Equilibrium Constant

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GRE Subject Test: Chemistry › Equilibrium Constant

Questions 1 - 1

$2NO_{(g)}+2H_{2 (g)}\leftrightharpoons N_{2 (g)}+2H_{2}O_{(g)}$

In the above reaction, by what factor would the reaction quotient change if the concentration of $\small NO$ were doubled?

$\frac{1}4$

$\frac{1}{2}$

No change

Explanation

For a general chemical equation $\alpha A + \beta B \rightleftharpoons \gamma C + \delta D$ , where A, B, C, and D are elements and the Greek letters are their coefficients, we have the reaction quotient equation:

$Q=\frac{[C]^{\gamma}[D]^{\delta}}{[A]^{\alpha}[B]^{\beta}}$

We can find the reaction quotient equation for our reaction by substituting the variables.

$2NO_{(g)}+2H_{2 (g)}\leftrightharpoons N_{2 (g)}+2H_{2}O_{(g)}$

$Q=\frac{[N_{2}][H_{2}O]^{2}}{[NO]^{2}{[H_{2}]}^{2}}$

Notice that the concentration of $\small NO$ is in the denominator and is squared, so doubling the concentration of $\small NO$ changes the reaction quotient by a factor of one-fourth.

$Q_2=\frac{[N_{2}][H_{2}O]^{2}}{[2NO]^{2}{[H_{2}]}^{2}}=\frac{[N_{2}][H_{2}O]^{2}}{4[NO]^{2}{[H_{2}]}^{2}}$

$Q_2=\frac{1}{4}K_c$