Question

For the reaction, $H_2\left(g\right)+C{O}_2\left(g\right)\rightleftharpoons C{O}_2\left(g\right)+H_{2}O\left(g\right)$
If the initial concentration of $\left[H_2\right]=\left[C{O}_2\right]$ and $xmol/L$ of hydrogen is consumed at equilibrium the correct expression of $K_p$ is:

Answer 1

$H_2\left(g\right)+{CO}_2\left(g\right)\rightleftharpoons CO\left(g\right)+H_{2}O\left(g\right)$

$\Delta n=$ (number of moles of products) $-$ (no. of moles of reactants)

$=2-2=0$

$\Rightarrow$ $K_p=K_c{\left(RT\right)}^{\Delta n}\Rightarrow K_p=K_c$ ;

$H_2+{CO}_2\rightleftharpoons CO+H_{2}O$

$a$ $a$ $O$ $O$

$a(1-x)$ $a(1-x)$ $ax$ $ax$

$K_c=\frac{\left[CO\right]\left[H_{2}O\right]}{\left[H_2\right]\left[{CO}_2\right]}=\frac{\left(ax\right)\left(ax\right)}{a(1-x).a(1-x)}=\frac{x^2}{{(1-x)}^2}$