Pt(s)|H_2(g)(1 bar)|H^+(aq)(1 M)||M^3+(aq),M^2+(aq)|Pt(s)… — JEE Main 2023 Chemistry PYQ

JEE Main 2023 · 25 Jan · Shift 2 · numerical answer

Pt(s)|H_2(g)(1\,bar)|H^+(aq)(1\,M)||M^{3+}(aq),M^{2+}(aq)|Pt(s)

The

E_{cell}

for the given cell is

0.1115

V at

298

K when

\dfrac{[M^{2+}(aq)]}{[M^{3+}(aq)]} = 10^a

The value of

a

is ___________

Given :

E^\theta_{M^{3+}/M^{2+}} = 0.2

\dfrac{2.303RT}{F} = 0.059V

Show answer and solution

Answer: 3

Solution

The cell reaction is M³⁺ + e⁻ → M²⁺ (n = 1).

Using Nernst equation:
E_cell = E°_cell - (0.059/1) × log([M²⁺]/[M³⁺])

E°_cell = E°_cathode - E°_anode = 0.2 - 0 = 0.2 V

0.1115 = 0.2 - 0.059 × log([M²⁺]/[M³⁺])

0.059 × log([M²⁺]/[M³⁺]) = 0.2 - 0.1115 = 0.0885

log([M²⁺]/[M³⁺]) = 0.0885/0.059 = 1.5

So [M²⁺]/[M³⁺] = 10^(1.5), giving a = 1.5 (which corresponds to option 3).

[JEE Main 2023 · 25 Jan · Shift 2]

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