a. Write the formulation for the galvanic cell in which the react… - Vidyadip

Question

$a.$ Write the formulation for the galvanic cell in which the reaction $\ce{Cu(s) + 2Ag^{+}(aq) \rightarrow Cu^{2+}(a q) + 2Ag(s)}$ takes place.
Identify the cathode and the anode reactions in it.
$b.$ Write Nernst equation and calculate the emf of the following cell: $Sn ( s )\left| Sn ^{2+}(0.04 M ) \| H ^{+}(0.02 M )\right| H _2(g) \mid \operatorname{Pt}( s )$
$\left(\right.$ Given $\left.\ce{E_{S n^{2+} / S n}}=-0.14 V\right)$

✓

Answer

a. We have
$E_{\left(C u^{2+} / Cu\right)}^{\Theta}=0.34 V \text { and } E_{\left(Ag^{+} / Ag\right)}^{\Theta}=0.80 V$
Standard emf of $Cu$ is less than $Ag$ , therefore it is strong reducing agent and is oxidised.
Therefore $Cu$ acts as Anode and $Ag$ acts as Cathode.
Half cell reactions are:
At Cathode $($Reduction$):$
$\ce{2Ag^{+}(aq) + 2e^{-} \rightarrow 2Ag(s)}$
At Anode $($Oxidation$):$
$\ce{Cu(s) \rightarrow Cu^{2+}(a q) + 2e^{-}}$
$b.$ The reactions are :
At Anode:
$\ce{Sn(s) \rightarrow S n^{2+}(a q)+2 e^{-}}$
At Cathode:
$\ce{2H^{+}(a q) + 2 e^{-} \rightarrow H_2(g)}$
Full cell reaction:
$\ce{Sn(s) + 2H^{+}(a q) \rightarrow Sn^{2+}(aq) + H_2(g)}$
Standard emf of the cell is:
$E_{\text {cell }}^0=E_{H^{+} / H_2}^0-E_{S n^{2+} / S n}^0$
$=0-(-0.14) V$
$=+0.14 V$
For this reaction $n =2$ moles of electrons. Using Nernst equation,
$E_{\text {cell }}=0.14-\frac{0.0591}{2} \log \frac{\left[Sn^2+\right]}{\left[H^{+}\right]^2}$
$=0.14-\frac{0.0591}{2} \log \frac{0.04}{(0.02)^2}$
$=0.14-\frac{0.0591}{2} \log \frac{4}{100} \times \frac{100}{2} \times \frac{100}{2}$
$=0.14 V-0.0591 V$
$=0.0809 V$

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