Le Chatelier's Principle, Temperature Effects, and Entropy J. Arthur Campbell Harvey Mudd College, Claremont, CA 9171 1 One of the most useful methods of understanding and dealing with chemical (dynamic) equilibria is provided by Le Chatelier's Principle: A system at equilihrium, when subjected to any attempted change in temperature, concentration, andlor pressure, responds in such
a way as to moderate the change. Le Chatelier's Principle requires only a knowledge of the equation for the net reaction in order to predict shifts in eauilihria caused by concentration (including .-partial pressure) changes. In order to predict the effect of changes in temperature you need also to know whether the reaction is exothermic or endothermic-a fact not usually deducible from the equation for the net reaction. However, for many reactions a guide based on the net equation is readily available. For any closed system a t constant temperature and pressure
Table 1. Thermodynamic Data' (at 298 K) lor Some Net Reactions Commonly Used to Illustrate Le Chatelier's Prlnclple, Plus a Few Others
AP(kJlrno1) Ae(J1mol.K) 436 498 151 242 -92 -283
-137 57
-99
An
Net reaction
98
1
117 100 45 -198 -88 -120 175
1
-94
1
% -2
-% -1 1
-%
Hdg) = 2H(g) Odd = 20(9) I&) = 21(9) H&W= Hdg) + %O&) Ndg) + 3H&l = 2NHdgI COW + %O&) = COdg) C2Hdg)+ H A ) = CIHB(O) Nz04(9) = 2N02(g) S O k l ) + '1*02(g)= SO&)
AG=AH-TAS If the system is also a t equilihrium and AH= TAS So, because T is always positive, the signs of AH and AS must he the same for an equilihrium system. All exothermic processes have A S < 0, all endothermic ones have A S > 0 a t equilihrium. I t is well known that the actual value of AH usednormally in applying Le Chatelier' Principle is the standard enthalpy change (all concentrations and partial pressures unity) a t the temperature of interest, AHo. For many systems AHo is almost constant over long ranges in concentration and temperature and seldom changes sign. So the sign of the tabulated AHo value a t 298 K is normally quite satisfactory for application with Le Chatelier's P r i n c i ~ l ea t anv T. and will also usually he the same as the sign of k at equilibrium (hut often not for ions dissolved in water, as we shall see). On the other hand, A S often varies appreciably with both temperature and concentrations and may even change . sign, . esp&ially if concentrations vary greatti. But the entropy change in the standard state, ASo, is highly correlated with the net equation. The correlation for reaciions involving gases is especially easy. If An (change in number of moles of gas from reactants to products) is positive, ASois usually positive. If An < 0, then ASo < 0. So it was highly rewarding to search a laree set of texts dealine with Le Chatelier's Princinle and comkup with the data in?ahle 1.Not only was therLthe expected correlation between An and AS0. There was an equal correlation between the signs of tabulated values (at 298 K) of AS0 and AH0. Note the inclusion of Trouton's Rule. So a useful extension of Le Chatelier's Principle seems in order: An increase in temperature of a gas-phase equilibrium often shifts the equilibrium to the right if An > 0,to the left if An < 0.
If students use this extension thev can nredict both concentration, pressure, and temperatur"e effe& solely from the eauation for the net reaction hased on the correlation between an, ASo, and AHo. THISJOURNAL has had a series of articles discussing some of the limitations on the use of Le Chatelier's ~rinciple.de Heer ( I ) and Treptow ( 2 )have expanded earlier treatments such as those of Ehrenfest (3)and Epstein (4) to reiterate that i t is changes in intensive properties (temperature, pressure, concentration1 which ..resist'%hange in equilihrium~systems. Changes in thc correspondmg extensive prupcrties (enthalpy, volume, mole number) are a&ually enhanced by attempts to change that extensive property. Katz (5) points out, as do manv texts. that direct use of eauilihrium constant exnressions obviates use of Le ~hateiier'sPrinciple. ello on 16) points out that shifts in equilihrium are correlated with the change in K , not simply with the sign of AGO, most obviously so if AS0 and AHo have dittercnt signs. Mazo and Barnhard and Brice [ l o )discuss (71, Bodner (a), Fernandez-Prini (9). the application of 1.e (!hateher's Principle to the effect of temperature change on solubility. The most impurtant point emphasized on solubility is that the value of AH needed is that Volume 62 Number 3 March 1985
231
Table 2. Thermodvnamlc Data a (at 298 K ) tor Some Net Reactions Involving Gases Where the Sign of AS' 1s Not the Same as That of An0, Even Though An and ASo Agree In Sign
Prediction of signs is more apt to be valid with large values of An because this enhances the chance that the sign of AS will be correctly deduced from the sign of An. Equilibria for which An = 0 mav well have either positive or negative values of ASo(and &),"but the temperature effects on such systems will probably be relatively small for equilibrium systems where all species are present a t appreciable concentrations. Is it desirable, then, to adhere only to gas-phase reactions? As Bodner ( 8 ) points out, over 84%of the salts for which he could find data increased in solubility with increasing temperature. Two-thirds of the exceptions were salts of the oxyions: S042-, SeOq2-, S032-, As043-, and PO&-. All but four of the forty exceptions Treptow (11) found also contain oxyanions. These findings are easy to correlate with a possible sign of AS, and AH, for the saturated solution. Dispersion of the salt into the water gives AS > 0 and AH > 0, so solubility increases with risine"temnerature. At hieh solubilitv the dis. persion effects become small and, especially with iighly hydrated ions (multichareed oxvions es~eciallv).entroov of < 0 foithe hydration may dominate. hen AS < 6 and saturated solution. so soluhilitv decreases with temperature rise. With gases, thk dispersion iffed upon solution iskeversed and essentiallv. all -aases decrease in solubilitv in anv liquid or solid as temperature rises (AS and AH both > 0j. he An approach works well. .. Values of AHo (or of AH) for suhstancesdissolving in pure solvent, are hiphlv unreliable for predicting the intluence of temperature changes on solubility. For solutions, the change in saturation concentration with temperature is related to &(sat), the change in enthalpy from pure solid to saturated solution. The use of AH(sat), rather than AHo, correlates with the NaOH case of increasing solubility as T increases in spite of the large negative AH in making up solutions. AH(sat) is nositive for NaOH in HvO. So the suggested extension is to deduce the sign of the desired enthalov chanae from the equation for the net reaction (most readii;from the value of a n ) . Such deductions can fill in when true enthalpy change values are unavailable. The extension also encourages the use of entropy ideas in a practical context. ~
AW(kJ1mol)
AS"(J/ml.K)
-100 66 82 -184 14
32 -122 -75 20 -26
An
'I2 -1
-% 0 -113
Net equation
+
H202(1)= H2MI) %0&) Ndg) 20&1 = 2 N O M Ndg) '/20&) = N20Lg) Hdg) GI&) = 2HCI(g) C(s) %HA91 = 'IeCsHdg)
+ +
+
values are given far one mole of the first reacts" listed. Nde that all mere systems are tar from equlllbrivmandlor have small valms of An
for the substance dissolving into the saturated solution. Treptow (I I ) deals with this point most effectively. Goldman (12) discusses ionic equilibria. Now here are some similar caveats to my suggestion that ASo is often easier to approximate than is AHo, and has the same sign especially in gas-phase equilibria. The fact that all the examples in Table 1agree is satisfying but certainly not sufficient to be conclusive. Table 2 is included to emphasize this. An obvious difficulty is that i t is the sign of AHo that is usually desired, but it is the sign of ASo that is obtained from An. Yet it is only at equilibrium that AH = TAS and that both AH and AS must have the same sign. However, under what conditions will AS0 and AS (at equilibrium) have the same sign so we can use the extension confidently? The most obvious such condition occurs when the equilibrium condition is close to the standard state (all substances present at unit activity, both concentrations and partial pre&res~. Fortunarelv. shifting an eauilihrium i i of greatest interesr under just this liditation, thatall substancesbe present a t appreciable concentrations. However, our extension may not apply to a system where equilibrium is far from the standard state, hecause then AS f ASo. The decomposition of Hz02 in Table 2 is such an example. Moreover, the generalization will apply best if only gases are involved in the equilibrium. Condensed phase effects on AH and AS can often be estimated but not as safely as in gases. For example consider
k
Literature Cited (1) de Heel, J., J CHEM. EDUC.. 34,375 (1957).
An = 1,
AHo= -153-
kJ mol Zn'
'yy = -
21 kJ
.
mol Zn K
The hydration of ZnZ+(aq) compared to 2H+(aq) lowers ASo and more than offsets the positive entropy change from the generation of hydrogen gas, so AS" < 0 even though An > 0. Third, a t equilibrium AS would be even more negative because of the enormous partial pressure of the Hdg) making An almost useless in evaluating AS and AH.
232
Journal o f Chemical Education
(2)
Tmptow,R. S..J
CHEM E~uc.,57,417 (1980).
(3) Ehrenfnt. P..J Russ Phys. Sm., 41,347 (1SW:Z Physik. Chem, 77,227 (1911). (4) Epstein. P. S.,"Terfboakof Thermdmsmics,"John Wilw &Sons, he.. New York.
1939,Chap. XXI. (5) Katz, Lewis.J. CHEM. EDuc., 38,375 (1961). (6) Mellon,E. K., J. CHEM.EDUC.,56,380 (1979). (7) Mazo, Robert M.,and Barnhard, Ralph, J. CHEW.Emuc.,49.639 (8) Bdner, George M.,J CHEM.EDUC..~~, 117 (1980). (9) Fernsnder-Prini, R., J. CHEMEouc.,59.50 (1982).
110) Brim.L.K.,J.C~eM.EDuc,60,387 (1983). (11) rhepfow,RiehardS., J.C~eM.EoUC.61.499(19W (12) Goldman, James A,, J. CHEM.EDUC, 44,658 (1967).
(1972).
