Question

K for the reaction $X_2+Y_2\rightleftharpoons 2XY$ is 100.

K for this reaction $XY\rightleftharpoons \frac{1}{2}{X}_2+\frac{1}{2}{Y}_2$ would be:

• A. $\frac{1}{10}$
• B. $\frac{1}{100}$
• C. $100$
• D. $\frac{1}{2}$

Answer 1

The correct option is A $\frac{1}{10}$

K for the reaction $X_2+Y_2\rightleftharpoons 2XY$ is 100 K for this reaction $XY\rightleftharpoons \frac{1}{2}{X}_2+\frac{1}{2}{Y}_2$ would be $\frac{1}{\sqrt{K}}=\frac{1}{\sqrt{100}}=\frac{1}{10}$
Note first reaction is reversed and divided by 2 to obtain second reaction.
Hence, $K=\frac{[XY{]}^2}{\left[X_2\right]\left[Y_2\right]}$
$K^{\prime }=\frac{\left[X_2{]}^{1/2}\right[Y_2{]}^{1/2}}{\left[XY\right]}=\frac{1}{\sqrt{\frac{[XY{]}^2}{\left[X_2\right]\left[Y_2\right]}}}=\frac{1}{\sqrt{K}}$