JEE Advanced 2022 Paper 2 Q10 Chemistry Thermodynamics & Thermochemistry Thermodynamics Hard

JEE Advanced 2022 Paper 2 · Q10 · Thermodynamics

The correct option(s) about entropy (S) is(are) [R = gas constant, F = Faraday constant, T = Temperature]

  1. A. For the reaction, M(s) + 2H$^+$(aq) $\rightarrow$ H$_2$(g) + M$^{2+}$(aq), if $\frac{dE_{cell}}{dT} = \frac{R}{F}$, then the entropy change of the reaction is R (assume that entropy and internal energy changes are temperature independent).
  2. B. The cell reaction, Pt(s) | H$_2$(g, 1 bar) | H$^+$(aq, 0.01 M) || H$^+$(aq, 0.1 M) | H$_2$(g, 1 bar) | Pt(s), is an entropy driven process.
  3. C. For racemization of an optically active compound, $\Delta S > 0$.
  4. D. $\Delta S > 0$, for [Ni(H$_2$O)$_6$]$^{2+}$ + 3 en $\rightarrow$ [Ni(en)$_3$]$^{2+}$ + 6 H$_2$O (where en = ethylenediamine).
JEE Advanced multi-correct — pick every correct option, then check.
Reveal answer + step-by-step solution

Correct answer:B, C, D

Solution

Evaluate each option.

(A) Thermodynamic identity: $\Delta S = nF \left(\frac{dE_{cell}}{dT}\right)$. With $n = 2$ and $dE_{cell}/dT = R/F$: $\Delta S = 2F \cdot (R/F) = 2R$, NOT $R$. (A) is WRONG.

(B) Concentration cell with H$^+$ going from 0.01 M (anode) to 0.1 M (cathode). $E^\circ_{cell} = 0$. The driving force is purely the entropy of mixing (ions moving from low to high concentration is the spontaneous direction here — actually the cell drives the spontaneous transfer of H$^+$ from 0.1 M to 0.01 M, increasing the entropy of the system). $\Delta G < 0$ and $\Delta H \approx 0$ (no bond/standard-state change), so the process is entropy-driven. (B) is CORRECT.

(C) Racemisation of a pure enantiomer yields a 50:50 racemic mixture — increases configurational entropy. $\Delta S > 0$. (C) is CORRECT.

(D) Chelate effect: [Ni(H$_2$O)$_6$]$^{2+}$ + 3 en $\rightarrow$ [Ni(en)$_3$]$^{2+}$ + 6 H$_2$O. Number of particles goes 1 + 3 = 4 on left to 1 + 6 = 7 on right. More particles ⇒ $\Delta S > 0$. (D) is CORRECT.

Correct options: B, C, D.

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