The correct option(s) about entropy (S) is(are)

[$\mathrm{R}=$ gas constant, $\mathrm{F}=$ Faraday constant, $\mathrm{T}=$ Temperature]

• A

  For the reaction, $\mathrm{M}\left(\mathrm{s}\right)+2{\mathrm{H}}^{+}\left(\mathrm{aq}\right)\to {\mathrm{H}}_2\left(\mathrm{g}\right)+{\mathrm{M}}^{2+}\left(\mathrm{aq}\right)$, if $\frac{{\mathrm{dE}}_{\mathrm{cell} }}{\mathrm{dT}}=\frac{\mathrm{R}}{\mathrm{F}}$ then the entropy change of the reaction is $\mathrm{R}$ (assume that entropy and internal energy changes are temperature independent).
• Correct answer
  B

  The cell reaction, $\mathrm{Pt}\left(s\right)\mid {\mathrm{H}}_2\left(\mathrm{g},1 \mathrm{bar}\right)\left|{\mathrm{H}}^{+}\left(\mathrm{aq},0.01\mathrm{M}\right)\Vert {\mathrm{H}}^{+}\left(\mathrm{aq},0.1\mathrm{M}\right)\right|{\mathrm{H}}_2\left(\mathrm{g},1\mathrm{bar}\right)\mid \mathrm{Pt}\left(\mathrm{s}\right)$ , is an entropy driven process.
• Correct answer
  C

  For racemization of an optically active compound, $\Delta \mathrm{S}>0$
• Correct answer
  D

  \(\Delta \mathrm{S}>0\), for \(\left[\mathrm{Ni}\left(\mathrm{H}_2 \mathrm{O}\right) 6\right]^{2+}+3 \mathrm{en} \rightarrow[\mathrm{Ni}(\mathrm{en})_{3}]^{2+}+6 \mathrm{H}_2 \mathrm{O}\) (where en \(=\) ethylenediamine)

Hence, the correct answer is options: 'B', 'C', 'D'.