Physical Chemistry Third Edition

338 7 Chemical Equilibrium

a system will respond to a stress placed upon it by reacting in the direction that lessens

the effect of that stress on intensive properties of the system.^4

The transfer of heat to a system is an example of an applied stress. From Eq. (7.6-4)

we see that the equilibrium constant for an endothermic reaction (∆H>0) has a

positive temperature derivative. The stress causes the reaction to shift toward the right,

producing more products and absorbing part of the heat put into the system. For a given

amount of heat, the temperature of the system rises by a smaller amount than it would

if the reaction were somehow prevented from shifting its reaction equilibrium. The

heat added to the system is the stress, and the moderation of the temperature rise is the

lessening of the effect of the stress referred to in the statement of the principle. For an

exothermic reaction (∆H<0) transfer of heat to the system will cause the equilibrium

to shift toward the left, again causing the temperature of the system to rise by a smaller

amount than if the reaction were frozen.

The principle of Le Châtelier applies to other cases, including the shift in the equilib-

rium of a gas-phase reaction produced by changing the volume of a system at constant

temperature. Let us write an equilibrium expression for a gaseous reaction in terms of

the mole fractions. The mole fraction of substanceiis given for an ideal gas mixture

by Dalton’s law:

xi

Pi

Ptot

(7.6-12)

wherePtotis the total pressure. Equation (7.2-2) for the equilibrium constant of a

gaseous reaction becomes

K

∏c

i 1

(

xi

Ptot

P◦

)νi



(

Ptot

P◦

)∆ν∏c

i 1

xνii



(

Ptot

P◦

)∆ν

Kx (7.6-13)

where∆νis the sum of the stoichiometric coefficients:

∆ν

∑c

i 1

νi (7.6-14)

equal to the net change in the number of moles of gas in the system if 1 mol of reaction

occurs. It is positive if the products consist of a greater number of moles of gas than

the reactants. The quantityKxis not a true equilibrium constant, since it depends on

pressure:

Kx

(

Ptot

P◦

)−∆v

K (7.6-15)

If the products consist of fewer moles of gas than the reactants and if the volume of the

system is decreased (increasing the pressure),Kxwill increase and the mole fractions

of the products will increase. If the products consist of more moles of gas than the

reactants, the mole fractions of the reactants will increase. In either case, a reduction of

(^4) See J. A. Campbell,J. Chem. Educ., 62 , 231 (1985) for an interesting rule for predicting the direction
of the shift in a reaction equilibrium produced by a change in temperature if the sign of∆H
◦
is not known,
and also for references to articles discussing the correct statement of the principle of Le Chˆatelier.