First slide

Nernst Equation

Question

For the following cell Zn / Zn²⁺// Cd²⁺/ Cd E_cell = 0.30V and E⁰_cell = 0.36V. Then the value of [Cd²⁺] / [Zn²⁺] is

Easy

Solution

Cell reaction
$Z{n_{\left( s \right)}} + Cd_{\left( {aq} \right)}^{ + 2} \rightleftharpoons Zn_{\left( {aq} \right)}^{ + 2} + C{d_{\left( s \right)}}$
Applying Nernst equation
${E_{cell}} = E_{cell}^o + \frac{{0.0591}}{2}\log \frac{{\left[ {C{d^{ + 2}}} \right]}}{{\left[ {Z{n^{ + 2}}} \right]}}$
$0.3 = 0.36 + \frac{{0.0591}}{2}\log \frac{{\left[ {C{d^{ + 2}}} \right]}}{{\left[ {Z{n^{ + 2}}} \right]}}$
$\frac{{ - 0.06 \times 2}}{{0.06}} = \log \frac{{\left[ {C{d^{ + 2}}} \right]}}{{\left[ {Z{n^{ + 2}}} \right]}}$
$\frac{{\left[ {C{d^{ + 2}}} \right]}}{{\left[ {Z{n^{ + 2}}} \right]}} = {10^{ - 2}}$

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