Question

Determine $K_p$ for the following reactions:
(a) $CO\left(g\right)+H_{2}O\left(g\right)\rightleftharpoons C{O}_2\left(g\right)+H_2\left(g\right);K_c=23.2$ at $600K$
(b) $N_2{O}_4\left(g\right)\rightleftharpoons 2N{O}_2\left(g\right);K_c=4.62\times {10}^{-3}M$ at $298K$
(c) $2S{O}_2\left(g\right)+O_2\left(g\right)\rightleftharpoons 2{SO}_3\left(g\right);K_c=2.8\times {10}^2{M}^{-1}$ at $1000K$

Answer 1

We have $K_P=K_C{\left(RT\right)}^{△n}$

Now, $\left(a\right)$ $Co\left(g\right)+H_{2}O\left(g\right)\rightleftharpoons {CO}_2\left(g\right)+H_2\left(g\right);K_C=23.2$

$\therefore △n=1+1-1-1=0$

$\Rightarrow K_P=K_C{\left(RT\right)}^0$

$\Rightarrow K_P=K_C=23.2$

$\left(b\right)$ $N_2{O}_4\left(g\right)\rightleftharpoons 2{NO}_2\left(g\right);K_C=4.62\times {10}^{-3}$

$\therefore n=2-1=1(T=298K)$

$\Rightarrow K_P=K_C{\left(RT\right)}^1$

$\Rightarrow K_P=4.62\times {10}^{-3}\times 0.0821+298$

$=0.113$

$\left(c\right)$ $2{SO}_2\left(g\right)+O_2\left(g\right)\rightleftharpoons 2{SO}_3\left(g\right);K_C=2.8\times {10}^2$

$\therefore △n=2-2-1=-1(T=1000K)$

$\Rightarrow K_P=K_C{\left(RT\right)}^{-1}$

$\Rightarrow K_P=\frac{K_C}{RT}=\frac{2.8\times {10}^2}{0.0821\times {10}^3}=3.4$