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${X_2} + {O_2} \rightleftharpoons 2XO\,\,\,\,\,\,\,\,\,\,\,{K_1} = 5$
${X_2} + 2{O_2} \rightleftharpoons 2X{O_2}\,\,\,\,\,\,\,\,\,\,\,{K_2} = 10$
$2 A + B \longrightarrow C + D$
| Experiment | $[ A ] / molL ^{-1}$ | $[ B ] / molL ^{-1}$ | Initial $rate/molL$ $^{-1}$ $\min ^{-1}$ |
| $I$ | $0.1$ | $0.1$ | $6.00 \times 10^{-3}$ |
| $II$ | $0.1$ | $0.2$ | $2.40 \times 10^{-2}$ |
| $III$ | $0.2$ | $0.1$ | $1.20 \times 10^{-2}$ |
| $IV$ | $X$ | $0.2$ | $7.20 \times 10^{-2}$ |
| $V$ | $0.3$ | $Y$ | $2.88 \times 10^{-1}$ |
$X$ and $Y$ in the given table are respectively :
$[ R =$ gas constant, $F =$ Faraday constant, $T =$ Temperature $]$
$(A)$ For the reaction, $M (s)+2 H ^{+}(a q) \rightarrow H _2(g)+ M ^{2+}(a q)$, if $\frac{ dE _{c o l l}}{ dT }=\frac{ R }{ F }$, then the entropy change of the reaction is $R$ (assume that entropy and internal energy changes are temperature independent).
$(B)$ The cell reaction, $Pt (s) \mid H _2(g, 1$ bar $)\left| H ^{+}(a q, 0.01 M ) \| H ^{+}(a q, 0.1 M )\right| H _2(g, 1 bar ) \mid Pt (s)$, is an entropy driven process.
$(C)$ For racemization of an optically active compound, $\Delta S >0$.
$(D)$ $\Delta S >0$, for $\left[ Ni \left( H _2 O \right)_6\right]^{2+}+3$ en $\rightarrow\left[ Ni ( en )_3\right]^{2+}+6 H _2 O$ (where en $=$ ethylenediamine).