The Foundations of Chemistry

Reversing an equation is the same as

multiplying all coefficients by 1. This

reverses the roles of “reactants” and

“products.”

We see that Kcis the square root of Kc.

Kc1/2means the square root of Kc.

17-3 Variation of Kcwith the Form of the Balanced Equation 715

VARIATION OF KcWITH THE FORM OF THE BALANCED

EQUATION

The value of Kcdepends on the form of the balanced equation for the reaction. We wrote
the equation for the reaction of SO 2 and O 2 to form SO 3 , and its equilibrium constant
expression as

2SO 2 (g)O 2 (g) 34 2SO 3 (g) and Kc0.15

Suppose we write the equation for the same reaction in reverse. The equation and its equi-
librium constant, written this way, are

2SO 3 (g) 34 2SO 2 (g)O 2 (g) and Kc

K

1

c

 6.7

We see that Kc, the equilibrium constant for the reaction written in reverse, is the recip-

rocalof Kc, the equilibrium constant for the original reaction.
If the equation for the reaction were written as

SO 2 (g)^12 O 2 (g) 34 SO 3 (g) KcKc1/20.39

If an equationfor a reaction is multipliedby any factor, n,then the original value of Kc
is raised to the nth power. Thus, we must always write the balanced chemical equation to
accompany the value of Kcfor a chemical reaction.

EXAMPLE 17-3 Variation of the Form of Kc

You are given the following reaction and its equilibrium constant at a given temperature.

2HBr(g)Cl 2 (g) 34 2HCl(g)Br 2 (g) Kc4.0 104

Write the expression for, and calculate the numerical value of, the equilibrium constant for
each of the following at the same temperature.

(a) 4HBr(g)2Cl 2 (g) 34 4HCl(g)2Br 2 (g)

(b) HBr(g)^12 Cl 2 (g) 34 HCl(g)^12 Br 2 (g)

Plan

We recall the definition of the equilibrium constant. For the original equation,

Kc4.0 104

Solution

(a) The original equation has been multiplied by 2, so Kcmust be squared.

Kc Kc(Kc)^2 (4.0 104 )^2  1.6 109

(b) The original equation has been multiplied by ^12 (divided by 2), so Kcmust be raised to the
^12 power. The value of Kcis the square root of the original Kcvalue.

[HCl]^4 [Br 2 ]^2



[HBr]^4 [Cl 2 ]^2

[HCl]^2 [Br 2 ]



[HBr]^2 [Cl 2 ]

[SO 3 ]



[SO 2 ][O 2 ]1/2

1



0.15

[SO 2 ]^2 [O 2 ]



[SO 3 ]^2

[SO 3 ]^2



[SO 2 ]^2 [O 2 ]

17-3

See the Saunders Interactive

General Chemistry CD-ROM,

Screen 16.7, Manipulating Equilibrium

Expressions.

A coefficient of 2 ^1 refers to ^12 of a mole,

not^12 of a molecule.