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Question

Derive Nernst equation.


Solution

Derivation of Nerst Equation.

from thermodynamics, we know
$$|Delta G = \Delta G^{\circ} + 2.303 RT \log Q$$ ___(1)

and $$\Delta G = -nFE^{\circ}_{cell}$$ ___(2)

by (1) and (2)

$$- nFE_{cell} = - nFE^{\circ}_{cell} + 2.303 RT \log Q$$

$$E_{cell} = E^{\circ}_{cell} - \dfrac{2.303 RT}{nF} \log Q$$

Fro $$T = 298 F$$

$$F = 96,500 C$$

$$R = 8.314 J.mol^{-1} K^{-1}$$

$$E_{cell} = E_{cell}^{\circ} -\dfrac{0.059}{n} \log Q$$

Chemistry
NCERT
Standard XII

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