## Chapter 13

## Q. 13.4

**Judging Whether a Mixture Is at Equilibrium **

The following pictures represent mixtures of A molecules (red spheres) and B molecules (blue spheres), which interconvert according to the equation A \rightleftharpoons B. If mixture (1) is at equilibrium, which of the other mixtures are also at equilibrium? Explain.

**STRATEGY **

The equilibrium constant for the reaction is given by K_c = [B]/[A], where the concentrations are equilibrium concentrations in units of mol/L. Since the equilibrium-constant expression has the same number of concentration terms in the numerator and denominator, the volume cancels and K_c = (moles of B)/(moles of A). Because the number of moles is directly proportional to the number of molecules, K_c = (molecules of B)/(molecules of A) in the equilibrium mixture, mixture (1). To determine whether the other mixtures are at equilibrium, count the number of molecules and compare the B/A ratio in mixtures (2)–(4) with the B/A ratio in the equilibrium mixture.

## Step-by-Step

## Verified Solution

For mixture (1), K_{\mathrm{c}}=[\mathrm{B}] /[\mathrm{A}]=2 / 6=1 / 3

For mixture (2), [\mathrm{B}] /[\mathrm{A}]=4 / 4=1 \neq K_c .

For mixture (3), [\mathrm{B}] /[\mathrm{A}]=3 / 9=1 / 3=K_{\mathrm{c}}

For mixture (4), [\mathrm{B}] /[\mathrm{A}]=9 / 3=3 \neq K_{\mathrm{c}}

Mixture (3) is at equilibrium, but mixtures (2) and (4) are not at equilibrium because their equilibrium-constant expressions [B]/[A] do not equal K_c.