Which of the following statement(s) is/are incorrect for a reaction, ${\mathrm{A}}_2\left(\mathrm{g}\right)+\mathrm{B}\left(\mathrm{g}\right)\to {\mathrm{A}}_2\mathrm{B}\left(\mathrm{g}\right)$ assuming ideal gas behaviour if ${\mathrm{\Delta H}}_{\mathrm{R}}^{\circ }=-100$ kcal/mole and ${\mathrm{\Delta S}}_{\mathrm{R}}^{\circ }=-\frac{1}{3}$kcal/mole K at 3 temperature T = 300 K.

$\begin{array}{l}{\mathrm{A}}_2\left(\mathrm{g}\right)+\mathrm{B}\left(\mathrm{g}\right)⟶{\mathrm{A}}_2\mathrm{B}\left(\mathrm{g}\right)\\ {\mathrm{\Delta H}}_{\mathrm{R}}^{\circ }=-100 \mathrm{kcal}/\mathrm{mole}\\ {\mathrm{\Delta S}}_{\mathrm{R}}^{\circ }=-\frac{1}{3}\mathrm{kcal}/\mathrm{mole}-\mathrm{K}\\ \mathrm{T}=300 \mathrm{K}\end{array}$

(a)  At 1 bar 

$\begin{array}{l}\mathrm{\Delta }{G}^{\circ }=\mathrm{\Delta }{H}^{\circ }-T\mathrm{\Delta }{S}^{\circ }\\ =-100-\left(300\times -\frac{1}{3}\right)\end{array}\begin{array}{r} \\ \end{array}$

${\mathrm{\Delta G}}^{\circ }=0$ reaction is at equilibrium.
(b) ${\mathrm{\Delta G}}^{\circ }=0$ no non-PV work can be obtained from the reaction.
(c) In rigid container V= constant

$\begin{array}{l}{\mathrm{\Delta H}}^{\circ }={\mathrm{\Delta U}}^{\circ }+{\mathrm{\Delta n}}_{\mathrm{g}}\mathrm{RT}\\ -100\mathrm{kcal}={\mathrm{\Delta U}}^{\circ }+\left[-\frac{1\times 2\times 300}{1000}\right]\\ {\mathrm{\Delta U}}^{\circ }=-99.4\mathrm{kcal}\\ {\mathrm{\Delta A}}^{\circ }=\mathrm{\Delta U}-{\mathrm{T\Delta S}}^{\circ }\end{array}$

${\mathrm{\Delta A}}^{\circ }=+$ ve reaction is non-spontaneous.
(d) ${\mathrm{\Delta U}}^{\circ }=-99.4 \mathrm{kcal}$ reaction will be exothermic.
 Not correct (c,d)