'
cherniccrl principle/ revMted
Edited by Charles D. Mickey Texas A8M at Galveston Galve~ton.TX 77553
Using the Equilibrium Concept Charles D. Mickey Texas A&M University at Galveston. Galveston, TX 77553
T h e concept of equilibrium in chemical systems is one of the most useful principles in chemistry. For example, the esters of carboxylic acids are usually prepared commercially by the reaction of the acid with an alcohol or by the reaction of an acid anhydride with an alcohol CH~CO?H+ ROH
SCH:EO~R + HOH
+
(CH:ICO)~O ROH = CH:,COnR + CH:,COzH
Esterifications carried out with an alcohol, for example butanol, and acetic acid are reversible, and the equilibrium is reached a t 67% ester H*
CH:IC02H + C4HgOH $CH:ICO&IHS
+ HOH
In order to establish an equilibrium rapidly, a strong acid catalyst is employed, usually sulfuric acid or a polystyrene resin containing sulfonic acid groups. The water formed as a product is removed so that the reaction is driven to completion. The n-butyl acetate is a choice solvent for nitrocellulose lacquers. The industrial and laboratory applications of the fundamental principles of chemical equilibrium are extensive (some of theseare described later). Moreover, many of the complicated vital life processes also are controlled by these principles. Consider the reactions of hemoglobin and oxygen and hemoglobin and carbon monoxide in the body. The transport of oxveen ,~. from the lunes to the various cells of the bodv is an important biolodical pn,ce;s carr~edour by hemoglobin in the h red blood cells. Hemoelobin fHHl11combined a ~ t oxwen, while circulating through the lungs, to form oxyhemogiibin (HHb02): HHb + 0
2
= HHbOz
T h e oxybemoglobin is transported to the various regions of the body. In tissue capillaries where the oxygen concentration is low, oxyhemoglobin dissociates and releases oxygen for use in the cell's metabolic processes. Consequently, the body's oxygen budget depends on this equilibrium. Unfortunately, hemoglobin will also combine with other small molecules, such as carbon monoxide and nitric oxide, if they are present in the lungs. Carbon monoxide is toxic because it prevents oxygen transport by combining with hemoglobin about 200 times more firmly than oxygen, according to the equilibrium HHb + CO
-- HHbCO
In other words if both oxygen and carbon monoxide are present, hemoglobin preferentially combines with carbon monoxide because
,
IHHbCol = [HHbOi K = IHHbl~ LO21 In such a situation the oxveen ~ o.l vis depleted and the tis." s u.. sue cells are starved for oxygen. Death results unless nearly 56 1 Journal of Chemical Education
pure oxygen is administered to disrupt the equilibrium by displacing the molecules of carbon monoxide and making up for the oxygen deficiency. Predictlng the Position of Equillbrlum Inasmuch as the equilibrium constant (K,,)is characteristic of a particular reaction a t a given temperature, it can provide both qualitative and quantitative meaning to considerations of equilibrium ~henomena. &me of the qualitative aspects of chemical equilibrtum can be illustrated by considerinn the Haber process,. the .urinci~le industrial method for manifacturing ammonia. For the gasphase reaction, N2(el 3H2(K)= 2NH3(gl K, = pp3PRm = 5.2 X at450°C
+
N2
Hs
According to the stoichiometry, one molar volume of nitrogen reacts with three molar volumes of hydrogen to produce two molar volumes of ammonia. Obviously, four molar volumes of reactant yield two molar volumes of product, providing concomitant decreases in molar volume and pressure as the . increasing reaction proceeds from left to r i ~ h tConseauentlv, the exrerial pressure on the sysrem ail1 c a k e thereaction t a proceed to the rinht in the dirertion of the smaller molar vol"me, because a decrease in molar volume will tend to relieve the added stress (pressure). Conversely, if the stress is a decrease in pressure, the reverse reaction in which there is a volume increase will be favored, since the increase in molar volume will tend to minimize the effect of decreasing pressure. This will result in a displacement of the equilibrium to the left. Thus according to Le Chatelier's principle ( I ) , a high pressure will be favorable in the production of ammonia by the Haber process, since the hieher the oressure, the ereater the dis;lacem& of theequkbrium to the right. 1.e Chatelier's urinri~lesuaaests that when the temmrature of a system a t ec$uilihhum &hanged, the system is momentarily no longer a t equilibrium. Since the value of the equi-
-
This t e a w e is aimed as a review of basic
YW-
be sent to the feature editor. Charle, Mlckey received his BS. from Trinity University in 1957. MA from St. Mary's University in 1966, and his PhD from Texar A8M University in 1973. He taught chemistry at Alamo Heights Senior High School. San Antonio. Texar. for 13 years. He alsa hm over seven years univmity experience, having taught at San Antonio Juniw College and Texas A&M University. He is presmtly an Associate Professor of Chemistry in the Department of Marine Science at the Galvestan branch of Texas A8M. Dr. Mickey's excellence and dedication to teaching has been sighted in his achievement of the ACS James Bryant Conant Award in 1970 and the 1976-77 "Most Effective Teacher Award: Texas A8M Universitv at Galvestan."
lihrium constant is influenced bv the temperature, the eauilibrium adjusts so as to relieve the stress. The change depends on whether the reaction is endothermic or exothermic. For an endothermic process, the value of the equilibrium constant increases as the temperature increases. Conversely, for the exothermic process,the value of the equilibriumconstant decreases as the temperature increases. The synthesis of ammonia hy the Haber process is exothermic, so thevalue of the equilibrium constant decreases with increasing temperature. In other words, as the temperature increases the relative amount of ammonia a t equilihrium decreases. From a practical standpoint, if ammonia is to be produced by the Haber process, it would he desirable to have the equilibrium shifted as far to the right as possible, since this would mean a greater yield of ammonia. In order to accomplish this a high pressure and low temperature are desirable. Ammonia is actually produced industrially by the Haher process a t a pressure of several hundred atmospheres and a temperature of 4M)-500°C. This temperature is high, but it is the minimum temperature feasible for the process, since the reaction hetween nitrogen and hydrogen to attain equilibrium proceeds too slowly a t lower temperatures. If nitrogen and hydrogen gases are mixed a t 25% the reaction between them is so slow that centuries would elapse before eauilibrium would be established. However. a t 400500°C, equilibrium is established within minutes. Although the equilihrium concentrations a t the higher temperature are not as favorable as a t lower temperatures, the time required to reach equilibrium is very much reduced. In other words, it is economically feasible to obtain an 1%20% yield of ammonia in minutes by using 400-500°C temperature and 200 atm pressure and then to condense out the ammonia and recycle the unreacted nitrogen and hydrogen. Although equilibrium considerations suggest a hetter yield a t lower temperatures, it is not economically feasible to use 25°C and 200 atm pressure to attain a hetter yield, for it requires too much time. Therefore, industrially a compromise among the various factors of kinetics, equilibrium, and economics provides the method of choice.
in which direction a reaction will proceed spontaneously under a given set of circumstances ( 3 ) .Thus for Q < K,, the forward reaction (1) is spontaneous; if Q > K,,, the reverse reaction is spontaneous; and when Q = K , , the system is a t equilibrium.
Predicting.Spontaneity of a Reaction . The equilibrium constant can he used to predict the spontaneity of a particular reversible reaction, in the forward or reverse direction under specific conditions. Consider the conversion of ozone to oxygen. The equation is
BaSOq,, = Ba& + SO&,, Applying the Law of Mass Action to this system gives
20:%1,,= 3021,l
and
Quantitative Applications of the Equilibrium Constant Most reactions of weak acids, weak bases, and slightly soluble salts occur in aqueous solution, and these necessarily involve the interaction of ions. Moreover, these processes are usually reversible to some extent and, as a result equilibrium conditions orevail. These ionic equilibria conform to the general principles of equilibrium processes and follow Le Chatelier's principle ( I ) . The concepts of ionic equilibria are particularly important, not only in problems of a purely chemical nature hut also in biological systems involving the blood and other body fluids. For examole. in many. systems it is very important that not . unly the hydrogen ion cuw~,ntr:itionhe ,.:~n+ullycmrrc,llc-d hut rhnt ;I .;ource of hydroget! ioni lw at h ; i d 10 rt'plil~ethose which may be used up. ~ o l e c u l e of s weak acids act as such a hydrogen ion reservoir and their roles along with equilihrium considerations of weak bases and buffers is the subject of an earlier article in this series ( 4 ) . ~
~~~
~
. ...
but not necessarily of the same value. If the calculated value for Q is 2.54 X loiY,the system is a t equilibrium because Q = K,. If the value of Q # 2.54 X lo", the system is not a t equilibrium and by comparing the value of Q with the value of K,, one can predict the direction of spontaneous change for the chemical system that is not a t equilibrium. For example, if Q is larger than Kc, there is an excess of oxygen molecules present and the reaction proceeds spontaneouslv from rieht to left toward eauilibrium. When Q is " smaller than Kc, there is a relative excess of ozone molecules and the reaction oroceeds soontaneonslv from left to rirht to estahlish equilib;ium and maintain the-constant, K,. In general, a comparison of the actual concentration ratio (Q) with the equilibrium constant (K,,) allows one to predict
~
~
Heterogeneous Equilibrium Any equilibrium which involves some kind of boundary surface is classified as heterogeneous. The evaporation and condensation of gasoline in a closed container is a simple example of this type equilibrium. Here the gasoline vapor in the container is in contact with the liquid gasoline through its surface. Another type of heterogeneous equilihrium occurs when a relatively insoluhle salt, such as barium sulfate, is shaken with water. Ions from the crystal lattice of the solid harium sulfate pass into the water until the resulting solution becomes saturated. In the saturated solution thus formed, an equilibrium exists between the ions in solution and the ions present in the crvstal lattice of the undissolved solid. The equilihrium for barium sulfate is
The term in the denominator refers to the concentration of solid harium sulfate. Since the pure solid's effect on the equilibrium is invariable, its concentration term may be incorporated in the constant K, to give a new constant, Ksp; ~~
By measuring the concentrations of ozone and oxygen in the system a t 1727'C and substituting these values into the expression for Kc, a ratio designated by Q and called the reaction quotient is obtained (2,3).This ratio of product concentration to reactant concentration is identical to the equilihrium constant in form
~
~
in which K,, is the solubility product constant. In other words, the product of the concentrations of ions in a saturated solution of a sparingly soluble salt, such as barium sulfate, a t a given temperature is constant. Generally the solubility product of any sparingly soluble salt (M,A,) is expressed by
K, = [MI"IAlx in which K, is called the solubility product, the brackets [ 1, represent the molar concentrations, while a and x are the subscripts for cation (M) and anion (A), respectively, in the formula of the salt. This conceot. known as the solubilitv product principle full~,wsdirectly from the y r n ~ r nconvenl tions deicrihed in an earlier paper in this w r w s 0 ). Determination of the Solubility Product Constant The numerical value for K , can he calculated easily when the concentrations of the ions in a saturated solution are known. For example, in a saturated solution of barium sulfate a t 20°C, the solubility, determined by analysis is 8.89 X 10W Volume 58, Number 1, January 1981 1 57
M. Barium sulfate is completely ionized; therefore, each Bas04 unit dissolved will furnish one Ba" and one SO:- ion in solution. Consequently, the [Ba2+]= [SO:-] = 8.89 X 10W6 M. Suhstituting these concentrations in the solubility product expression, K,, = [Ba2+][SO:-]
gives, K,, = (8.89 X 10-q2 = 7.9 X lo-". In writing the soluhility product expression for a salt yielding more than one ion of any single species in solution, the concentration of that ion is raised to a power equal to its coefficient in the K,?, expression. For example, the sparingly soluble calcium fluoride dissolves until equilihrium is estah-
C a F m = Ca&
+ 2F&
and the solubility product expression is, K,y, = [Ca2+][F-12. The soluhility of calcium fluoride in water a t 20°C, as determined experimentally, is 2.92 X 10W M. Thus, the [Ca2+]= = 5.84 X 10-%. 2.92 X M a"d [F-] = (2)(2.92 X Suhstituting these concentrations in the soluhility product expression gives, K,,
= (2.93 X 10-4j)5.84 X 10-4)2= 1.0 X
S O ; ions present when either of these ions has been added in some form other than barium sulfate. The addition of an ion which is the same as one already present in the equilihrium is termed the common-ion effect. Obviously, this effect is of great value, for it provides a practical way of materially reducing the solubility of precipitates and of securing complete precipitation, a matter of considerahle importance in qualitative analysis. Another practical application of the common-iun effect is found in medical technology. Most ions of the "heavy" metals are toxic to humans in moderate concentrations, often because of their action in damaeine vital enzvme svstems. Yet. normal use harium sulfate is used for X-ray examinations of the gastrointestinal tract as an aqueous slurry of the salt. To maintain a very low concentration of the toxic Ba2+ion, suspensions of harium sulfate may contain added sulfate ion. Therefore, in the preparation of barium sulfate suspensions for radiographic studies of the gasterointestinal tract, it is feasible to add enough Epsom Salts (MgSOa7H20) to give a sulfate ion concentration of 0.01 M. The molarity of "free" Ba2+ ion in the suspension can he determined by substituting in the solubility product expression
K,, = [Ba2+][SO':-] K,-The Criterion for Predicting Precipitation and and solving for [Ba2+]; Dissolution 'I'h,. iormilticm d a prniptatv dt pvnd- 1.1, the i.mnnri..n d':,siturdted ,u.~~ti Ksp) either precipitation of the substance from solution (in which case the reverse reaction is spontaneous) or a supersaturated solution will result. If precipitation occurs, it will continue until the solution is saturated (i.e., IP = K,,). Any solution in which IP < K,, is unsaturated and is capable of dissolving more solute. Moreover, any undissolved salt will dissolve spontaneously. In other words, the forward reaction is favored until IP = Ksp. Consider the harium sulfate soluhilitv eauilibrium: when [Ba'+][SO:-] exceeds 7.9 X lo-", the sait will precipitate. In the heteroeeneous eauilibrium resultine from the dissolution of solid bahum sulfke, the [Ba2+]= [s@]. It is not necessary, however. that the concentrations of the respectivg ions have equivalent values to bring about precipitation so long as their product exceeds K,,. For example, suppose that the concentration of Ba2+ ions in a solution is known to he 2.5 X 1 0 - W . The concentration of S O : ions necessary to form a saturated solution can be determined by calculation. Suhstituting in the solubility product expression, K,, = [ ~ a z + ] [ S O f = ] 7.9 X
and solving for [SO:-] gives,
,.1 _- 7.9 _ ,,xx lo-" 10-6 - 3.16
[SO;
lo-"
Values
Once the numerical value of K., for a suarinrlv soluble compound has been determined it can be used from that time svstem in which the same ions on to describe anv. eauilibrium . in solution coexist with excess solid compound. For example, the K,, value of a compound can he used to determine the molar soluhility of the compound. The key to finding the molar soluhility lies in the recognition of the mole relationships among the undissolved compound and its aqueous ions as expressed by the chemical equation for the soluhility equilibrium ( 5 ) . In the case of a saturated solution of hismuth(II1) sulfide the solubility equilibrium is described hy Si2S:3,,l + ZBi:&]
+ 3S&
The coefficients indicate that for each mole of bismuth(II1) sulfide dissolved, two moles of Bi:'+ ion and three moles of S2ion are produced. By expressing the molar soluhility of hismuth(II1) sulfide in terms of S, it is apparent from the equation for the soluhility equilihrium that the molarities of the respective ions are given by [Bi:'+] = 2S and [p-] = 3S Suhsequently, a mathematical relationship can he established by using the conventional K,, expression of bismuth(II1) sulfide; a t 25'C
K,, = [Bi:3+]2IS'%]:i= (ZS)'(:IS):l = 1 X 10-97 X
10-'M
This concentration of S O : ions will just form a saturated will cause precipisolution, hut any [SO:-] > 3.16 X lo-" tation of BaS04. The Common-Ion Eflect
By consideration of Le Chatelier's principle one can predict that the effect of adding either Ba2+ or S O : ions to a saturated solution of harium sulfate will he to shift the equilihrium in such a way as to decrease the amount of dissolved barium sulfate. From the Law of Mass Action, which in fact is a concise and exact expression of Le Chatelier's principle, it is possible to calculate the extent to which the equilihrium is shifted and to calculate the concentrations of the Ba2+ and 5 8 / Journal of Chemical Education
Finding Solubilities from K,
= 7.9 X
from which the molar soluhility of the compound may be calculated
mole11 of hismuth(II1) In other words, a t 25°C 1.56 X sulfide will dissolve to produce a saturated solution. This is a general approach and should be used with caution because the process, as descrihed, is hased on some fundamental approximations, viz., that the sole source of ions involved is the hismuth(II1) sulfide. Furthermore, this approach does not consider the aspect of competing reactions and simultaneous equilibria or the fact that K,, is constant only for a particular temperature. It is, however, a method that pro-
vides useful approximations for a large number of practical situations involving semiquantitative work. Dissolution ol ~recipilates Inasmurh as a prec~pilateis formed when the product of ion concentrations exceeds K.,, so a precipitate will dissolve when the ion concentrations are'decreased sufficientlv. to .. eive an ion product lrss than K.,. Furthermore, any stress that lowers the rmcentrntions of ions in the solution will alter the equilibrium wlth the undissolved sulid. In order to supply more ions lo re-estsl)lish eauilihrium. more solid will pass into solution. This process will contin"e until all the solid has dissolved, providing the concentrations of ions are continuously lowered. Some physical and chemical methods that may he used to decrease the concentration of ions in solution are discussed in the sections below. ~
~
Dilution
When a saturated solution in contact with undissolved solute is diluted, the ionic concentrations are reduced and more solid oasses into solution. For example, lead poisoning is part&larly insld~ousbecause it mayresult from a gradual of lead ion tPb'+) from an unexpected source. :~ccumulat~an Symptoms may often he mistaken for those of less serious conditions until the lead concentration in the body has produced some permanent damage. Cases of slow poisoning from lead pigments in unglazed ceramic water vessels are commonplace. If the pigment chrome-yellow (PhCr04)is in contact with an aqueous system, an equilihrium is established by the dissolution of the pigment PbCrO~l.l* Pb& + CrO%,, Application of the solubility product principle indicates that if the concentration of either Ph2+ or CrOf- is decreased to such a low value that their ion product (IP) is less than K,,, then the solution is unsaturated with respect to PhCrO4 and more of the pigment dissolves. The pigment's dissolution is obviously enhanced by removal of the saturated solution and adding fresh water or merely by dilution of the saturated solution. Formation of a Weak Electrolyte
The dissolution of precipitates of magnesium and calcium carbonate, by the addition of aqueous hydrochloric acid, is common practice in some places where these minerals are deposited from hard water. Similarly, cases of gastric hyperacidity, where the stomach secretes an excess of hydrochloric acid beyond that required for normal digestive processes, is treated with various nonprescription drugs. One of these contains magnesium hydroxide for the antacid. The antacid system involves the following relationships
T h e addition of the antacid to the gastric juice forms slightly dissociated water
-
Ms(OHhw+ 2HLj M& + 2HOHrll T h e critical reaction in the system is Hi.,] + OH&,] t HOHIII for which, K,, = [H+][OH-] = 1.0 X 10-14. Since the [H+]in the gastric juice is high, the [OH-] has to decrease. This decrease in [OH-] results in a diminution of the ion product (IP) value for Mg(OH)z so that IP < K,; therefore, some Mg(OH)z must dissolve to replenish the supply of hydroxide ions. If sufficient hydrochloric acid is present, all of the magnesium hydroxide will dissolve. Formation of an Insoluble Gas
An important strategy in qualitative analysis, used to separate various metal ions takes advantage of the fact that many
metal sulfides have relatively large solubility product constants. Conseauentlv. the hvdroeen " - ions vrovided hv strone acids will low& the sulfide ion concentration enough ( h i forming the relatively insoluble hydrogen sulfide) to allow the precipitated metal sulfide to dissolve. For example, the solubility of iron(I1) sulfide is enhanced by the addition of hydrochloric acid FeS(,, + 2HLl- Fe?& + H&I The aqueous metal sulfide equilibrium involves the following relationships: FeS(,] = Fe& + S&, K, = [Fe2+][SZ-] = 4.0 X 10-19 As the sulfide ions are removed by the formation of gaseous hvdroeen sulfide. more iron(I1) sulfide dissolves. .~hd;lisaolutionof precipitated irontll) sulfide hy its reaction with srrone acid mnv Iw interpreted in terms of LeChatelier's principie. For example, consider the equilibria FeS1.j = Fe&
SLl
++
2H$le H&I T h e hvdroeen ion decreases the concentration of sulfide ion by forming the volatile hydrogen sulfide. The decrease in sulfide ion shifts the equilihrium to the right, and iron(I1) sulfide dissolves. Oxidation-Reduction
Some metal sulfides, such as HgS, CuS, and PbS, will not dissolve in a strong acid because of the extremely low concentration of sulfide ions present in their saturated solutions. In other words, they have very small K,, values. Thus, for mercury(I1) sulfide, the magnitude of [Hg2+][S2-] is greater than the value of K,, (1.6 X The dissolution of such sulfides requires that the sulfide ion concentration be decreased by oxidation to elemental sulfur with aqua regia, a mixture of nitric and hydrochloric acids. The reactions in this system can he described hy the equations HgS1,1 = Hg& + S$, H ~ &+I4Clih lHgC4Ik1 S& + 2N0&,1+ 4H?,i =~NOSIZI + 2H20111+SLI +
Formation of Complex Ions
Black-and-white photographic film is covered with a thin layer of an emulsion of silver hromide in gelatin. Exposed film is develooed hv the selective reduction of the activated silver hromide to black metallic silver using a solution of a mild reducine azent such as hvdrouuinone. Suhsequentlv, the film . is fix& Gy washing it in an aqueous solution of sodium thiosulfate (photographer's hypo), which dissolves any unreacted silver hromide that was not affected during the exposure stage. The slightly soluble silver hromide can he washed from the film by the hypo because of the formation of the stable dithiosulfatoargentate(1) complex AgBq.,+ 2S20$& = [Ag(S20:,)21?;1+ BI& Fixing with hypo serves the dual purpose of stopping development a t the right stage and of dissolving out of the emulsion unused silver hromide, which, if allowed to remain, would ultimately he converted t o free silver and ruin the picture. Literature Cited I11 Micke%C. D . . J C H e M En~c.,57.801 11980). 121 W k e s r , R. S. and Edeiaon. E.. "Chemical Principles? Harper& Raw. New Yerk. 1978. p. 414. (8) Dickersun. R. E., Gray. H. B.,and Haight, Jr., G . P.,"Chemiral Principles."3rd. Ed., BenjaminiCurnmin~sPublixhingcempany,Inc.. Menle Park. 1979, p. 148. 14) Kulh.D., J. CHEM. Enu~..S6,19(19791. 151 0'Cunnor.R.. Mickey, C. O.,snd Hasell. A.;'Solving Puihlems inCharniUry."2nd Ed., Harper & Row. New York, 19'77.p. 245.
Volume 58, Number 1. Januaiy 1981 1 59
