Consider the following reactions in which…

Single correct+4 / -1Answer matches NTA’s final key

Consider the following reactions in which all the reactants and products are present in gaseous state

$2\,xy \rightleftharpoons x_2 + y_2 \qquad K_1 = 2.5 \times 10^5$

$xy + \tfrac12 z_2 \rightleftharpoons xyz \qquad K_2 = 5 \times 10^{-3}$

The value of $K_3$ for the equilibrium $\tfrac12 x_2 + \tfrac12 y_2 + \tfrac12 z_2 \rightleftharpoons xyz$ is:

Solution

Build the target from the two given reactions.

Reverse the first and halve it: $\frac12 x_2 + \frac12 y_2 \rightleftharpoons xy$ , with $K = \dfrac{1}{\sqrt{K_1}} = \dfrac{1}{500} = 2 \times 10^{-3}$ .
Add the second: $xy + \frac12 z_2 \rightleftharpoons xyz$ , $K_2 = 5 \times 10^{-3}$ .

Adding reactions multiplies their constants:

$K_3 = 2 \times 10^{-3} \times 5 \times 10^{-3} = 1.0 \times 10^{-5}.$

Answer: $1.0 \times 10^{-5}$ .

Answer checked against the official answer key. The solution is our own working.