emf of the following cell at 298 $K$ in $V$ is $x$ $\times 10^{- 2}$

$Z n (s) | Z n^{2 +} (0.1 M) | | A g^{+} (0.01 M) | A g (s)$

The value of $x$ is____. (Rounded off to the nearest integer)

Given: $E_{Z n^{2 +} / Z n}^{0} = - 0.76 V; E_{A g^{+} / A g}^{0} = + 0.80 V; \frac{2.303 R T}{F} = 0.059$

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Solution

$Z n (s) | Z n^{+ 2} (0.1 M) | | A g^{+} (0.01 M) | A g (s)$
$Z n (s) + 2 A g^{+} ⇌ 2 A g (s) + Z n^{+ 2}$

$E^{0} = 0.80 + 0.76 = 1.56;$
$Q = \frac{Z n^{2 +}}{(A g^{+})^{2}}$
$E = E^{0} - \frac{0.059}{n} l o g (Q)$

$E = 1.56 - \frac{0.059}{2} l o g [\frac{0.1}{(0.01)^{2}}]$

$E = 1.56 - \frac{0.059}{2} l o g [(10)^{3}]$

$E = 1.4715 = 147.15 \times 10^{- 2} v o l t = x \times 10^{- 2}$

$x = 147.15 \approx 147$

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