Question

The partial pressure of $C{H}_{3}OH\left(g\right),CO\left(g\right)$ and $H_2\left(g\right)$ in equilibrium mixture for the reaction, $CO\left(g\right)+2H_2\left(g\right)\rightleftharpoons C{H}_{3}OH\left(g\right)$ are 2.0, 1.0 and 0.1 atm respectively at $427$. The value of $K_p$ for the decomposition of $C{H}_{3}OH$ to $CO$ and $H_2$ is:

• A. ${10}^{2}atm$
• B. $2\times {10}^2{atm}^{-1}$
• C. $50{atm}^2$
• D. $5\times {10}^{-3}{atm}^2$

Answer 1

Answer: (D)

$5\times {10}^{-3}{atm}^2$

Reaction:

$CO\left(g\right)+2H_2\left(g\right)\rightleftharpoons C{H}_{3}OH\left(g\right)$

$K_p=\frac{P_{C{H}_{3}OH}}{P_{CO}\times P_{H_2}^2}=\frac{2}{1\times {\left(0.1\right)}^2}=200{atm}^{-2}$

$K_p$ for reverse reaction is $=\frac{1}{K_p}=\frac{1}{200}=5\times {10}^{-3}{atm}^2$