54. Write a relation between $∆\mathrm{G}$ and Q and define the meaning of each term and answer the following.

(a) Why a reaction proceeds forward when Q

(b) Explain the effect of increase in pressure in terms of reaction quotient Q. For the reaction, $\mathrm{CO}\left(\mathrm{g}\right)+3{\mathrm{H}}_{2}\left(\mathrm{g}\right)⇌{\mathrm{CH}}_{4}\left(\mathrm{g}\right)+{\mathrm{H}}_{2}\mathrm{O}\left(\mathrm{g}\right)$

The relation between $∆\mathrm{G}$ and Q is
(a)
If Q < K, $∆\mathrm{G}$ will be negative and the reaction proceeds in the forward reaction.
If Q = K, $∆\mathrm{G}=0$ reaction is in equilibrium and there is no net reaction.
(b) $\mathrm{CO}\left(\mathrm{g}\right)+3{\mathrm{H}}_{2}\left(\mathrm{g}\right)⇌{\mathrm{CH}}_{4}\left(\mathrm{g}\right)+{\mathrm{H}}_{2}\mathrm{O}\left(\mathrm{g}\right)$
${\mathrm{K}}_{\mathrm{c}}=\frac{\left[{\mathrm{CH}}_{4}\right]\left[{\mathrm{H}}_{2}\mathrm{O}\right]}{\left[\mathrm{CO}\right]{\left[{\mathrm{H}}_{2}\right]}^{3}}$
On increasing pressure, volume decreases. If we doubled the pressure, volume will be halved but the molar concentrations will be doubled. Then,
${\mathrm{Q}}_{\mathrm{c}}=\frac{2\left[{\mathrm{CH}}_{4}\right]·2\left[{\mathrm{H}}_{2}\mathrm{O}\right]}{2\left[\mathrm{CO}\right]{\left\{2\left[{\mathrm{H}}_{2}\right]\right\}}^{3}}=\frac{1}{4}\frac{\left[{\mathrm{CH}}_{4}\right]\left[{\mathrm{H}}_{2}\mathrm{O}\right]}{\left[\mathrm{CO}\right]{\left[{\mathrm{H}}_{2}\right]}^{3}}=\frac{1}{4}{\mathrm{K}}_{\mathrm{c}}$
Therefore, Qc is less than Kc, so Qc will tend to increase to re-establish equilibrium and the reaction will go in forward direction.