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Equilibrium Constant from Nernst Equation

The temperatu...

Question

The temperature coefficient of the EMF of the cell is given by:

\frac{n F}{Δ S}

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\frac{Δ S}{n F}

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\frac{Δ S}{n F T}

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- n F E

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Solution

The correct option is B $\frac{Δ S}{n F}$
For cell reaction,
$a A + b B \to c C + d D; E_{c e l l}$

$Δ G = - n F E_{c e l l}$

For a substance,
$d G = V d p - S d t$

For a chemical reaction,
$d (Δ G) = (Δ V) d p - (Δ S) d T$

At constant pressure,
dP =0

$d (Δ G) = - (Δ S) d T$
$Δ S = - \frac{d}{d T} (Δ G)$

$Δ S = n F \frac{d E_{c e l l}}{d T}$

$\frac{d E_{c e l l}}{d T}$ is the temperature coefficient of cell reaction.
Hence,

$\frac{d E_{c e l l}}{d T} = \frac{Δ S}{n F}$

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Similar questions

The temperature coefficient of the e.m.f. of cell, ${(\frac{d E}{d T})}_{p}$ is given by:

(A) $\frac{n F}{△ S}$

(B) $\frac{△ S}{n F}$

(D) $- n F E$

E = 1.02 - 4.0 \times 10^{- 5} (T - 20) - 9.0 \times 10^{- 7} (T - 20)^{2}

T

^{\circ} C

E

30^{\circ} C

- 5.0 \times 10^{- 5} V k^{- 1}

^{o}

(E_{c e l l})

Δ G = n F E_{c e l l}

Δ G

d (Δ G) = (Δ V) d p - (Δ S) d T

d (Δ G) = - (Δ S) d T

Δ G = Δ H - T Δ S

∴ Δ G = Δ H + T {(\frac{d (Δ G)}{Δ T})}_{P}

{(\frac{d E_{c e l l}}{d T})}_{p}

{(\frac{d E}{d T})}_{p}

Z n + {C u}^{2 +} ⇌ C u + {Z n}^{2 +}

Δ S^{o}

96.5

J {m o l}^{- 1} K^{- 1}

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