b400 physical chemistry

8/13/2019 B400 Physical Chemistry

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Philippine Handbook Physical Chemistry In Chemical Engineering

F. PHYSICAL CHEMISTRY

F.1. SOLID STATE Solids have two common crystallographic forms, cubic and hexagonal , classified and

characterized based on the type of unit cell. A unit cell is characterized by an array of lattice points in three dimensions, e.g., there are

three lattice points in a unit cell in three dimensions. A crystallographic unit cell is a parallelepiped formed by connecting the eight lattice

points. Cubic unit cell is characterized by the six square faces and the three equal non-coplanar

edges denoted as a , b and c. (i.e., a = b = c . !he volume of a cubic unit cell is"

V a ! (f - #

Hexagonal unit cell is characterized by four rectangular faces with edges that are eitherside ac or side bc, two parallelograms with equal sides (e.g., a = b and interior angles of60o and 120 o. !he volume of a hexagonal unit cell is abcsin(#$% o or

(f - $

F.1.1. Si"#le Cubic C$%&'al

!here are three types of cubic crystals" simple, face centered and body centered. &n simplecubic crystal (' unit cell, there is one lattice point at each of the eight corners of a cube.!his type of unit cells where there is lattice point only at the eight corners is called the

primitive type of unit crystal. An example of an ' is shown in )igure ) - #. !he number oflattice points in a given unit crystal is denoted by Z .

Figu$e F ( 1. *xample of 'imple ubic rystal

) - #


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'uppose an atom of radius r occupies a lattice point and is tangent to all the ad+acent atoms,there are six contacts wherein each of the unit cells edges is the sum of two atomic radii.!hus, an edge of a cubic crystal is equal to $r. !he volume, therefore, of a simple cubiccrystal is

Vc )*$+! ,$ ! (f -

&n ' there is only one host atom inside the cube because each of the eight corner atomscontributes one eighth of an atom to the cell interior. !he volume of the cell occupied by theatoms is

VSCC )- !+ $! / . (f -

!he p acking e iciency of a lattice is defined as the ratio VSCC 0Vc thus, for the simple cubicunit cell the pac/ing efficiency is about 0$. 1.

F.1.*. 2o3% Cen'e$e3 Cubic C$%&'al&n 2ody entered ubic (2 unit cell there is one host atom at each corner of the cube andone host atom in the center of the cube" 3 = $. *ach corner atom touches the central hostatom along the diagonal of the cube. !hus, the atoms at the lattice points are tangent to thehost atoms along the diagonal but not to each other, )igure ) - $. !he length of the edge ofthe unit cell is $( 4 #4$ and the volume of the cube is

V c )!* !+)- !+ 1 *$! (f - 0

Figu$e F 4 *. *xample of 2ody entered ubic rystal

!he pac/ing efficiency in this type of lattice is about 561, which is much higher than that in' .

F.1.!. Face Cen'e$e3 Cubic C$%&'al

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!ace Centered Cubic () unit cell has one host atom at each corner and one host atom ineach face. !he corner atom contributes one-eighth of its volume while the face atomscontribute half of its volume. !hus the face atoms contributions are equivalent to atoms andthe corner atoms contribution is equivalent to one. !he total number of lattice points is , i.e.,

3 =#

46.

6 7#

4$.

5 = ()igure ) - .

Figu$e F 4 ! . *xample of )ace entered ubic rystal

!he corner and face atoms of this type of cubic crystal touch along the diagonal of the faceand are tangent to each other. !he unit length of ) edge is equal to $ 4$r. !hus, the volumeof the crystal is

Vc )* ! *$ +! (f - 5

!his type of crystal has a pac/ing efficiency of about 8 1 and is the most closely pac/edamong cubic crystals.

F.1.-. P$i"i'i5e Face Cen'e$e3 Cubic

&n any lattice it is possible to choose a primitive unit cell, i.e., 3 = #. !here are actually anumber of choices. All the primitive unit cells on a lattice have the same volume. 9owever,only one of these primitive unit cells has the three shortest cell edges (a,b,c and this is the&'an3a$3 $e3uce3 cell . )or ) lattice, the standard reduced cell is a $ho"bohe3$on , where a b c *$ . !hethree interior angles formed between unit cell edges are denoted as"

angle between the edges b and cangle between edges a and c

angle between edges a and b

)or ) rhombohedral standard reduced cell, 67 o. A cube is a specialrhombohedron where = = = :%o.

) -


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Figu$e F ( -. "#"$%

F.1.8. P$i"i'i5e Hexagonal

!he most densely pac/ed (i.e., least amount of empty space possible arrangement of spheresis where each of the sphere touches six other spheres arranged in the form of a regularhexagon, )igure ) - 0.

Figu$e F 4 8. ;ensely


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A primitive hexagonal unit cell as outlined by bold blac/ lines in the crossed stereo pair in)igure # - 5, has cell edges a b *$ and c *$ ' hus, the ratio c0a 1. T he pac/ingefficiency of this three dimensional lattice is about 5%1 (compared to 8 1 for closest

pac/ing , even though the atoms are closest pac/ed in two dimensions.

Coordination in HCP

*ach host atom in a 9 < lattice is surrounded by and touches #$ nearest neighbors, each at adistance of $r"

a. !here are six atoms in the planar hexagonal array (the central A layer > b. !here are three atoms in the 2 layer above the A layer>c. !here are three atoms in the 2 layer below the A layer.

!he six atoms in the two 2 layers form a '$igonal #$i&" around the central atom in the Alayer> the length of this prism is $ .


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diffraction has been developed to study the structure of all states of matter with any beam,e.g., ions, electrons, neutrons, and protons, with a wavelength similar to the distance betweenthe atomic or molecular structures of interest.

Bragg's Law

onsidering the conditions necessary to ma/e the phases of the beams coincide when theincident angle equals and the reflecting angle can easily be derived using 2ragg s aw. !herays of the incident beam are always in phase and parallel up to the point at which the top

beam stri/es the top layer at atom z ()igure ) - 6 . !he second beam continues to the nextlayer where it is scattered by atom 2. !he second beam must travel the extra distance A2 72 if the two beams are to continue traveling ad+acent and parallel. !his extra distance must

be an integral (n multiple of the wavelength (l for the phases of the two beams to be thesame"

n & '( )(C (f - 6

Figu$e F ( ,. ;eriving 2ragg@s aw sing the CeflectionEeometry and Applying !rigonometry

!he lower beam must travel the extra distance (A2 7 2 to continue traveling parallel andad+acent to the top beam.

Cecognizing d as the hypotenuse of the right triangle A2z, we can use trigonometry to related and q to the distance (A2 7 2 . !he distance A2 is opposite q so,

'( & d sin * (f - :

2ecause A2 = 2 , eq. (f - 6 becomes,

n & 2'( (f - #%

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'ubstituting eq. (f - : in eq. (f - #% , we have

n & 2 d sin * (f - ##

and 2ragg@s aw has been derived. !he location of the surface does not change the derivationof this aw.

F.*. =ASES

Eases are materials of very low density that must be enclosed to /eep together and have nodefinite shape and volume, and completely fill a container. !hus, the volume of gases is thevolume of the container. Eases exert pressure on all sides of the container and can becompressed by a pressure greater than the pressure it exerts on its container. !he term vapor,fume, air, or miasma also describes a gas. Air indicates the common mixture of gases in theatmosphere (i.e., oxygen and nitrogen and miasma is the bad-smelling or poisonous gas.Fapor and fume suggest that the gas come from a particular liquid.

aseo!s "tate

&n the gaseous state, matter is made up of particles (atoms or molecules that are notattached to each other.

!he intermolecular or interatomic force that holds solid and liquid molecules together

are overcome by the motion of the molecules in gases. !he particles of gases have too much thermal energy to stay bound to each other.

!he motion and vibration of the atoms pull the individual molecules apart.

Eases consist mostly of unoccupied space. A gas molecule has to travel a longdistance before it encounters another molecule. &t can be pictured as having a @pointsource of mass@, where the volume of the molecule is negligible compared to the space itoccupies.

?hen two gas molecules collide with each other they bounce off, ideally in acompletely elastic encounter. !here is pressure within the gas caused by the gasmolecules in motion stri/ing each other and anything else in their path. !he pressure thata gas exerts on its container comes from the molecules of gas hitting the inside of thecontainer.

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!here are some materials that do not exist in the gaseous form because the amount ofmolecular motion is not enough to pull the molecules apart. )or this reason it is unli/elyfor large biological molecules such as proteins, fats, and ;DA to appear the form of a gas.

Physical Properties Li#!id $ir

iquid air, with all the molecules touching each other, has a density of about %.680grams per milliliter (g4m .

Avogadro@s law states that one mole of any gas occupies a volume of $$. liters atstandard temperature and pressure or '!< (# atmosphere pressure and %G . At '!< gasair weighs about $6.:5 g and occupies a volume of $$. or #.$: g4 .

iquid air is over 580 times denser than gas air at one atmosphere. !his means eachmolecule of the gas has more than 580 times its own volume to move around.

F.*.1. I3eal =a& La; Fo$"ula

+ & n-" (f - #$

Eases may be completely described by its ma/eup, pressure, temperature, and volume asshown in equation f H #$, where < is the pressure, F is the volume, n is the number of moles

of gas, ! is the absolute temperature, and C is the niversal Eas onstant. !he ideal gas la. ormula is pretty accurate for all gases as the gas molecules are assumed as point masses andthe collisions of the molecules are totally elastic. A completely elastic collision means theenergy of the molecules before collision equals the energy of the molecules after collision, orto put it another way, there is no attraction among the molecules.

!he ideal gas formula becomes less accurate as the compression increases and temperaturedecreases. )or each gas, however, corrections can be introduced to both factors, which willconvert the &deal Eas aw )ormula to Ceal Eas aw )ormula. !he ideal gas formula canserve as a good estimation of the way gases act.

!he niversal Eas onstant, C, can be expressed in several ways, depending on the units ofine'ic Molecula$ Theo$% o< =a&e&

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!hese statements are made only for what is called an ideal gas. !hey cannot all be rigorouslyapplied (i.e. mathematically to real gases, but can be used to explain their observed behaviorqualitatively.

All matter is composed of tiny, discrete particles (molecules or atoms . &deal gases consist of small particles (molecules or atoms that are far apart in

comparison to their own size. !he molecules of a gas are very small compared to thedistances between them.

!hese particles are considered to be dimensionless points occupying practically zerovolume. !he volume of real gas molecules is assumed to be negligible for most

purposes. Ceal gas molecules do occupy volumes and have an impact on the behaviorof the gas.

!hese particles are in rapid, random, constant straight-line motion and can bedescribed by well-defined and established laws of motion.

!here are no attractive forces between gas molecules or between molecules and the

sides of the container with which they collide. &n a real gas, there actually is attraction between the molecules of a gas.

Jolecules collide with one another and the sides of the container. *nergy can be transferred in collisions among molecules. *nergy is conserved in these collisions, although one molecule may gain energy at the

expense of the other. *nergy is distributed among the molecules in a particular fashion /nown as the

Jaxwell-2oltzmann ;istribution. At any particular instant, the molecules in a given sample of gas do not all possess the

same amount of energy. !he average /inetic energy of all the molecules is proportional to the absolute temperature.

F.*.!. Dal'on?& La; o< Pa$'ial P$e&&u$e&

?hen the volume and temperature are held constant the ideal gas equation can be written as P% kn where k & &

'T / )rom the given formula , it is apparent that < is directly proportional tothe number of moles of gas in the container.

&n a mixture of gases, both the pressure and number of moles are additive. !o illustrate this point, consider a two-gas system where < # is the partial pressure of n #moles of the first gas

and


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$# P P P T (f - #

&f + & kn , then for the first gas + 1 & kn1 and for the second gas + 2 & kn2. Adding the twogives + " & k n1 ) n 2 & kn" . !his relation can be extended to systems of gas mixtures wherethere are n different or similar gases. !he relation is /nown as ;alton@s aw of


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$ supercritical luid is a s!bstance that is abo+e its critical temperat!re. Tc and press!re. Pc /

F.*.:. @on4I3eal E ua'ion& o< S'a'e

An equation of state relates the molar density (or specific molar volume of a fluid to thetemperature and pressure of that fluid. (Dote that the term fluid was used rather than gas

&irial E#!ations of "tate

A primarily mathematics motivated (theory is from statistical mechanics equations of state,the virial equation uses a power series in the form"

(f - #5

where 2, , and ; (etc. are material dependent constants. !hese constants are sometimesdifficult to determine (theoretically and the expression is typically truncated after the 2values so that there is only one KfittingK parameter, (i.e.,

(f - #8EThis expression is good for non-polar gases. The constant, B, can be obtained from thefollowing relation:

(f - 18)

where T c and P c are the critical temperature and pressure, and B o and B 1 are given by thefollowing expressions:

(f - 19)

(f - 20)

e inition

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The reduced temperature (pressure) is a dimensionless temperature (pressure) given asthe ratio of the actual temperature (pressure) to the critical temperature (pressure) and isdenoted by T r (P r).DEFINITION

The Pitzer ascentric factor ( ) is a material parameter that reflects the polarity and"shape" of the molecule, i.e., it is different for every molecule and therefore must be lookedup!

C!bic E#!ations of "tate

Another important class of equations of state is the cubic ones. !hey are called cubicequations of state because, mathematically, the equations are third order polynomials orcubic equations in . (Dote that the truncated virial equation is quadratic ubic equationsare basically better than quadratic equations in estimating the relation among the physical

parameters. !he shape of the curve in the phase envelope can explain it. !he two most

important cubic equations of state are van der ?aals equation and 'oave-Cedlich-Iwong('CI equation. Fan der ?ants equation is similar in form to 'CI.

&an der -aals E#!ation

Fan der ?aal@s equation is a second order approximation of the equation of state of a gas andwill wor/ even when the density of the gas is not low.

(f - $#

where a and b are constants particular to a given gas and can be rearranged to a form ofequation (*qn xx which is interesting to examine because it is easy to discuss qualitativelythe origin of its deviation from ideality.

(f - $$

'ymbols L bB and LaB are material dependent constants and can be calculated from a set ofmaterial independent equations. !hey represent roughly the volume of the gas molecules ( band the KinteractionK of the gas molecules (a . As usual, the constants are correlated to thecritical constants of the materials"

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(f - $

(f - $

!he ideal gas law, P& % n T can be derived by assuming that the molecules that ma/e up thegas have negligible sizes, that their collisions among themselves and with the walls are

perfectly elastic, and that the molecules have no interactions with each other.

Table F ( 1. 'ome van der ?aals onstants

Sub&'ance A(M. m 4mole

b(m 4mole

P c(J


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Figu$e F ( 17 TITLE

Nbserve that inert gases li/e helium have a low value of a as one would expect since suchgases do not interact very strongly, and that large molecules li/e freon have large values of b .!here are many more equations of state that are even better approximation of real gases.

F.*.,. Co"#$e&&ibili'% Fac'o$ an3 Co$$eon3ing S'a'e&

A simpler (mathematical way of representing non-ideality is through compressibilityfactor

+ &3n-" or (f - $0DEFINITION!he co"#$e&&ibili'%


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(f - $5OBJECTIVES:

Use one (or even all) of the covered non-ideal equations (SRK,compressibility factor, van der Waals, virial equation) to determine P, V, or T

F.*. . @on4I3eal =a& Mix'u$e&

&t is unclear how one would use any of the above expressions for mixtures because wehave material-dependent quantities li/e , 2, a, b, etc. 9owever, empirical (experience-

based rules have been developed and we will discuss the one for the compressibilityfactor.DEFINITION

Suggested Approach . Use pseudo-critical properties to calculate pseudo-reducedquantities that are then used in the generalized compressibility charts. That is

T' c = y AT cA+y BT cB+... (f - 27)

P' c = y AP cA+y BP cB+... (f - 28)

(f - 29)

sing the same procedure as in single-component systems, you can then get the pseudo-reduced quantities and obtain the (generalized compressibility factor off a chart.

F.!. LI IDS

iquids are mobile and have the ability to move around, to change their shapes to conform tothat of the container, to flow in response to pressure difference (gradient , and to displaceanother substance or ob+ect. iquids occupy a ixed volume and possess a definite sur ace,though it cannot be discounted that the surface is visible due to the large difference in density

between the liquid and the space above it. !his observable surface is actually the reflectionand refraction of light as it passes through the boundary between the two phases with differentdensities /nown as the index o re raction .

iquid is considered by most as the preferred state of any substance at temperaturesintermediate between the realms of solid and gas. 9owever, the temperature difference

between the melting and boiling points of many compounds the temperature range at which

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most substances can exist as liquid is small compared to solids and gases. !his ma/esliquids somewhat perilous and tenuous, as if liquids have little or no right at all to exist.

'ubstance )ormulaJelting


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/inetic energy of the molecules ma/ing them more mobile, which wea/ens or even disruptshydrogen bond formation due to thermal agitation. Another example is lubricating oils, whichconsist of long-chain hydrocarbon molecules that interact through dispersion forces. !heinteraction of long hydrocarbon molecules could result to molecular entanglement.

!he dependence of the viscosity of liquids (fluids in general on temperature has beenobserved in daily activities and has been /nown even in early times. *dible and automotiveoils are viscous at low temperatures.

Fiscosity impedes motion or flow. &t is noticeable that when a syrup is poured out of thecontainer different parts of the fluid move at different rates and at times in differentdirections. !he intermolecular attractive forces restrain molecules from pulling away fromtheir immediate neighbors and attaching themselves to new molecules. A fluid can movefreely only if its particles are able to flow independently.

!he pressure drop observed when a liquid flows through a pipe is the result of viscosity. !heexplanation for this is that intermolecular forces greatly influence the molecules right next tothe walls> these molecules tend to adhere to the walls, which hinders their movement. !hislayer of molecules then holds bac/ and impedes the movement of the next layer. !he effect istransmitted inward towards the center of the pipe. !his is called the viscous drag effect and is

proportional to pressure drop. !he viscous drag effect normally decreases towards the centerof the tube.

!hese attractive forces depend on the nature of the walls and the moving fluid. 'moothsurfaces li/e those of tubes made of plastics have wea/ attractive forces towards water andsome organic solvents. 9owever, metal pipes and even glasses have relatively high attractive

forces to water and solutions of electrolytes.

F.!.!. Su$


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Figu$e F ( 11. TITLE

the resulting force is zero (see )igure . Nn the other hand, if a molecule is located at thesurface of a liquid, the attraction from the interior of the medium wor/s further on one side,

whereas there are no more molecules on the other side. 9ence the resulting force is directedtowards the interior of the liquid. Nn the microscopic scale this causes drops of liquid to beround since the surface of the liquid is minimized that way. !herefore surface tension, O isdefined as the energy, w needed to stretch or increase the surface area, A of the liquid and wewrite

d$dw=

!he unit of surface tension is energy per unit area say +oules per sq. meter (M4m$

. Eenerally,values of O are reported in newtons per meter (Dm -# since #M= #Dm or dynes per cm.

Capillary action !he upward movement of a liquid in a narrow tube against the force of gravity, which iscalled capillary action is a consequence of surface tension> such is also responsible for theshape of the meniscus curved surface in a capillary tube.

!he force f # (downward pull exerted by a column of liquid of height, h is

ghr f $# =

where is the density of the liquid, r is the radius of the capillary and g is the accelerationdue to gravity. !he force f $ (upward pull due to surface tension is

r f $$ =

At equilibrium f #=f $, hence the surface tension is equal to

grh$

#=

(#

!his simple expression (eq.# provides a reasonably accurate way of measuring the surfacetension of liquids by capillary rise method when the contact angle is negligible.

F.-. SOL TIO@S

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'olutions are homogeneous mixtures of two or more components" the solutes and thesolvent(s . !he solvent is the substance in greater amount and usually but not necessarily a

liquid. ?ater is the most common among the usual solvents used. 'olutions in which wateris the solvent are called aqueous solutions. !he solute is the substance in lesser amount.

A mixture is defined as the combination of different substances where each substance retainsits chemical properties. Eenerally, mixtures can be separated by non-chemical means such asfiltration, heating, centrifugation or distillation.

Jost chemical reactions that are carried out in industries, laboratories and living organismsta/e place in solution. 'olutions provide a convenient and accurate means of introducing/nown small amounts of a substance to a reaction system, e.g. titration.

A mixture is homogeneous when all particles exist as individual molecules or ions. Ahomogeneous mixture is uniform throughout such that two same-size samples, one from the bottom and the other from the top, are identical. 9omogeneous mixtures do not settle out ifleft undisturbed, whereas a heterogeneous mixture would. 2lood is an example of aheterogeneous mixture. 'ome homogeneous mixtures have particle size that is much largerthan individual molecules. 9owever, the particle size is so small that the mixture never settlesout. olloid, sol, and gel are examples of mixtures.

oncentration refers to how much solute is dissolved in solution. ;ilute means that only alittle solute is dissolved and concentrated means a lot is dissolved. !here are two commonconcentrations used that are numerical in nature" molarity and molality.

Jolarity of a solution is determined by calculating the number of moles of solute per liter ofsolution.

(f - #

!o dilute a solution, means to add more solvent without the addition of more solute.Assuming that volume is additive, the following formula is applicable"

moles before dilution = moles after dilution

4 1 1 & 4 2 2 (f - $

!he subscript L#K refers to the situation before dilution while the subscript L$K refers to afterdilution, though the subscript is immaterial.

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Jolality of a solution is determined by calculating the number of moles of solute per/ilogram of solvent.

(f -

"ol!bility

!he general dividing line between soluble and insoluble is %.#J at $0G . !hus, anysubstance that can form %.# J or more is soluble otherwise it is insoluble. !his value was

pic/ed with a purpose. !here are e. substances that have their maximum solubility close to%.# J. Almost every substance of any importance in chemistry is either much more solubleor much less soluble. &n the past, some would have a third category slightly soluble.

Solubili'% $ule& 'ha' a##l% 'o ;a'e$ &olu'ion&0

#. All al/ali metals (lithium, sodium, potassium, rubidium, and cesium andammonium compounds are soluble.

$. All acetates, perchlorates, chlorates, and nitrates compounds are soluble.. 'ilver, lead, and mercury(& compounds are insoluble.. hlorides, bromides, and iodides are soluble.

0. arbonates, hydroxides, oxides, phosphates, silicates, and sulfides areinsoluble. 'ulfates are soluble except for calcium and barium.

!hese rules are to be applied in the order given. )or example,


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!he escaping tendency of the solvent in the presence of a solute depends in part on how muchdisorder the solute can create on the solvent. !his is also similar to the escaping tendency ofthe solute. 2asically it is based on how much disorder is created when two or moresubstances are mixed. *vaporation for instance creates a large disturbance due to the greater

volume occupied by the vapor as compared to the liquid. &f the liquid solvent is diluted in the presence of the non-volatile solute, the increase in disorder in entering the vapor phase is less(Caoult s aw . !he vapor pressure of the solvent can be linearly expressed as shown in theequation below.

p & + o x (f -

where + o and P xP are the vapor pressure and mole fraction of the pure solvent,respectively.

!he vapor pressure lowering is defined as the difference between + o and p" + & + o5p. )or

dilute solutions, this can be presented as a function of the amount solute preset in the solutionas shown below"

p solvent &+ o solvent 15x solute (f - 0

+ & + o5p & + o solvent x solute (f - 5

!his shows that the depression in vapor pressure is linearly dependent on mole fraction ofnon-volatile solute.

!he lowering of vapor pressure increases the temperature to restore the vapor pressure to thevalue corresponding to the pure solvent, in particular the boiling point. !hus, the lowering ofvapor pressure increases the boiling point of the pure solvent in the presence of non-volatilesolute. !he difference in boiling point or the boiling point rise is defined as ! b = !-! o. !hisrelation is quite complicated at a relatively high concentration of the solute due tointermolecular interactions among and between solutes and solvents. 9owever, for relativelydilute solutions this relation is linear and can be derived using the lausius- lapeyronequation. (oiling point elevation is when the solution boils at a temperature above the boiling

point of the pure solvent at a given pressure. )or dilute solutions, the following relationholds"

" b & "5" o & bm (f - 8

?here ! o is the normal boiling point of pure solvent, I b is the ebulloscopic constant and m ismolality of the solution.

!he freezing point is the temperature at which the solid and liquid can simultaneously coexistwhich means the escaping tendency of the molecules from the two phases is the same.

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'imilarly, ree3ing point depression is when the solution freezes at a temperature below thatof the pure solvent.

7smosis is the net movement of the solvent in the direction opposite to the diffusion of the

solute. !ypically it involves the use of a semipermeable membrane (membrane that allowsonly the solute to transfer from one side of the membrane . Nsmosis is an important biological function and if forced to run in reverse ( 8reverse osmosis8 becomes an importanttechnology for production of fresh water from seawater.

Jany pure liquids, and even some solids, evaporate to a slight extent at almost anytemperature producing a slight gas pressure above the surface. &magine what happens whenyou introduce some pure liquid water into a rigid-walled container that is empty (in vacuum .


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as the difference in the levels in the two open tubes increases, so does the pressure differenceexerted by the atmosphere. ?hen the pressure difference exerted on the surfaces of the liquidscontained in the two tubes is +ust enough to stop the flow, that pressure difference is /nown asthe osmotic pressure/

!his pressure difference is easy to measure. 'imply measure the difference in heights in thetwo tubes and convert that height to the equivalent height of mercury by multiplying bydensity solvent4density9g

97"%: !his conversion of pressure units is reasonably valid as long as the concentration ofthe solution is low enough that the density of the solution is approximately the same as that ofthe pure solvent.

!he amount of osmotic pressure exerted can be measured and explained via an easy equation,

which is discussed in the Nsmosis *quation file. = C-" (f - 6

F.8.*. 2oiling Poin' Ele5a'ion

A solution containing a non-volatile solute will boil at a temperature higher than that of the pure solvent. !he more non-volatile solute is present in solution the greater is its effect. Anequation has been developed for this behavior.

" & b m (f - :

!he boiling point temperature difference between the pure solvent and the solution is directly proportional to the molality of the solute in solution. !he proportionality constant I b is/nown as the ebullioscopic constant or molal boiling point constant (refer to the derivation of

b in textboo/s. !able # presents the list of common solvents and their corresponding bvalues.

Table F ( *. 'ome ommon 'olvents and orresponding b Falues

'ubstance I b

2enzene $.0amphor 0.:0arbon tetrachloride 0.%

*thyl ether $.%$?ater %.0$

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!he unit of the constant is degrees elsius per molal (G m S # . !here are some variationssuch as"

# I m-# - the distance between a single elsius degree and a Ielvin are the same.

$ G /g mol-#

- this one ta/es molal (mol4/g and brings the /g.

!he last one is very useful because it splits out the mol unit. ?e will be using this equation(or the freezing point to calculate molecular weights. Ieep in mind that the molecularweight unit is grams 4 mol (molal , which is moles solute over /g solvent.

F.8.!. F$eeGing Poin' De#$e&&ion

A solution will solidify (freeze at a lower temperature than the pure solvent. !he more solutein the solution the greater is the effect. An equation has been developed for this behavior. &tis"

" & m (f - %

!he temperature change from the pure solvent to the solution is equal to two constants timesthe molality of the solution. !he constant is actually derived from several other constantsand its derivation is covered in textboo/s of introductory thermodynamics. 9ere are someKmolal freezing point depression constantsK"

Table F ( !. 'ome ommon 'olvents and orresponding Falues

'ubstance I f benzene 0.#$camphor %carbon tetrachloride %.ethyl ether #.8:water #.65

!he unit discussion pertaining to b also applies to /

F.8.-. 2oiling Poin' an3 F$eeGing Poin' o< Solu'ion&


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example, as pure water vapor leaves the liquid, only pure water is left behind. Dot so with asolution.

As a solution boils, if the solute is non-volatile, only pure solvent enters the vapor phase. !he

solute stays behind (this is the meaning of non-volatile . 9owever, the consequence is thatthe solution becomes more concentrated hence, its boiling point increases. &f you were to plotthe temperature change of a pure substance boiling versus time, the line would stay flat. ?itha solution, the line would tend to drift upward as the solution became more concentrated.

A non-volatile solute is one that stays in solution. !he vapor that boils away is the puresolvent only. A volatile solute, on the other hand, boils away with the solvent.

'alt in water is an example of a non-volatile solute. Nnly water will boil away and, when dry,a white solid (Da l remains. 9exane dissolved in pentane is an example of a volatile solute.!he vapor will be a hexane-pentane mixture. 9owever, here is something very interesting.

!he hexane-pentane percentages in the vapor will be di erent from the percentages of each inthe solution. ?e will get into that.

Nne last thing that deserves a small mention is the concept of an azeotrope. !his is a constant boiling mixture. ?hat this means is that the mixture of the vapor coming from the boilingsolution is the same as the mixture of the solution. !he first occurrence was reported by;alton in #6%$, but the word was not coined until #:##.

Nne example of a binary azeotrope is 1 (by weight water and :51 ethyl alcohol. ?hat thismeans is that you cannot produce pure or #%%1 alcohol (called absolute alcohol by boiling.Tou must use some other means to get the last 1 water out. &t also means that absolute

alcohol is hygroscopic, Hi.e., it absorbs water from the atmosphere.

!he #::$ 9andboo/ of hemistry and


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Ditromethane 8. %!etrachloroethylene $#.#0n- a 5 parts tin to 8 parts lead electrical solder is one such eutectic mixture.

Immiscible Li#!ids

A mixture of two immiscible ideal liquids, say liquids A and 2 will exert their own vapor pressure as if each one is present alone. &f the vapor pressures of the pure components are

o B

o $ P P C , then the total vapor pressure ( + is

o B

o $ P P P (f - #

&f we consider $n and Bn to be the moles of each component present in the vapor,then the composition of the vapor expressed as mole ratio is

o B

o $

B

$

P

P

n

n= (f - $

'ince the ratio of partial pressures is constant at a given temperature the ratio B

$n

nmust

also be constant. !hus the composition of the vapor (or distillate is constant as long as bothliquids are present.

!he fact that the total vapor pressure of the immiscible mixture is the sum of the purecomponent s vapor pressure (as shown in eq.# serves as the basis of the steam distillation

process. 'team distillation allows some heat-sensitive> water-insoluble oils and other organiccompounds to be distilled at a lower temperature than their normal boiling point. !he onlydrawbac/ is that the distillate is in proportion to the vapor pressure of the components (seeequation $ , so oils of low volatility distill in low abundance. !he moles of organic liquid

purified per mole of steam used maybe calculated using equation ($ . &f the weight ratio in thedistillate is the desired then equation ($ is simplified to obtain

Bo

B

$o

$

B

$

,- P

,- P

w

w= (f -

where $w is the weight of the organic liquid in the distillate and Bw is the weight of wateror steam in the distillate. $ ,- and B ,- are the molecular weights of components A and2 respectively .

) - $8


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0ernst Distrib!tion Law

&f a third substance is added to a two-phase liquid mixture, it distributes itself according to itsrelative solubility in each phase. )or example, acetone is soluble in both water and chloroform H two nearly immiscible liquids. &f a mixture of acetone and water is contacted withchloroform, acetone distributes itself between the water and chloroform layers in such a waythat at equilibrium the ratio of the concentrations of acetone in the two layers is constant atany given temperature.'uppose A and 2 are immiscible liquids and a solute is distributed between the phases of anA-2 mixture. !he partial molal free energy of the solute in liquid A, $ is represented by

$o

$ $ a 'T ln (f - and for liquid 2

Bo

B B a 'T ln (f - 0

where o Bo $ and are the standard Eibbs free energies while a A and a2 are the activities ofthe solute in solvents A and 2, respectively. 'ince A and 2 are completely immiscible, twolayers will be formed. *ach layer contains the dissolved solute.

At equilibrium where ! and < are constant, the Eibbs free energy of the layers are equal, i.e., B $ = . 9ence, *quations (# and $ are equal. *quating the two equations will result to

the simplified equation presented in *quation .

= B

$aaln

'T o $o B (f - 5

9owever, at constant temperature, o Bo $ C are constant for any given substance in the particular solvents. 9ence

t consa

a

B

$ 'anln =

1 a

a

B

$

=ln

(f - 8

*quation ( is the mathematical statement of the Dernst distribution law, which states that atequilibrium the ratio of the activities of the solute distributed between two phases is constantat any given temperature.

) - $6


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)or dilute solutions or when the solute behaves ideally, the activity of the solute is equal to itsconcentration> hence, equation ( becomes

B $

C

C 1 =

(f - 6 where the constant I is called the distribution or partition coefficient of the solute betweenthe two immiscible solvents. *quation 0 can be used only when the solute in both phases ischemically the same, which means that no association, dissociation, or reaction with thesolvent ta/es place.

*xtraction is one of the most common analytical and industrial operations .&t refers to thetransfer of a compound from one phase to another phase, which are immiscible with eachother.

'uppose ; o grams of substance is dissolved in # m of solution, and say this solutionis sha/en repeatedly with $ m samples of pure immiscible second solvent in n separateextractions. &n each extraction, the solute is allowed to distribute in the two solvents untilequilibrium is attained. !he weight ; n of unextracted solute after n extractions will be

(f - :

and the 1 of solute extracted (1* is

( )#

1 #%% ##

n

m

% 2

= +

(f - 0%

where#

$

&

& 1 D m .

F.6. SOL TIO@S OF ELECTROLYTES

*lectrolytes are substances whose aqueous solutions conduct electric current. &t is the presence of ions, which can move through the solution, that allow the conduction ofelectricity. 'ometimes the ions are already there in the ionic salt, and at other times they resultfrom the reaction of the substance with the solvent. ?hen an ionic substance is bro/en apart

) - $:

n

on & 1&

1& 2 2

$##


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into solvated cations and anions, the process is called 3i&&ocia'ion , since the ions which arealready present in the salt simply separate or dissociate. 9owever, when the ions are formed

by the reaction of the substance with water and do not exist in the original substance, the process is called ioniGa'ion . !he solution of potassium chloride and sodium hydroxide

illustrates dissociation of ionic solids by solvent molecules

I l (s 7 9 $N V I 7(aq 7 l -(aq

DaN9(s 7 9 $N V Da 7(aq 7 N9 -(aqwhile the solution of acetic acid in water and of hydrogen chloride in liquid ammoniaillustrates ionization of neutral molecules

9 $9 N$(l 7 9 $N(l V 9 N7 7 $9 N$-

9 l(g 7 D9 (l V D9 7 7 l -

'olutions of electrolytes maybe classified as strong electrolytes or wea/ electrolytes. S'$ongelec'$ol%'e& are substances, which are completely dissociated in water or substances forwhich the ionization reaction goes to completion. &n other words, after the substance hasdissolved in water, the original substance no longer exists at any appreciable concentration.!he types of substances which are typically classified as strong electrolytes are soluble salts(e.g. Da l, Jg l $ , strong inorganic acid (the common ones are hydrochloric acid,hydrobromic acid, sulfuric acid, chloric acid and perchloric acid and strong inorganic bases( e.g. DaN9 . ea9 elec'$ol%'e& only ionize partially in water and carries small amount ofelectric current. !he types of substances, which behave as wea/ electrolyte are wea/

inorganic acids (e.g. carbonic acid, nitrous acid, hypochlorous acid , organic acids (carboxylicacids e.g. acetic acid , ammonia and organic amines, e.g. methyl amine.

!o /now what happens when a strong electrolyte dissolves, lets consider A x2 y as an exampleof a strong electrolyte. )or complete ionization"

Ax2 y (s 7 9 $N (l -----W xAy7 (aq 7 y2 x- (aq

*ach mole of A x2 y dissolved generates x moles of cations and y moles of anions. )or

example, Da l generates one mole of Da7

ions and one mole of l-

ions or a total of $ molesof ions while Al $('N forms 0 ions.

'ince the colligative properties are linearly related to the number of non-volatile solute present in the solution, it can be deduced that the dilution effect of the solvent also increasesin proportion to the increase in the number of solute. &n most cases, dissociations ofelectrolytes are not complete. !hus the total number of ions in the solution is equal to the sum

) - %


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of cations, anions and the unionized salt present in the solution. !his leads to the van t 9offfactor Li, which is the ratio of the colligative properties of the ionized salt to those of theunionized form. &n case of complete ionization, the factor is equal to the sum of x and y. )orexample, the freezing point of the electrolyte is equal to"

we can wor/with very dilute solutions and still have a considerable osmotic pressure. ?or/ing at lowerconcentrations means that the limiting law is more closely followed by experiment. 2ecauseosmotic pressure is very large, it is often used to determine the molecular weights ofun/nowns rather than freezing point depression.

Ceverse osmosis is used in countries near a body of salt water such as the ocean to remove thesalts from the water. !he salt water is forced through the semipermeable membrane to removethe salts from the water. Ce-hydration of patients in hospitals is done with an isotonic (iso-osmotic solution so that the solution does not cause an abnormal osmosis to occur in thecells.

?e can calculate the ex#ec'e3 freezing point of a %.#%% molal aqueous solution of sodiumchloride using the following information"

) - #


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&an 't Hoff 3actor

!he van @t 9off factor, symbolized by the lower-case letter i , is a dimensionless constantdirectly associated with the degree of dissociation of the solute in the solvent. 'ubstances

which do not ionize in solution such as sugar have i = #, while those that will completelyionize into two ions such as Da l have i = $ and into three ions such as Jg l $, have i = andso on.

Colligati+e Properties of "ol!tions of Electrolytes

!he colligative properties of electrolyte solutions do not coincide with those of non -electrolytes. !he disparity is caused by the dissociation of electrolytes into ions in solution,which in turn increases the total number of particles in solution. !o account for this effect,Fan t 9off suggested the following modified equations"

$ 0 iP P o= (f - 0

mi1 T bb = (f - 00

mi1 T f f = (f - 05

iC'T (f - 08

where i is /nown as the van t 9off factor and is defined as follows"

solutionindissolvedinitiallyunitsformulaof numberondissociatiaftersolutionin particlesof numberactual

=i

!he factor i is greater than one and it changes with concentration. )or strong electrolytes indilute solution, the Fan t 9off factor is approximately equal to the total number of ionsyielded by a molecule of the electrolyte, thus for 9 l, Da l, etc. i= $> for Da$'N , 2a l $ etc.i= . 9owever, for wea/ electrolytes, the van t 9off factor i involves the degree of thedissociation. 'uppose one molecule of a wea/ electrolyte produces X ions when completelydissociated. &f Y is the degree of dissociation, then the number of ions actually produced is YX,and the number of molecules left undissociated is #-Y. !he number of particles produced fromone molecule is

i& 15> ) >? (f - 06

and therefore

##

=

i (f - 0:

) - $


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)or wea/ electrolytes, the formula shown in equation 0 measures approximately the degree ofdissociation or ionization of ionic solutes in solvents of low dielectric constant and the degree

of ionization of covalent solutes. &t does not measure the degree of dissociation or ionizationof strong electrolytes because the ionic concentration is large such that inter-ionic effectdominates.

Ionic "trength

!he ionic strength (Z of a solution is defined as

$$#

i i

i 4 c (f - 5%

where c i is the molar concentration and z i is the valence of the ions of type i/ !he ionicstrength of a solution may come from a single salt or a mixture of any number of salts. )or #-# electrolytes li/e Da l and IDN the ionic strength is equal to the molarity but for othertypes of electrolytes the two are not equal. )or example in a solution of Da


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F.:. ELECTROCHEMICAL CELLS#H

!he p9 of a solution is a measure of the molar concentration of hydrogen ions in the solutionand as such is a measure of the acidity or basicity of the solution. !he letters p9 stands forKpower of hydrogenK and the numerical value is defined as the negative base #% logarithm ofthe molar concentration of hydrogen ions.

pH & 5log 10@H ) A (f - 5

!he measurement of the p9 of a sample can be done by measuring the cell potential of thatsample in reference to a standard hydrogen electrode, as in the accepted procedure formeasuring standard electrode potentials . !his procedure would give a value of zero for a #Jolar solution of 9 7 ions, so that it defines the zero of the p9 scale. !he cell potential forany other value of 9 7 concentration can be obtained with the use of the 9ernst e*uation . )ora solution at $0G this gives

% cell & 50/0B 2 log 10@H ) A (f - 5or

pH & % cell =0/0B 2 (f - 50

)or this expression, a base change from the natural log to the base #% logarithm is made in the Dernst equation. &n practice, the p9 is not usually measured this way because it requireshydrogen gas at standard pressure, and the platinum electrode used in the standard hydrogenelectrode is easily fouled by the presence of other substances in the solution (*bbing .)ortunately, other practical electrode configurations can be calibrated to read the 9 7 ionconcentration. aboratory p9 meters are often made with a glass electrode consisting of asilver wire coated with silver chloride immersed in dilute hydrochloric acid. !he electrodesolution is separated from the solution to be measured by a thin glass membrane. !he

potential, which develops across that glass membrane, can be shown to be proportional to thehydrogen ion concentrations on the two surfaces. &n the measuring instrument, a cell is made

with the other electrode being a mercury-mercury chloride electrode. !he cell potential is thenlinearly proportional to the p9 and the meter can then be calibrated to read directly in p9.

) -
http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/electrode.html#c1http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/electrode.html#c3http://hyperphysics.phy-astr.gsu.edu/hbase/logm.html#c3http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/electrode.html#c1http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/electrode.html#c3http://hyperphysics.phy-astr.gsu.edu/hbase/logm.html#c3


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Figu$e -.-. ( !he p9 electrode. (C Dumerical *xamples of p9 ('hipman et al., DATE

!he usual range of p9 values encountered is between % and # , with % being the value forconcentrated hydrochloric acid (# J 9 l , 8 the value for pure water (neutral p9 , and #

being the value for concentrated sodium hydroxide (# J DaN9 . &t is possible to get a p9 of-# with #% J 9 l, but that is about a practical limit of acidity. At the other extreme, a #% Jsolution of DaN9 would have a p9 of #0.

&n pure water, the molar concentration of 9 7 ions is #%-8 J and the concentration of N9 - ionsis also #%-8 J. Actually, when loo/ed at in detail, it is more accurate to classify theconcentrations as those of \9 N]7 and \N9] -. !he product of the positive and negative ionconcentrations is #%-# in any aqueous solution at $0G .

An important example of p9 is that of the blood. &ts nominal value of p9 = 8. is regulatedvery accurately by the body. &f the p9 of the blood gets outside the range 8. 0 to 8. 0 theresults can be serious and even fatal.

&f you measure the p9 of tap water with a p9 meter, you may be surprised at how far from a p9 of 8 it is because of dissolved substances in the water. ;istilled water is necessary to get a

p9 near 8.

Jeters for p9 measurements can give precise numerical values, but approximate values can be obtained with various indicators. Ced and blue litmus paper has been one of the commonindicators. Ced litmus paper turns blue at a basic p9 of about 6, and blue litmus paper turnsred at an acid p9 of about 0. Deither changes color if the p9 is nearly neutral. itmus is anorganic compound derived from lichens.

) - 0


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An electrochemical cell, which produces external electric current flow, can be created usingany two different metals since metals differ in their tendency to lose electrons. 3inc morereadily loses electrons than copper, so placing zinc and copper metal in solutions of their saltscan cause electrons to flow through an external wire that leads from the zinc to the copper

As a zinc atom provides the electrons, it becomes a positive ion and goes into aqueoussolution, decreasing the mass of the zinc electrode. Nn the copper side, the two electronsreceived allow it to convert a copper ion from solution into an uncharged copper atom, whichdeposits on the copper electrode, increasing its mass. !he two reactions are typically written

3n(s -W 3n$7(aq 7 $e-

u $7(aq 7 $e- -W u(s

!he letters in parentheses are +ust reminders that the zinc goes from a solid (s into a watersolution (aq and vice versa for the copper. &t is typical in the language of electrochemistry torefer to these two processes as Khalf-reactionsK which occur at the two electrodes.

3n(s -W 3n$7(aq 7 $e-

!he zinc Khalf-reactionK is classified as oxidation since it loses electrons. !he terminal atwhich oxidation occurs is called the KanodeK. )or a battery, this is the negative terminal.

u $7(aq 7 $e- -W u(s

!he copper Khalf-reactionK is classified as reduction since it gains electrons. !he terminal atwhich reduction occurs is called the KcathodeK. )or a battery, this is the positive terminal.

) - 8


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)or the voltaic cell to continue producing an external electric current, there must be amovement of the sulfate ions in solution from the right to the left to balance the electron flowin the external circuit. !he metal ions themselves must be prevented from moving betweenthe electrodes, so some /ind of porous membrane or other mechanism must provide for the

selective movement of the negative ions in the electrolyte from right to left.

*nergy is required to force the electrons to move from the zinc to the copper electrode, andthe amount of energy per unit charge available from the voltaic cell is called the electromotiveforce (emf of the cell. *nergy per unit charge is expressed in volts (# volt = #

+oule4coulomb .

learly, to get energy from the cell, you must get more energy released from the oxidation ofthe zinc than it ta/es to reduce the copper. !he cell can yield a finite amount of energy fromthis process, which is limited by the amount of material available either in the electrolyte or inthe metal electrodes. )or example, if there were one mole of the sulfate ions ('N $- on the

copper side, then the process is limited to transferring two moles of electrons through theexternal circuit. !he amount of electric charge contained in a mole of electrons is called the)araday constant, and is equal to Avogadro s number times the electron charge"

)araday constant = ! & 9 ' e = 5.%$$ x #%$ x #.5%$ x #%-#: = :5, 60 oulombs4mole

!he energy yield from a voltaic cell is given by the cell voltage times the number of moles ofelectrons transferred times the )araday constant.

*lectrical energy output = n!% cell (f - 55

!he cell emf % cell may be predicted from the standard electrode potentials for the two metals.)or the zinc4copper cell under standard conditions, the calculated cell potential is #.# volts.

F.9. OPTICAL METHODS

ambert-2eer or 2ouger-2eer aw are the two simple laws underlying colorimetric analysis.!hey are based on the fact that the degree of absorption of light by an absorbing medium is afunction of the depth of the medium through which the light passes. !o put it simply, when aray of monochromatic light passes through an absorbing medium, its intensity decreasesexponentially as the length of the medium increases, i.e., expressed by the symbols below"

l k

#

# " @

%

#%=

= (f - 58

or

l k #

# @log

%#% =

(f - 56

) - 6


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2eer s law is based on the fact that the extent of absorption of light by a solution of a coloredsolute is a function of the concentration of the solution. &t states that the intensity of a ray ofmonochromatic light decreases exponentially as the concentration of the absorbing medium

increases.

ck

#

# " K

%

#%=

= (f - 5:

or ck

#

# Klog

%

#% =

(f - 8%

ombining these two laws the ambert-2eer or 2ouguer-2eer law is obtained and expressedin symbols as

kcl

# #

" =

= #%

% (f - 8#

or kcl #

# =

%

#%log (f - 8$

where" # 0 = intensity of incident light (i.e., light entering a solution # = intensity of transmitted light (i.e., light leaving a solutionc = concentration of the solutionl = length of absorbing layer

=

% # #

" = transmittance of the solution (f - 8

#%%! = percentage transmittance of the solution (f - 8

=

%#%log #

# ' = absorbance, or optical density of the solution (f -80

2eer s law applies to monochromatic light and holds true only when changes in concentrationare not accompanied by changes in degree of ionization, association, dissociation, or solvationof the solute. onversely, the degree of divergence from the law can be used as a means of

) - :


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studying these phenomena quantitatively. &t follows from the ambert-2eer law that if lightof the same intensity enters two solutions (A and 2 and ad+ustments of depths are made sothat the emerging beams are of the same intensity, then the transmission are the same, and

( ( ' ' l cl c =

F. .1. Colo$i"e'$%

olorimetry is a useful quantitative method using the concept of 2eer s law. &t is used formeasuring the quantity of a colored constituent by measuring the relative amount ofabsorption of light passing through a solution of the constituent. omparison can be madedirectly or indirectly by either visual or electrical means, between the intensity of light

passing through the solution and the intensity of light of the same wavelength passing throughthe solution (or series of solutions of the same substance, termed us the standard solutions orreference solutions.

!here are several ways where colorimetry can be applied depending on the nature of thesubstance or its capability to form colored derivatives or compounds. (# &tself is coloredthus, can be determined directly, e.g. permanganate ion. ($ Allowed to react with anothersubstance to form a colored compound, e.g. copper after reaction with ammonia to form deep

blue complex ions. ( sed to displace an equilibrium existing between two coloredcompounds and thus give a definite, determinable, intermediate shade of color to the solution,e.g., determination of the p9 value of a solution from the color produced by the addition of anindicator. !his method is limited to relatively low concentrations where it is reasonable toassume linearity of the absorbance.

F. .* S#ec'$o#ho'o"e'$%'pectrophotometry is a colometric method using filter photometer or spectrophotometer. &tmeasures the relative amount of light transmitted by an absorbing medium. &ts principaldifference lies in the fact that instead of ma/ing the measurement at the particularwavelengths passed by a color filter in the system, it ma/es the measurement at any desired,and easily controlled, range of wavelengths.

&n effect, the light from the source (e.g. incandescent lamp is divided into its spectrumcomponents by means of either a prism or a diffraction grating. !he desired region or band isselected by moving the prism or grating to appropriately control the slits in the system. !henarrower the slit, the more nearly monochromatic is the beam but the less is the intensity ofthe light. &n general, slits are as narrow as is consistent for accurate readings. !he resultinglight over any controlled narrow range of wavelengths is passed through the absorption cell,and the diminution in intensity is measured as in the case of most of the colorimetric methodsdescribed before. !he intensity of measurements can be made visually but are moreaccurately made by photoelectric devices. A curve can then be plotted to show therelationship between the wavelength and either percent extinction or transmittancy. !heresult is often characteristic of a given substance and can be used to identify the constituents.

) - %


41/56


F. .!. Pola$i"e'$%

&n light waves the vibrations are wholly at right angles to the ray direction, and howevercomplicated these vibrations are at right angles to each other. ertain crystals (e.g.,tourmaline have the property of transmitting vibrations in a single plane and absorbing theothers. !he light emerging from such crystal is called polarized light. &f the polarized light is

passed through a second crystal held at right angles to the first, all the light is absorbed.'olutions of those organic substances possessing one or more asymmetric carbon atoms (e.g.,the natural carbohydrates have the power to rotate the plane of polarized light to a certainextent. !o an absorber loo/ing toward the light source, some rotations are cloc/wise(dextrorotatory , while others are countercloc/wise (levorotatory . &f a solution of such asubstance is inserted between the above two polarizing crystals, the plane of the lightemerging from the first crystal (the polarizer is rotated to some extent and the second crystal(the analyzer has to be turned through an angle in order to cut out the light again. !his angledepends on the wavelength of the light, the temperature of the solution, the nature of the

solute, the depth of the solution, and the concentration of the solution. 2y /eeping the otherfactors constant, the angle through which the analyzer must be turned is therefore a measureof the concentration of the solution. ;ifferent substances have different characteristic angles.

F. .-. Re


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F.17. 2ATTERIES

2atteries use a chemical reaction to do wor/ on charge and produce a voltage between theiroutput terminals. !he basic element is called an electrochemical cell, which ma/es use of anoxidation4reduction reaction. An electrochemical cell, which produces an external current, iscalled a voltaic cell. Foltages generated by such cells have historically been referred to as emf(electromotive force .

F.17.1. Ca$bon4/inc 2a''e$ie&

) - $


43/56


!he carbon-zinc cell or echlanche@scell was invented in #655. &t was themost common small batterythroughout most of the $%th centuryuntil largely supplanted by al/alinecells. !he oxidation at the zincelectrode (the anode isstraightforward and similar to that inother cells li/e the ;aniel cell. !heother reactions involve JnN $, whichis contained near the carbon centerrod, and the D9 l and 3n l $ whichma/e up the bul/ of the paste

between the cathode and anode.

!he chemical reactions in this cell may be approximated by

3n(s -W 3n$7(aq 7 $e-Anode

$D9 7(aq 7 $JnN $(s 7 $e- -W Jn $N (s 7 9 $N(l 7 $D9 (aqathode

'ome of the complexities of this reaction come from the fact that the reduction of theammonium ion produces two gaseous products

$D9 7(aq 7 $e- -W $D9 (g 7 9$(g

that must be absorbed to prevent the buildup of gas pressure. !hat is accomplished with twofurther reactions in the paste electrolyte. 3inc chloride reacts with ammonia to form solidzinc ammonium chloride and manganese dioxide reacts with hydrogen to form soliddimanganese trioxide plus water (9ewitt .

3n l $(aq 7 $D9 (g -W 3n(D9 $ l$(s$JnN $(s 7 9 $(g -W Jn$N (s 7 9 $N(l

!he voltage of this cell is initially about #.0 volts, but decreases as energy is ta/en from thecell. &t also has a short shelf life and deteriorates rapidly in cold weather. Nxidation of thezinc wall eventually causes the contents to lea/ out, hence such batteries should not be left inelectric equipment for long periods. ?hile these batteries have a long history of usefulness,they are declining in application since some of their problems are overcome in al/aline

batteries.

) -


44/56


F.17.*. Al9aline D$% Cell&

Al/aline cells have solved some of the problems encountered in carbon-zinc batteries throughthe use of potassium hydroxide in place of ammonium chloride in the electrolyte.


45/56


F.17.-. Lea34Aci3 2a''e$%

!he reaction of lead and lead oxide with the sulfuric acid electrolyte produces a voltage.'upplying energy and external resistance discharge the battery.

F.11. ELECTRIC POTE@TIAL E@ER=Y


46/56


is fixed at some point in space, any other positive charge, which is brought close to it willexperience a repulsive force and will therefore have potential energy. !he potential energy ofa test charge q in the vicinity of this source charge will be"

where / is oulomb s constant.

&n electricity, it is usually more convenient to use theelectric potential energy per unit charge calledelectric potential or voltage.

F.11.1. S'an3a$3 Elec'$o3e Po'en'ial&&n an electrochemical cell, an electric potential is created between two dissimilar metals. !his

potential is a measure of the energy per unit charge, which is available from theoxidation4reduction reactions to drive the reaction. &t is customary to visualize the cellreaction in terms of two half-reactions, an oxidation half-reaction and a reduction half-reaction.

Ceduced species -W oxidized species 7 ne - Nxidation at anode

Nxidized species 7 ne - -W reduced species Ceduction at cathode

!he cell potential (often called the electromotive force or emf has a contribution from theanode, which is a measure of its ability to lose electrons - it is referred to as its Koxidation

potentialK. !he cathode has a contribution based on its ability to gain electrons - itsKreduction potentialK. !he cell potential can then be written as

* cell = oxidation potential 7 reduction potential

&f we could tabulate the oxidation and reduction potentials of all available electrodes, then wecould predict the cell potentials of voltaic cells created from any pair of electrodes. Actually,tabulating one or the other is sufficient, since the oxidation potential of a half-reaction is thenegative of the reduction potential for the reverse of that reaction. 9owever, two main hurdlesmust be overcome to establish such tabulation. !hese are

#. !he electrode potential cannot be determined in isolation, but in a reaction with someother electrodes.

$. !he electrode potential depends upon the concentrations of the substances,temperature, and pressure in the case of a gas electrode.

&n practice, the first of these hurdles is overcome by measuring the potentials with respect to astandard hydrogen electrode. &t is the nature of electric potential that the zero of the potential

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is arbitrary. &t is the difference in potential that has practical consequence. !abulating allelectrode potentials with respect to the same standard electrode provides a practical wor/ingframewor/ for a wide range of calculations and predictions. !he standard hydrogen electrodeis assigned a potential of zero volts.

!he second hurdle is overcome by choosing standard thermodynamic conditions for themeasurement of the potentials. !he standard electrode potentials are customarily determinedat solute concentrations of # Jolar, gas pressures of # atmosphere, and standard temperature,which is usually $0G . !he standard cell potential is written with a degree sign as asuperscript.

!he example below shows some of the extreme values for standard cell potentials.

athode (Ceduction9alf-Ceaction

'tandard


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Jg $7(aq 7 $e- -W Jg(s -$. 6

Al 7(aq 7 e- -W Al(s -#.55

$9 $N(l 7 $e- -W 9$(g 7 $N9 -(aq -%.6

3n $7(aq 7 $e- -W 3n(s -%.85

r 7(aq 7 e- -W r(s -%.8

)e $7(aq 7 $e- -W )e(s -%. #

d $7(aq 7 $e- -W d(s -%. %

Di$7(aq 7 $e- -W Di(s -%.$

'n $7(aq 7 $e- -W 'n(s -%.#


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N$(g 7 97(aq 7 e- -W $9$N(l #.$

r $N8$-(aq 7 # 97(aq 7 5e- -W $ r 7(aq 7 89 $N(l #.

l$(g 7 $e- -W $ l-(aq #. 5

e 7(aq 7 e- -W e 7(aq #.

JnN -(aq 7 69 7(aq 7 0e- -W Jn $7(aq 7 9$N(l #. :

9 $N$(aq 7 $9 7(aq 7 $e- -W $9$N(l #.86

o 7(aq 7 e- -W o$7(aq #.6$

' $N6$-(aq 7 $e- -W $'N $-(aq $.%#

N (g 7 $9 7(aq 7 $e- -W N$(g 7 9 $N(l $.%8

) $(g 7 $e- -W $)-(aq $.68

Calcula'ion o< Vol'aic Cell Po'en'ial&

?hen an electrochemical cell is arranged with the two half-reactions separated but connected by an electrically conducting path, a voltaic cell is created. !he maximum voltage that can be produced between the poles of the cell is determined by the standard electrode potentialsunder the standard conditions under which those potentials are defined.

onsider the historic ;aniel cell in which zinc and copper were used as electrodes. !he datafrom the table of standard electrode potentials are"

athode (Ceduction9alf-Ceaction

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&n general, a real voltaic cell will differ from the standard cell, so we need to be able to ad+ustthe calculated cell potential to account for the differences. !his can be done through theapplication of the Dernst *quation.


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Cust is then quic/ly produced by the oxidation of the precipitate.

)e(N9 $(s 7 N$(g -W $)e$N ^9 $N(s 7 $9 $N(l

Custing of unprotected iron in the presence of air and water is then inevitable because it isdriven by an electrochemical process. 9owever, other electrochemical processes can offersome protection against corrosion. Jagnesium rods can be used to protect underground steel

pipes by a process called cathodic protection.

Ca'ho3ic P$o'ec'ion Again&' Co$$o&ion

nderground steel pipes offer the strength to transport fluids at high pressures, but they arevulnerable to corrosion driven by electrochemical processes. A measure of protection can beoffered by driving a magnesium rod into the ground near the pipe and providing an electricalconnection to the pipe. 'ince magnesium has a standard potential of -$. 6 volts compared to

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-. # volts for iron, it can act as the anode of a voltaic cell with the steel pipe acting as thecathode. ?ith damp soil serving as the electrolyte, a small current can flow in the wireconnected to the pipe. !he magnesium rod will be eventually consumed by the reaction

Jg(s -W 7 Jg$7

(aq 7 $e-

while the steel pipe as the cathode will be protected by the reaction

N$(g 7 $9 $N(l 7 e- -W N9-(aq .

F.1*. ELECTROLYTIC CELLS

An electrolytic cell is an electrochemical cell in which the energy from an applied voltage isused to drive an otherwise non-spontaneous reaction. !his type of cell can be produced byapplying a reverse voltage to a voltaic cell, li/e the ;aniel cell.

&f a voltage greater than #.#% volts is applied as illustrated to a cell under standard conditions,then the reaction

u(s 7 3n $7(aq -W 3n(s 7 u$7(aq

will be driven by removing u from the copper electrode and plating zinc on the zincelectrode.

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( )atm H H #$$ $+ +

5!inhydrone Electrode . &n actual practice, the hydrogen gas electrode is seldom used. &trequires carefully prepared platinum blac/ and hydrogen gas of a high degree of purity, and itis cumbersome to operate. !he quinhydrone electrode, on the other hand, consists merely of afew crystals of an equimolar mixture of quinone and hydroquinone (made by pouring a hotsolution of ferric ammonium sulfate into a solution of ahydroquinone and recrystallizing the

precipitated crystals added directly to the solution to be titrated. A platinum wire and theregular calomel cell are used as electrodes.

$$.5$.5 $$ H 7 H C H 7 H C ++ + (quinone (hydroquinone

An'i"on% elec'$o3e . 'everal metal-metal oxide electrodes can be used in acidimetricmeasurements, but the most satisfactory one consists of metallic antimony coated with aspecial crystalline form of antimonous oxide. Although several equilibria are involved, the netequation

( ) ( ) 7 H sSb H s7Sb $-$ -$55 +++ + shows the principal relationship.

lass electrode/ !he glass electrode is the one commonly used in modern p9 meters. &tconsists of a thin-walled bulb of special glass in which is sealed an electrode (usually silver-silver chloride and 9 l solution. !he exact mechanism of this electrode is not entirely

understood, but hydrogen ions can apparently move in and out of the surface of the glass, andthe glass bulb thus seems to act li/e a semipermeable membrane between the referencesolution and the solution being tested. 2ecause of the high resistance of the glass bulb,electronic amplification of the current is necessary. &n some forms this is offset by the factsthat (# there is no contamination of the solution being tested> ($ measurements can be madeon very small volumes of solution (by using small glass electrodes > and ( the presence ofoxidizing, reducing or complexing agents does not influence the results of a p9determination.

2ecause of variations in composition of the glass used in the glass electrode, the formula fordetermining the p9 value with a given electrode is usually provided by the manufacturer, but

slight changes can occur over long periods of time due to crystallization of the glass. &t is, ofcourse, possible to calibrate the electrode at any time against a prepared solution of /nown p9value.

Jost modern portable p9 meters use glass electrodes and calomel cells in compact form andare of such construction that p9 values can be read directly from the instrument. 2y means ofsuch a meter a p9 measurement can be made very quic/ly, and the manipulative technique

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involved is very simple. !itrations can be made almost as rapidly as by a chemical indicatormethod.

Cond!ctance/ 'olutions of strong acids, strong bases, and most salts are good conductors of

the electric current and obey Nhm s law ( %- . !he resistance ( - of a solution is expressedin ohms> the conductance of a solution is the reciprocal of its resistance and is expressed inreciprocal ohms (=ohms -# , or mhos.

b400 physical chemistry

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