20. For the reaction ${\mathrm{N}}_{2}{\mathrm{O}}_{4}\left(\mathrm{g}\right)⇌2{\mathrm{NO}}_{2}\left(\mathrm{g}\right)$, the value of K is 50 to 400 K and 1700 at 500 K. Which of the following option(s) is/are correct?

(a) The reaction is endothermic

(b) The reaction is exothermic

(c) If ${\mathrm{NO}}_{2}\left(\mathrm{g}\right)$ and ${\mathrm{N}}_{2}{\mathrm{O}}_{4}\left(\mathrm{g}\right)$ are mixed at 400 K at partial pressures 20 bar and 2 bar respectively, more ${\mathrm{N}}_{2}{\mathrm{O}}_{4}\left(\mathrm{g}\right)$ will be formed.

(d) The entropy of the system increases

(a, c, d)
For the reaction ${\mathrm{N}}_{2}{\mathrm{O}}_{4}\left(\mathrm{g}\right)⇌2{\mathrm{NO}}_{2}\left(\mathrm{g}\right)$
At 400 K, K=50
At 500 K, K=1700
(a) As the value of K increase with increase of temperature and $\mathrm{K}=\frac{{\mathrm{K}}_{\mathrm{f}}}{{\mathrm{K}}_{\mathrm{b}}}$, this means that Kf increases, i.e., forward reaction is favoured. Hence, reaction is endothermic.
(c) Since, number of moles of gaseous products are greater than the number of moles of gaseous reactants. Thus, higher pressure favours the backward reaction, i.e., more ${\mathrm{N}}_{2}{\mathrm{O}}_{4}\left(\mathrm{g}\right)$ will be obtained, If Pproduct>Preactant.
(d) As reaction is accompanied by increase in the number of moles, entropy increases.