Solutions of Electrolytes

ElectrolysisElectrolyte is a substance which when dissolve in water dissociate into ions and its aqueous solutions conduct electric current.These are also called electrolytic conductorsThe electronic conductors, such as metals, conduct electric current by transfer of electrons. When an electric current is passed through the electrolytic conductors (such as solution of CuCl2 in water) the cations move towards the cathode and anions move towards the anode. The process of decomposition of electrolyte by the passage of electric current through its solution is called electrolysis.

Faradays law of electrolysisFaradays first lawThe amount of substance W deposited or dissolved at the electrode is proportional to quantity of electricity Q passed through the solution.W QW= ZQW=ZitWhere I is the current in amperes passed through the solution for t secs;Z is the electrochemical equivalent of the element deposited at the electrode.

Faradays second law

The amounts of different substances deposited or dissolved by the passage of the same quantity of electricity are proportional to their chemical equivalents.

Let Q coulombs of electricity be passed through the solutions of two substances of chemical equivalent weights E1 and E2 resp.W1 E1W2 E2

W1 = eE1W2 = eE2 where e is a constant

W1/W2 =E1/E2

One gm equivalent weight of any substance is deposited or dissolved by 96500 coulombs of electricity. This quantity (96500 coulombs) is called a Faraday of electricity.

Electrolytic conductanceThe resistance, R, in ohms of a metallic or electrolytic conductor of uniform thickness is proportional to its length , l and is inversely proportional to its area of cross section, A in cm2. Thus,R l/AR = . l/AWhere is the proportionality constant and is called the specific resistance of the metal.This equation is also applicable to the electrolytic solutions. l is the length of the liquid column between the two electrodes of cross-sectional area of A, then is the specific resistance of the solution.R=l when l=1 and A=1 sq.cm and hence specific resistance of a solution may be defined as the resistance of 1 cm length of the solution of 1 sq.cm cross sectional area.

Conductance C of a solution is the reciprocal of its resistanceC = 1/RC = (1/p).A/lC = KA/l where k is specific conductance.When l=1cm,A=1sq.cm, hence specific conductance may be defined as the conductance of cube of solution of 1cm side placed between two electrodesConductance is expressed in mhos/cmSpecific conductance, K = C.l/A =1.l/R.A

Equivalent conductanceSolutes of equal normality produce the same number of ions when completely dissociated and equivalent conductance measures the current carrying capacity of this given number of ions.Specific conductance measures the current carrying capacity of all the ions in a unit volume of solution.Equivalent conductance is the conductance of a solution containing 1 gm equivalent weight of the electrolyte, when whole of the solution is placed between two parallel electrodes 1 cm apart. If V cc of the solution contains 1 gm equivalent of the solute, then there will be V number of cubes of 1 cm side between two electrodes separated by a distance of 1 cm.

Equivalent conductance c at a concentration of c gram equivalents per liter is calculated from the product of the specific conductance and the volume V in cm3 that contains 1 gram equivalent of solute. V=(1000 cm3/liter)/(c Eq/liter) = 1000/c cm3/Eq It is obtained when is multiplied by V, hence c is expressed in units of mho cm2/Eq and it is given by expression c = * V = 1000 /c mho cm2/Eq

Molecular conductance is the conductance containing 1 gm mole of the solute when placed between two parallel electrodes 1 cm apart.

= k.VWhere k is the specific conductance and V is the volume of the solution in cc containing 1 gm mole of the solute.

Transference or Transport Number or Hittorfs numberThe fraction of total current carried by the cations or by anions is known as the transport or transference number t+ or t-t+ = Current carried by cations/total currentt- = Current carried by anions/total currentThe sum of the two transference numbers is equal to unity.t+ + t- =1Transference number are related to velocities of ions, the faster moving ion carrying the greater fraction of current.Velocities of ions in turn depend on hydration as well as ion size and charge.Speed and transference numbers are not same for positive and negative ions.

Determination of Transport NumberThere are two methods for determination of the transport number of an ion:1. Hittorfs method2. Moving boundary methodHittorfs method:Acc. To this rule, the loss of concentration around any electrode is proportional to the speed of the ion moving away from that electrode.The apparatus consist of two vertical glass tubes joined together through a U-tube in the middle.All the three tubes are provided with stopcocks at the bottom.The U- tube is also provided with stopcocks at the tops of the two limbs.By closing these stopcocks, the communication between the solutions in the cathode and anode limbs can be stopped.

The silver anode is sealed in a glass-tube and the cathode is a piece of freshly silvered foil.The apparatus is filled with a solution of silver nitrate and a steady current of about 0.01 ampere is passed for two or three hours.It is an important precaution that the current is passed only for a short time so that too large a change in conc. does not take place.The apparatus is connected with a silver or copper coulometer.When the current has been passed for near about 2-3 hrs, the stopcocks at the top of the U-tube are closed.The whole of the liquid in the anode compartment is carefully drained into a weighed flask and its weight determined. Its silver content is determined by titrating against a standard solution of potassium thiocyante.The weight of silver deposited in the silver coulometer is also determined.

If copper coulometer is used in place of silver coulometer, the weight of silver equivalent to the copper deposited is calculated by multiplying it with 108/31.5.In the above expt. has been performed by using silver electrodes, I this case nitrate ions attack the silver anode.The same expt can also be performed by using platinum electrodes to avoid the attack of anions at the anode.Calculations:Two different cases may arise:Case I: When electrodes are unattackable (Pt electrodes are used)After passing electric current:Let the weight of anodic solution taken out = a gWeight of AgNO3 present in it by titration = b gWeight of water = (a- b) g

Before passing electric current:Let weight of AgNO3 in (a - b) g of water before passing electric current be = c gFall in conc. = (c - b) g of AgNO3 = (c b)/170 g eqvt of AgNO3 = d (say)Let the weight of silver deposited in silver coulometer be = w1 g = w1/108 g eqvt of Ag = W (say) g eqvt of AgTransport number of Ag+ (t Ag+) = d/WAnd transport number of NO3- ion (t No3-) = 1- d/W

Case II: When electrode are attackable (Ag electrodes are used).Increase in conc. Of anodic sol. = (b c) g of AgNO3 = (b c)/170 * 108 g of Ag = e (say)If no Ag+ ions had migrated from the anode, the increase in conc. Of Ag+_ ions would have been equal to WFall in concentration due to migration of Ag+ ion = W eHence, Transport number of Ag+ ion (tAg+) = W e / WAnd transport number of NO3- ion (t NO3-) = 1- (W e / W)

The moving boundary methodIt is based on the direct observation of migration of ions under the influence of applied potential.This method is very accurate and has been used in recent years for precision measurement.The apparatus used consist of a long vertical tube fitted with two electrodes at the two endsThe tube is filled with a solution of cadmium chloride(CdCl2) at the lower end and hydrochloric acid at the upper end in way that there is a sharp boundary between the two (due to differences in refractive indices.)The platinum cathode dipped in HCl solution is inserted at the top and the anode (cadmium stick) is introduced at the bottom.On passing electric current through the apparatus, hydrogen gas is evolved at the cathode and H+ ions move towards the cathode.

The H+ ions are replaced by Cd++ ions and hence the boundary line moves in the upward direction. By noting the length through which the boundary moves and the quantity of electricity passed through the cell, the transport number of H+ ion can be calculated.If the transport number of a cation A+ is to be determined, the electrolyte AX solution is taken in the upper part of the apparatus and a layer of another electrolyte BX having the common ion X- is introduced in the lower part of the apparatus. The electrolyte BX is selected so that the velocity of B+ ion is less than that of A+ ion.

Equivalent conductance of strong and weak electrolytesAs the solution of strong electrolyte is diluted the specific conductance decreases because the number of ions per unit volume of solution is reduced.Equivalent conductance of a solution of strong electrolyte steadily increases on dilution. According to definition quantity of strong electrolyte remains constant at 1 gm equivalent but the ions are less hindered by neighbor ions in dilute solution and hence moves faster.Equivalent conductance of weak electrolyte also increases on dilution.Kohlrausch first investigated this phenomenon.

He found that equivalent conductance was linear function of square root of the concentration for strong electrolytes in dilute solutions.Equivalent conductance at concentration c (Eq/L),c = 0 - bcwhere 0 is the intercept on vertical axis and it is known as equivalent conductance at infinite dilution. Constant b is the slope of the line for strong electrolytes Kohlrausch concluded that the ions of all electrolytes migrate independently as the solution is diluted and the ions are so far that they do not interact with each other.So the 0 is the sum equivalent conductance of the cations lc and the anions la at infinite dilution0 = lc + la

Arrhenius theory of electrolytic dissociationWhen electolytes are dissolved in water the solute exist in the form of the ions in the solution.Ionic compound H2O + Na+Cl- Na+ + Cl- + H2O (strong electrolyte)Covalent compoundH2O + HCl H3O+ + Cl- (strong electrolyte)Covalent compoundH2O + CH3COOH H3O+ + CH3COO- (weak electrolyte)

The first reaction indicates that sodium chloride exist as ions in crystalline state as shown by + and - signs.If the electrodes are placed in a mass of fused sodium chloride and attached to a source of electric current then the molten compound conduct the electric current because the crystal lattice of pure salt consists of ions.

The addition of water to the solid dissolves the crystal and separates the ions in the solution.In the second reaction, hydrogen chloride exist as neutral molecule rather than as ions in pure form and does not conduct electricity.But when it reacts with water it ionizes according to reaction shown and there is formation of hydronium or oxonium ion.In the third reaction, sodium chloride and hydrochloric acid are strong electrolytes because they exist completely in the ionic form in aq. solutions. Most inorganic and organic salts are highly ionized and belong to the class of strong electrolytes.In the fourth reaction, acetic acid is weak electrolyte and equilibrium is established between the molecules and the ions produced.Most of organic acids and bases and some inorganic compounds, some salts and complex ions belong to class of weak electrolyte.

Degree of DissociationAccording to Arrhenius strong electrolytes ionized completely except in extremely dilute solutions.He differentiated between strong and weak electrolytes by the fraction of molecules ionized i.e. the degree of dissociation .He determined the degree of dissociation directly from the conductance measurement.He recognized that the equivalent conductance at infinite dilution, 0 was a measure of complete dissociation of the solute into ions and that c represented the number of solutes particles presented as ions at a concentration c. Hence, the degree of dissociation was expressed by eq. = c / 0 in which c / 0 is known as the conductance ratio.

Vant HOFF FACTOR iIt is used to express the departure of concentrated solutions of non-electrolytes from the laws of ideal solutions. It can be explained on the same basis as deviations of real solutions from Raoults law.The Vant HOFF FACTOR i can be connected with the degree of dissociation by following way.The i factor equals to unity for an ideal solution of non-electrolyte, but an extra term is added for the particles produced when the molecules of an electrolyte dissociates.For an electrolyte yielding v ions,i = 1 + (v - 1) from which we can obtain an expression for the degree of dissociation = (i 1) / (v - 1)

Cryoscopic method is used to determined i from the expressionTf = iKfm or i = Tf /Kfm

Debye-Huckel TheoryDerived an equation based on the principles that strong electrolytes are completely ionized in dilute solutions and that the deviations of electrolytic solutions from ideal behavior are due to the electrostatic effects of the oppositely charged ions.This equation relates the activity co-efficient of a particular ion or the mean ionic activity coefficient of an electrolyte to the valence of the ions, the ionic strength of the solution, and the characteristics of the solvent.Acc. to the theory, the activity coefficient, i, of an ion of valence zi is given by the expressionLog i = - Azi2This equation gives the measure of the activity coefficient of an ion species up to an ionic strength, , of about 0.02.

For water at 25C, A, a factor that depends only on the temperature and the dielectric constant of the medium, is appro. equal to 0.51.The Debye-Huckel equation for a binary electrolyte consisting of ions with valences of z+ and z- and present in a dilute solution ( < 0.02) is Log += - Az+z-The symbol z+ and z- stand for valences or charges.The coefficient in above equation should actually be x, the rational activity coefficient but in dilute solutions for which the Debye-Huckel equation is applicable, x can be assumed to be equal also to the practical coefficients, m and c, on molal and molar scales.Thus the activity coefficient of a strong electrolyte in dilute solution depends on the total ionic strength of the solution, the valence of the ions involved, the nature of the solvent, and the temp. of the solution.

Extension of Debye-Huckel Theory to higher concentrationsThe last two equations are not satisfactory above an ionic strength of about 0.02.A formula that applies up to an ionic strength of perhaps 0.1 is Log += - Az+z- / 1+ ai B The term ai is the mean distance of approach of the ions and is called the mean effective ionic diameter or the ion size parameter. Its significance is not known but it is analogous to the term b in Vander Waals gas equation.The term B, like A, is a constant influenced only by the solvent and the temperature.The product of ai and B is approximately unity, then the above equation simplifies to Log += - Az+z- / 1+

For higher concentrations i.e. at ionic strength above 0.1 the activity coefficient for some electrolytes pass through minima and then increase with concentration and in some cases they become greater than unity.To account for increase in + at higher concentrations, an empirical term C can be added to the Debye-Huckel equationLog += - (Az+z- / 1+ ai B )+ CThis equation gives results in solutions of concentrations as high as 1M. The mean ionic activity coefficient obtained from above equation is x.

Coefficients for expressing colligative propertiesThe L valueThe vant Hoff expression Tf = iKfm can be modified slightly for convenience in dilute solutions by substituting molar conc. c and by writing iKf as L, so that Tf = Lc The value of L varies with the conc. of solution.For a drug conc. that is isotonic with the body fluids, L = iKf is designated here as Liso.It has a value equal to about 1.9 for non electrolytes, 2.0 for weak electrolytes, 3.4 for univalent electrolytes and larger values for electrolytes of high valences.

Osmotic CoefficientAs the solution becomes more dilute, i approaches v, the number of ions into which an electrolytes dissociates, and at infinite dilution, i = v, or i/v = 1.For more concentrated solutions, i/v becomes less than unity.The ratio i/v is designated as g and is known as the practical osmotic coefficient when exposed on a molal basis.In case of weak electrolytes it provides a measure of the degree of dissociation.For strong electrolytes, g is equal to unity for complete dissociation, and the departure of g from unity, i.e. 1 g, in moderately concentrated solutions is an indication of the inter-ionic attraction.Osmotic coefficients, g, for electrolytes and non-electrolytes are plotted against ionic concentration, vm.Because g = i/v or i = gv in a dilute solution, the cryoscopic equation can be written Tf = gvKfm

OsmolalityOsmotic Pressure is generally in atmospheres but in clinical practice it is expressed in terms of osmols (Osm) or milliosmols (mOsm).A solution containing 1 mole ( 1 gram molecular weight) of a non-ionizable substance in 1 kg of water ( a 1 m solution) is referred to as 1-osmolal solution. It contains 1 osmol (Osm) or 1000 milliosmols (mOsm) of solute per kg of solvent.Osmolality measures the total number of particles dissolved in 1 kg of water i.e. osmols per kg of water, and depends on the electrolytic nature of the solute.For an electrolyte that dissociates into ions in a dilute solutions osmolality and milliosmolality can be calculated fromMilliosmolality (mOsm/kg) = i.mmi is approximately the number of ions formed per molecule and mm is the millimolal concentration.

If no ionic interactions occurred in a solution of sodium chloride, i would equal 2.0.For a 1:1 electrolyte in dilute solution, i is approx. 1.86, owing to ionic interaction between positively and negatively charged ions.Osmolarity is used more frequently than osmolality in labeling parenteral solutions in hospital.Osmolarity = (measured osmolality) * (solution density in g/mL anhydrous solute concentration in g/mL)Osmolality is converted to osmolarity using equation mOsm/liter solution = mOsm/ (kg H2O) * [d1 (1-0.001 v2)]d1 = density of solvent v2 = partial molal volume of the solute at infinite dilution.

Colligative properties such as freezing point depression are related to osmolality through equations Tf = Kf imWhere i = gv and im = gvm is osmolality

KohlrauschLawBy Kohlrausch - The difference in the conductance at infinite dilution of potassium and sodium salts having common anion remained constant.Hence, he concluded that each ion has a definite contribution to equivalent conductance at infinite dilution.The values for KCl,NaCl,KNO3 and NaNO3 at 200C are 130,109,126.5,105.4 respectively.KCl - NaCl =130-109 =21 unitsKNO3 - NaNO3 =126.5-105.4 =21.1 unitsThis shows that K+ and Na+ ions will have a definite contribution to the equivalent conductance at infinite dilution.

Kohlrauschs law of independent Migration of ionsEach ion has a definite contribution to the equivalent conductance at infinite dilution. For a binary electrolyte such as KCL we can write,KCl = K+ + Cl- Where, K+ and Cl- are respective ion conductance at infinite dilution. Or in general = + + -

= ku+ + ku-

Since equivalent conductance of cation and anion are proportional to the velocity (speed) of the cation and anion viz u+ and u- resp.

Application of Kohlrauschs lawThe equivalent conductance of strong electrolyte at infinite dilution can be determined experimentally, by extrapolating the plot of vs concentration. This can not be done in case of weak electrolyte.It can be determined using the Kohlrauschs law.Eg. Equivalent conductance for the salt CH3COONa, for NaCl and HCl is determined experimentally from the plot of vs concentration.

From Kohlrauschs law of independent migration of ion we can write:

CH3COONa = CH3COO- + Na+1

HCl = H+ + Cl-2

NaCl = Na+ + Cl-3

Adding equation 1 and 2 and subtracting 3rd we get, CH3COO- H+ = CH3COONa + HCl -NaCl

Since all the terms on the RHS of above equation can be experimentally determined, the LHS ie CH3COOH can be calculated

Note: conductance at infinite dilution of CH3COONa, HCl and NaCl being strong electrolytes can be determined by extrapolation of conc plots.

Conductometric titrationTitrations in which conductance measurements are made in determining the end point of acid-alkali reactions, displacements reactions or precipitation reactions are called conductometric titrations.Advantage is taken of the fact the conductance of a solution at a constant temperature depends upon the number of ions present in it and their mobility.Titrant is added from a burette into a measured volume of the solution to be titrated which is taken in a conductance cell and the conductance readings corresponding to the various additions are plotted against the volume of the titrant.

Principle of conductometric titrationsAt infinite dilutions ions act independent of each other and they contribute to the conductance of the solution.Both cations and anions have varying degree of ionic mobilities (or conductance values).Thus, when a solution of one electrolyte is added (as a titrant) to the solution of another electrolyte the overall conductance of the solution (after addition) will depend whether a reaction occurs or not.If no chemical reaction occurs between the electrolyte solution and another added to it the overall conductance of the solution will increase. All ions will contribute to the conductance of the solution.When a chemical reaction occurs, replacement or substitution of ions takes place and depending upon ionic conductance of replacing and replaced ions conductance will either increase or decrease.

Principle of conductometric titration is based upon the substitution of ions of one mobility (conductance) by the ions of another mobility. Thus,A+ B- + C+ D- = A+ D- + C+ B-The conductance will increase or decrease depending upon whether the mobility of C+ ion is greater or lesser than that of ion A+.In conductometric titrations, titrant is added in small volume and conductivity is measuredThe points thus obtained after the addition of each increment of titrant are plotted to give a graph which consists of two straight lines intersecting at the equivalence point.Accuracy of the method is greater when the angle of intersecting line is more acute.Conductance of weak electrolyte is largely dependant upon the degree of ionization, which in turn is dependent upon the dilution and temperature.

Types of conductometric titrationsStrong acid with strong base:In the titration of HCl with NaOH, initial fall in conductance is due to replacement of H+ ions of high ionic mobility (350) with slow mobility Na+ (50) ions. After the end point conductance rises due to excess of OH- ions (199) being added.

Strong acid with weak baseThe titration of HCl or H2SO4 with dil. NH4OH solution.The progressive fall in conductance is due to the disappearance of hydrogen ions of high ionic mobility during neutralization.After the end point the graph becomes almost horizontal because ionization of ammonia is prevented in the presence of NH4Cl or NHSO4 formed during neutralization reaction.

Weak acid with strong baseTitration of weak acid like acetic acid or boric acid with strong base like NaOH, the shape of graph will depend upon the conc. and dissociation constant of the acid. Thus in neutralization of acetic acid initial conductance is due to ionization of small amount of acetic acid.The progressive salt formation increases conductance which in turn repress ionization of acetic acid.These two opposing influences show fall followed by rise in conductance.After the neutralization a break occurs showing rise in conductance due to OH- ions.

Weak acid with weak baseTitration of weak acid like acetic acid or phenol with weak base aq. Ammonia solution shows the this graph.The neutralization curve upto end point of weak acid is similar to that obtained with NaOH.Conductance rises due to the salt formation of weak acid.After the equivalence point an excess of aq. Ammonia solution has no effect upon the conductivity because of suppression of ionization of ammonia by the salt formed

Very weak acid with strong baseTitration of boric acid with NaOH solution.Initial conductance is very small but increases progressively as neutralization proceeds. This is because of salt formation which accounts for rise in conductance due to hydrolysis.After the equivalance point the sharp rise in conductance is due to excess OH- ion added as titrant.

Mixture of HCl (strong acid) and acetic acid (weak acid) with strong baseInitially conductance falls due to neutralization of strong acid and then rises as the weak acid is converted into its salt. After the complete neutralization of both acids conductance finally rises more steeply as the excess of OH ions are introduced.Two end points a and b for neutralization are observed.Titration of mixture of acids with weak base (NH4OH) will show graph similar upto neutralization of both acids.Afterwards conductance remains same due to suppression of ionization of weak base

Displacement titrationsTitration of salt of weak acid (sodium acetate) with strong acid (HCl) a and that of salt of weak base (NH4Cl) with strong base (NaOH) b can be followed by conductometer.In sodium acetate titration with HCl, the initial increase in conductivity is due to slightly greater ionic mobility of chloride ions than that of the acetate ion.Until replacement is complete, solution contains sufficient sodium acetate to suppress the ionization of liberated acetic acid.Near equivalence point the acetic acid is sufficiently ionized to give rise in conductance.Beyond equivalence point the excess of HCl accounts for high conductance.Similarly in titration of NH4Cl with NaOH, the initial fall in conductance is due to replacement of ammonium ion (high mobility) by the sodium ion (low mobility).

After equivalences point steep rise in conductance is due to OH- of NaOH

Precipitation and complex formation titrationsConductometric titrations of this type can be satisfactorily performed provided that:The reaction product is sparingly soluble,Forms stable complex andThe precipitate do not have strong adsorbent properties.The solubility of precipitate and its dissociation is kept below 5 % by addition of ethanol.A slow rate of precipitation prolongs the time of titration.Titration of AgNo3 with KCl or NaSo4 with BaCl2

Advatages:Even coloured solutions can be titrated as no indicator is required to judge the end point.Precipitation reaction can also be studied by this method.Care must be taken to use dilute solutions so that the electrodes are not covered by the precipitate.Eg. NaCl solution may be titrated against standard AgNO3.

Redox TitrationsThe redox type of titrations are not possible by conductometer.In most of redox reactions a large excess of acid or base is used for completion of reaction. This interferes by masking the changes in conductance.Hence redox titrations are not performed by using conductometer.

Solubility of a sparingly soluble saltThe solubility of a sparingly soluble salt such as AgCl or PbSO4 can be determined by conductivity experiment.

The specific conductance of water (kwater) is 1.6 x 10-6 ohm-1cm-1 at 250C; and is determined by a conductivity meter.

Also the specific conductance of saturated solution of AgCl. kAgCl(salt) in distilled water is determined using a conductivity meter.

= 1000k/c

Since the AgCl solution is very dilute solution may be replaced by for AgCl and the value of c, the concentration in gm.equivalents of AgCl/litre may be replaced by the saturation solubility of AgCl viz s and hence , we can write, = 1000k/s s=1000k/ = 100 (kAgCl(salt) kwater) /

Equivalent conductance of a weak electrolyte at infinite dilution The plot of equivalent conductance vs concentration is a straight line for solution of strong electrolytes and it is possible to extrapolate the straight line to obtain the equi conductance at infinite dilution.The Kohlrauschs law can be used to determine the equivalent conductance at infinite dilution of a weak electrolyte, since in the case of weak electrolytes extrapolation of vs c plot to obtained is not justified.

Eg:CH3COOH is determined by determining CH3COONa , HCl ,NaCl

CH3COOH = CH3COONa + HCl -NaCl

= CH3COO- + Na+ + H+ +Cl - - Na+ - Cl (By Kohlrauschs law)= CH3COO- + H+

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