Influences of Temperature and Pressure on Chemical Equilibrium in Nonideal Systems Huang Xijun and Yan Xiuping Taizhou Teachers College, Linhai. Zhejang Province, China The van't Hoff equation, d in K V d T = A , K I R P , describes the temperature dependence of the standard equilibrium constant, Ke, where A,HC,is the standard molar enthalpy for the reaction. The equlhhrium shift with change in temperature a t constant pressure has been described as follows in many textbooks. For an exothermic reaction (A?H,f < 0), K+ decreases and the equilibrium shifts from right to left with increase in temperature; but for an endothermic (A,HE > O), KO increases, and the equilibrium shifts from left to right with increase in temperature. Consider the following reactions with &.,HZ < 0 [A,H,f data from the literature' in which the standard state pressure is lo5 Pa]. FeC13.6H~O(s)+ aq + Fe3+(aq,sat) + 3Cl-(aq, sat) + 6H20(1)
+
+
+
MnS01.4HzO(s) aq == MnZ+(aq, sat) SO:- (aq, sat) 4Hz0(1) According t o the van't Hoff equation, KO decreases with increase in temperature. Thus, the solubility of these substances appears to decrease with increase in temperature. In fact, the solubility of these substances increases with temp e r a t ~ r e Therefore, .~ for these nonideal systems, the van't Hoff equation cannot be used alone to predict the equilibrium shift direction. For the general chemical reaction
where the stoichiometric coefficient of component B, VB,is negative for reactant and positive for product; K0 = IIB(aB)%,where aB is the equilibrium activity of component B at standard state pressure. Let K, be the saturated solution molality quotient that has the same form as KO, and let K,, he a combination of activity coefficients having the same
' Kaye. G. W. C.; Laby. T.H., Ed. Tables of Physical and Chemlcal
Constants and Some Mathematical Functions. 15th ed.; Longman. 1986;pp 269-281. Dean, J. A., Ed. Lange's Handbook of Chemishy, 9th ed.: Handbook Publishers Inc.: Sandusky, OH, 1956: pp 1094-1107.
form as K-under the same conditions as K+. Therefore, Ke = K , K,;. In nonideal systems, K,, depends on temperature and molalities. and KO depends only on temperature, so K , is not only temperature dependen< hut also molalities dependent. Thus, the function of K, as temperature and molality is complex. Increasing K+ does not necessarily mean increasing K, and shifting the equilibrium to the right; similarly, decreasing KOdoes not necessarily mean decreasing K,,, and shifting the equilibrium to the left. The present work is concerned with the temperature or pressure dependenceof K, and the useof these dependences in predicting the influence of temperature or pressure on the equilihrium shift direction in nonideal systems. In order to predict the influence of temperature or pressure on the equilibrium shift direction, we should find out how K, changes with temperature or pressure. Since the van't Hoff equation tells us correctly how K 0 changes with temperature, we must look a t the temperature dependence of K., to obtain the temperature dependence of K,. If the general reaction reaches equilibrium at temperature T and a t the standard state pressure P, then
.
where A?G,(O is the molar Gibbs function change for the reaction, G is the Gibbs function, ( i s the extent of reaction, piq is the chemical potential of component B a t equilihrium, and the superscript "eq" denotes equilibrium state. The chan e of excess molar Gihbs function a t equilibrium, h? A,G,(E), can be expressed as
where the superscripts n and i denote nonideal systems and ideal systems, respectively. Since
where ~ , ~ E a AJfe,9 n d are the excess molar enthalpy change and the molar enthalpy change for the reaction at equilibrium, respectively, and
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April 1991
295
Comparison between Evaluated Valuer and Literature Vatuas of the Solublllty tor Some Substances Solubilitye Substance
Temperature
'C
A&,," kJ/ml
..
Literature ValueZ
Evaluated Value
Relative Deviation %
-~ ~
'me
value is expressed in grams of anhydrous subslance mat Is soluble in 100 g d water. b l l w soiubilify valves for KC1 at 25 'C and for MnSO.. 4H,O at 17 'Care obtained by interplation t m ~lubilhyvalueobetween 10 'C and 30 OC in lhe literat~re.~
we have
Similarly, the pressure dependence of Ifm having the same form as K, a t any pressure can be obtained. Since
where A , V ~and A,Ve,9 are the excess molar volume change and the molar volume change for the reaction at equilibrium, respectively; A,.V, is the molar volume change for the reaction a t the state in which all factors agree with the standard state except pressure; and
where K'has the same form as Keand Ifa,has the same form as K., a t any pressure, we can get
Equation 8 (allowing A,H2 to be a function of temperature) tells us how K , changes with temperature and allows evaluation of K , a t an arbitrary temperature T2 from its known value a t temperature TI. Assuming that A,% is constant over the reasonably small temperature interval, the
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Journal of Chemical Education
values of the solubility for some substances a t different temperature have been evaluated from A,.He2 data3, and the known values of solubility a t certain temperature (25 OC for KC1 and 17 OC for MnS04. 4Hz0). A comparison between the evaluated values and the literature values has been made in the table. As can be seen from the table, the evaluated values are in good agreement with the literature values in view of temperature dependence of A,H9,4 to some extent. According to eq 8, for the reaction with A,.He,4 > 0, for examnle. reaction 1 ( A J P = 44.5 kJlmol) and reaction 2 (A,+$ = 10.0 k~/m0i)3:: ?I increases, a n d t h e equilibrium shifts from left to rieht as temoerature rises. Therefore, for > 0, the solubility of reaction 1 and reacGon 2 with A,= corresponding substance increases with temperature. Since A,He,4 is a function of temperature, pressure, and molalitv, the sien orland value of A X 2 may change with these f;lrtors. Thus, the influence of i&upGaturebn the equilihrium shift direction may he different over different ranges of temperature, pressure, and molaliFy. For example, for the reaction with A,H,4 > 0 a t lower temperatures, if A,C;q < 0 (A,C;q, is the molar heat capacity change for the reaction a t equlllbrium a t constant pressure), 4 H e 2 may become negative a t higher temperatures. Thus, the equilibriumshifts fromleft to right a t lower temperatures but shifts from right to left a t higher temperatures as temperature rises.
Treptow. R. S. J. Chem. Educ. 1984. 61,499402.
