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viii. Derive the relationship between standard cell potential and…..

**chapter 5 electrochemistry class 12 chemistry textbook solution**

### 3. Answer the following in brief

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- viii. Derive the relationship between standard cell potential and…..

viii. Derive the relationship between standard cell potential and equilibrium constant of cell reaction.

**Answer:-**

The relationship between the standard Gibbs energy change of a cell reaction and the standard cell potential is given by:
\[-\Delta G^\circ = -nF E^\circ_{\text{cell}} \quad \text{.....(1)}\]
The relationship between the standard Gibbs energy change of a chemical reaction and its equilibrium constant, as given in thermodynamics, is:
\[\Delta G^\circ = -RT \ln K \quad \text{.....(2)}\]
Combining equations (1) and (2), we have:
\[-nF E^\circ_{\text{cell}} = -RT \ln K\]
Therefore,
\[E^\circ_{\text{cell}} = \frac{RT}{nF} \ln K\]
\[= \frac{2.303RT}{nF} \log_{10} K\]
\[= 0.0592 \frac{1}{n} \log_{10} K\]
at 25°C.

**chapter 5 elctrochemistry textbook solution page 118**