The standard equilibrium constant of the reaction2Cu+(aq)⇌Cu2+(aq)+Cu(s)is about [Given: E∘Cu+∣Cu=0.53V and E∘Cu2+∣Cu=0.34V - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

A
$2.76 \times 10^{5}$
B
$2.76 \times 10^{6}$
C
$2.76 \times 10^{7}$
D
$2.76 \times 10^{8}$

Solution:

Consider the cell

$Cu (s) |{Cu}^{2 +} (1 M)| |{Cu}^{+} (1 M)| Cu$

The cell reaction is

$\begin{array}{ll} RHC {Cu}^{+} + e^{-} \to Cu \\ L H C Cu \to {Cu}^{2 +} + 2 e^{-} \\ Cell reaction 2 {Cu}^{+} \to Cu + {Cu}^{2 +} \\ Cell potential E_{cell}^{\circ} = E^{\circ} {Cu}^{+} ∣ {Cu}^{-} - E_{{Cu}^{2 +} ∣ Cu}^{\circ} \end{array}$

Thus $E_{cell}^{\circ} = E_{{Cu}^{+} ∣ Cu}^{\circ} - E_{{Cu}^{2} ∣ Cu}^{\circ} = 0.53 V - 0.34 V = 0.19 V$

$Finally - n F E_{cell}^{\circ} = - R T \ln K_{eq}^{\circ} or \log K_{eq}^{\circ} = \frac{n E_{cell}^{\circ}}{2.303 (R T / F)}$

or $\log K_{eq}^{\circ} = \frac{(2) (0.19 V)}{(0.059 V)} = 6.44$

$K_{eq}^{\circ} = 10^{6.44} = 2.76 \times 10^{6}$

The standard equilibrium constant of the reaction $2 {Cu}^{+} (aq) ⇌ {Cu}^{2 +} (aq) + Cu (s)$
is about [Given: $E^{\circ} ({Cu}^{+} ∣ Cu) = 0.53 V and E^{\circ} ({Cu}^{2 +} ∣ Cu) = 0.34 V]$

Solution:

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