The correct option(s) about entropy (S) is(are) [ R = gas constant,...

(A) $M\left(s\right) + 2{H}^{+}\left(aq\right) \to {H}_{2}\left(g\right) + {M}^{2 +}\left(aq\right)$

if $\dfrac{{dE}_{cell}}{dT} = \dfrac{R}{F}$

$\DeltaS = nF\dfrac{dE}{dT} = 2F\left(\dfrac{R}{F}\right) = 2R$

(B) ${E}_{cell} = \dfrac{- 2 . 303RT}{F}log\dfrac{0 . 01}{0 . 1} = \dfrac{2 . 303RT}{F}$

$\dfrac{{dE}_{cell}}{dT} = \dfrac{2 . 303R}{F}$

$∴ \DeltaS = nF\dfrac{dE}{dT} > 0$

It is an entropy driven process.

(C) It is correct

Racemisation is a thermodynamically favourable method, and it proceeds spontaneously if a suitable pathway is accessible for the interconversion of the enantiomers.

During racemisation of optically active compound, disorderness increases and hence, entropy increases.

(D) For ${\left[Ni{\left({H}_{2}O\right)}_{6}\right]}^{2 +} + 3en \to {\left[Ni{\left(en\right)}_{3}\right]}^{+ 3} + 6{H}_{2}O$
Entropy increases when bidentate ligands replace monodentate ligands due to increase in the number of molecules on the product side.

Hence, (B, C, D) are correct.