Question

Moist air is heated to a very high temperature. If the equilibrium composition consists of \(\mathrm{H}_{2} \mathrm{O}, \mathrm{O}_{2}, \mathrm{N}_{2}, \mathrm{OH}\), \(\mathrm{H}_{2},\) and \(\mathrm{NO} .\) The number of equilibrium constant relations needed to determine the equilibrium composition of the mixture is \((a) 1\) \((b) 2\) \((c) 3\) \((d) 4\) \((e) 5\)

Short answer

Answer: (b) 2

Step-by-step solution

1. Identify possible chemical reactions

In this case, two possible reactions must be considered to produce all species as noted in the equilibrium composition. The first reaction is the dissociation of H2O to form OH and H2: \(\mathrm{H}_{2}\mathrm{O}\rightleftharpoons\mathrm{OH}+\mathrm{H}_{2}\). The second reaction is dissociation of O2 and N2 to form NO: \(\mathrm{O}_{2}+\mathrm{N}_{2}\rightleftharpoons2\mathrm{NO}\).

2. Assign the equilibrium constants for each reaction

We now associate each reaction with its respective equilibrium constant: Reaction 1: \(\mathrm{K}_{1}=\frac{[\mathrm{OH}][\mathrm{H}_{2}]}{[\mathrm{H}_{2} \mathrm{O}]}\) Reaction 2: \(\mathrm{K}_{2}=\frac{[\mathrm{NO}]^2}{[\mathrm{O}_{2}][\mathrm{N}_{2}]}\)

3. Count the number of independent relations

Now that we have defined the two equilibrium constant relations, we can identify the number of independent relations needed to determine the equilibrium composition of the mixture. In this case, we have two independent reactions and two corresponding equilibrium constants (K1 and K2). Thus, we need two equilibrium constant relations to describe the equilibrium composition.

4. Identify the correct answer

From the available options, the number of equilibrium constant relations needed matches option (b) 2. Therefore, the correct answer is \((b) 2\).