If for the cell reaction, Zn + Cu 2+ leftharpoons Cu + Zn 2+ entropy change Δ S° is 96.5 J mol -1 K -1, then temperature coefficient of the emf of a cell is

Question

If for the cell reaction, Zn + Cu 2+ leftharpoons Cu + Zn 2+ entropy change Δ S° is 96.5 J mol -1 K -1, then temperature coefficient of the emf of a cell is (A) 5× 10-4 VK-1 (B) 1 × 10-3 VK-1 (C) 2× 10-3 VK-1 (D) 9.65× 10-4 VK-1

Tardigrade Admin · Accepted Answer

Δ G=Δ H-n F T((d E/d T))p and Δ G=Δ T-T Δ S ∴ (Δ S/n F)=((d E/d T))p or (96.5/2 × 96500)=((d F/d T))p ∴ ((d E text cell /d T))p=(1 × 10-3/2) =5 × 10-4 VK -1

Q. If for the cell reaction,
$Z n + C u^{2 +} ⇌ C u + Z n^{2 +}$
entropy change $Δ S^{\circ}$ is $96.5 J m o l^{- 1} K^{- 1}$ , then temperature coefficient of the emf of a cell is

$5 \times 1 0^{- 4} V K^{- 1}$

$1 \times 1 0^{- 3} V K^{- 1}$

$2 \times 1 0^{- 3} V K^{- 1}$

$9.65 \times 1 0^{- 4} V K^{- 1}$

$Δ G = Δ H - n FT (\frac{d E}{d T})_{p}$
and $Δ G = Δ T - T Δ S$
$∴ \frac{Δ S}{n F} = (\frac{d E}{d T})_{p}$
or $\frac{96.5}{2 \times 96500} = (\frac{d F}{d T})_{p}$
$∴ (\frac{d E _{cell}}{d T})_{p} = \frac{1 \times 1 0 ^{- 3}}{2}$
$= 5 \times 1 0^{- 4} V K^{- 1}$

Q. If for the cell reaction, Zn+Cu2+⇌Cu+Zn2+ entropy change ΔS∘ is 96.5Jmol−1K−1, then temperature coefficient of the emf of a cell is

5×10−4VK−1

1×10−3VK−1

2×10−3VK−1

9.65×10−4VK−1