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Electrochemical Cells, Galvanic Cells

For the elect...

Question

For the electrochemical cell:
$M g (s) | M g^{2 +} (a q, 1 M) | | C u^{2 +}) (a q, 1 M) | C u (s)$ the standard emf of the cell is 2.70 V at 300 K. When the concentration of $M g^{2 +}$ is changed to 'x' M, the cell potential changes to 2.67 V at 300 K. The value of 'x' is.

(given, $\frac{F}{R} = 11500 K V^{- 1}$ , where $F$ is the Faraday constant and $R$ is the gas constant, ln(10)=2.30)

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Solution

Case I:
$E_{c e l l} = E_{c e l l}^{0} - \frac{R T}{2 F} l n \frac{1}{1}$
=2.7 -0 = 2.7 V
Case II:
$E_{c e l l} = E_{c e l l}^{0} - \frac{R T}{2 F} l n \frac{x}{1}$
$2.67 = 2.7 - \frac{R \times 300}{2 F} l n x$
$- 0.03 = - \frac{R \times 300}{2 F} l n x$
$l n x = \frac{0.03 \times 2 \times F}{300 \times R} = 2.3$
x = 10

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