have dimensions greater than the average wavelength of light, they interfere with the passage of light. Light which strikes them may be reflected and a beam of light passing through a colloidal suspension is visible to an observer who is at or near right angles to the beam of light → Tyndall effect. The test is often used to prove the presence of a colloid, as true solutions and coarse suspensions do not produce the phenomenon. Tyndall effect is used as a basis of determining turbidity. 4.3.4 Adsorption



Colloids have tremendous surface area and, by that a great adsorptive power. Adsorption is normally preferential in nature, some ions being chosen and others excluded. This selective action yields charged particles and is the fundamental basis of the stability of many colloidal dispersions. 4.3.5 Effect on freezing and boiling point Colloidal dispersions affect the boiling and freezing points of liquids as do dispersions of submicroscopic particles. 4.3.6 Dialysis Colloids, because of their large particle size, do not pass through ordinary semipermeable membranes. Thus for stability reasons a separation of electrolytes and colloids can be accomplished by dialysis. 4.4 COLLOIDAL DISPERSIONS IN LIQUIDS 4.4.1 Introduction Colloidal dispersions of solids, liquids, and gases in liquids are commonly encountered and are of two types, solvent hating and solvent-loving. In terms of water, the solvent-hating are called hydrophobic and the solvent-loving are named hydrophilic . Colloidal dispersions of solids in liquids are often referred to as sols. The main concern is with the removal of colloidal solids from water and wastewater. These colloids are not always well defined hydrophobic sols, but they do lend themselves to separation when treatment designed to remove hydrophobic sols is used. The natural coloured matter in surface waters and the colloidally suspended matter of domestic wastewaters are examples of quasi hydrophobic-hydrophilic, negatively charged colloids. 4.4.2 Hydrophobic Colloids These are all electrically charged. The charge on all particles in a given dispersion is the same. It may be negative or positive depending on the nature of the sol. Most metallic oxide sols become positively charged, and non-metallic oxide, as well as metallic sulphide, sols are usually negatively charged. Electrokinetic properties The stability of hydrophobic colloids depends upon the electrical charge that they possess. This charge is obtained by adsorption of ions from the surrounding medium, as illustrated in the following figure. A sol considered as a whole cannot have a net charge, so that the charge that a given particle may possess must be counterbalanced by ions of opposite charge in the solution phase.



Figure: A positively charged colloidal particle with diffuse layer of ions of opposite charge The need for electroneutrality results in an electric double layer at the interface between the solid and water consisting of (1) the charged particle, and (2) an equivalent excess of counter-ions of appropriate charge which accumulates in the water near the surface of the particle. Athough the counter ions are attracted electrostatically and are thus concentrated in the interfacial region, they are rather loosely held and may diffuse away in response to thermal agitation, to be replaced by other ions. These competing forces (electrical attraction and diffusion) spread the charge over a diffuse layer such that the concentration of counter ions is greatest at the interface and decreases gradually with distance from the interface. Because of the primary charge on the particle, an electrical potential exists between the surface of the particle and the bulk of the solution. The charge is maximum at the particle surface and decreases with distance from the surface. If a colloidal particle moves, a water mantle filled with ions (Stern-layer) stays around the particle. As figure below indicates the potential at the plane of shear is called the zeta-potential. Measurement of the zeta-potential can give an indication of the effectiveness of the added electrolytes in lowering the energy barrier between colloids, and thus can serve to guide the selection of optimum conditions for coagulation. When two similar colloidal particles with similar primary charge approach each other, their diffuse layers begin to interact. As they come closer, the similar primary charges they possess result in repulsive forces. The closer the particles approach, the stronger the repulsive forces. These repulsive forces which keep particles from aggregating are counteracted to some degree by an attractive force termed van der Waals' force. All colloidal particles possess this attractive force regardless of the charge and composition. The magnitude of this force is a function of the composition and density of the colloid, but is independent of the composition of the aqueous



phase. The van der Waal's forces decreases rapidly with increasing distance between the particles. The figure below illustrates the effect of separating distance between two particles on the net force that exists between them. As two similar particles approach each other, the repulsive electrostatic forces increase to keep them apart. However, if they can be brought sufficiently close together to get past this energy barrier, the attractive van der Waals' forces will predominate, and the particles will remain together. So if it is desired to coagulate colloidal particles, then they must be given sufficient kinetic energy to overcome the energy barrier that exists, or else the energy barrier must be lowered by some means. Figure: The effect of liquid ion strength and separating distance between colloids on the forces of interaction between them 4.4.2.1 Destruction of Sols The destruction process of colloidal particles consists of: 1. Decrease or elimination of surface charge (destabilisation). With a reduced or eliminated

energy barrier, particles can come more easily together and aggregate. 2. Aggregation to larger particles or flocs (after collision) in order to be easily removed, e.g.

by sedimentation.



The destruction can be accomplished in four major ways: (i) Addition of chemicals (ii) Boiling (iii) Freezing (iv) Mutual precipitation by addition of a colloid of opposite charge

Addition of chemicals The common method of destroying hydrophobic colloids is by addition of electrolytes. One way in which electrolytes act is by double-layer compression and its thickness will reduce. Figure below shows what is happening with the zeta-potential after dosing chemicals.

Figure: Changes in zeta-potential due to addition of chemicals

a) Represents a negative colloidal particle in a low concentration of monovalent ions b) Represennts a higher ion concentration in the diffuse layer which results in a reduction of the zeta-potential c) A trivalent positive ion has entered the fixed double layer and so reduced the zeta-potential further and coagulation would probably result. A sufficient concentration of monovalent ions, such as NaCl, can bring about coagulation in this way. However, it has been noted that salts having divalent ions of charge opposite to that of the colloidal particle exert far greater coagulation powers. Salts having trivalent ions of opposite charge are even more effective. Shulze-Hardy rule The relation between ionic charge and precipitating power is usually called the Shulze-Hardy rule. The rule states that the precipitation of a colloid is effected by that ion of an added



electrolyte which has a charge opposite in sign to that of the colloidal particle, and the effect of such ion increases markedly with the number of the charges it carries. Table 1.3 Electrolytes and their relative coagulating power for positive and negative colloids

Relative power* of coagulation

Positive Negative Electrolyte colloids colloids

NaCl 1 1 Na2SO4 30 1 Na3PO4 1000 1 BaCl2 1 30 MgSO4 30 30 AlCl 3 1 1000 Al 2(SO4)3 30 > 1000 FeCl3 1 1000 Fe2(SO4)3 30 > 1000

* Values given are approximate and are for solution of equivalent ionic strength From the data given in table above, it becomes obvious why aluminium and iron salts are so widely used as coagulants for removing turbidity and colloidal colour. Multivalent ions of opposite charge are considered able to penetrate the diffuse layer of colloidal particles and in this way neutralise, in part, the charge on the colloid. Mutual precipitation by addition of a colloid of opposite charge The charge on a colloid can sometimes be neutralised by addition of molecules of opposite charge which have the ability to adsorb onto the colloid. For example, positively charged organic molecules such as dodecyammonium ion, C12H25NH3

+ tend to be hydrophobic and readily adsorb onto negatively charged turbidity particles. The opposite charges of the organic and the turbidity particles cancel each other out, and coagulation results. However, an overdose of the added chemical can result in charge reversal and the formation of a stable positively charged particle (restabilisation). The trivalent salts of Fe(III) and Al(III) used in coagulation of water remove colloidal colour and turbidity are considered to function as coagulants by other mechanisms as well. When added to water they do ionize to yield trivalent metallic ions, the amount and life of which are a function of the pH of the water. Some of the trivalent ions undoubtedly reach the target and neutralise the charge of some of the colloidal particles. The majority of the trivalent ions, however, unite with the available hydroxyl ions to give polynuclear colloidal metallic hydroxides which generally carry a positive charge and may adsorb onto the colloid, causing charge neutralisation. The amount of the positively charged metallic hydroxide is normally in excess of the amount needed to react with the negatively charged colour or turbidity particles that may have escaped



neutralisation by trivalent metallic ions. Anions from the salt, like SO42-, help to complete the

coagulation of the colloidal system by compressing the diffuse layer of the metal colloid. 4.4.3 Hydrophilic Colloids Soluble starch, proteins, protein degradation products, gum arabic, pectines, and synthetic detergents are examples of hydrophilic colloids. These materials occur in domestic wastewater and in many industrial wastes. The hydrophilic colloids are readily dispersed in water, and their stability depends upon their love for the solvent rather than upon the slight charge, usually negative, that they possess. This property makes it difficult to remove them from aqueous suspensions. Most hydrophilic colloids serve in a protective capacity for hydrophobic colloids. When acting in this way they are called protective colloids. It is believed that they envelop the hydrophobic colloid in a manner to shield it from the action of the electrolytes. Coagulation of such systems requires rather drastic treatment with large doses of coagulant salts.

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