For the electrochemical cell, \[ \operatorname{Mg}(\mathrm{s})\left|\mathrm{Mg}^{2+}(\mathrm{aq}, 1 \mathrm{M}) \| \mathrm{Cu}^{2+}(\mathrm{aq}, 1 \mathrm{M})\right| \mathrm{Cu}(\mathrm{~s}) \] the standard emf of the cell is 2.70 V at 300K. When the concentration of \(\mathrm{Mg}^{2+}\) is changed to \(\boldsymbol{x}\) M, the cell potential changes to 2.67 V at 300 K. The value of \(\boldsymbol{x}\) is ____. (given, \(\frac{F}{R}=11500 \mathrm{~K} \mathrm{~V}^{-1}\), where \(F\) is the Faraday constant and \(R\) is the gas constant, \(\ln (10)=2.30)\)

JEE Advanced · 2018 · 20 May 2018 · Paper 1 · Redox Reactions and Electrochemistry

For the electrochemical cell,

Mg (s) Mg^{2 +} (aq, 1 M) ∥ Cu^{2 +} (aq, 1 M) Cu (s)

the standard emf of the cell is 2.70 V at 300K. When the concentration of

Mg^{2 +}

is changed to

x

M, the cell potential changes to 2.67 V at 300 K. The value of

x

is ____.

(given,

\frac{F}{R} = 11500 K V^{- 1}

, where

F

is the Faraday constant and

R

is the gas constant,

ln (10) = 2.30)

Answer: 10

The cell reaction is:

Mg (s) + Cu^{2 +} (aq) \to Mg^{2 +} (aq) + Cu (s)

Using the Nernst equation:

E_{cell} = E_{cell}^{0} - \frac{R T}{n F} ln \frac{[ Mg ^{2 +} ]}{[ Cu ^{2 +} ]}

Given:

E_{cell}^{0} = 2.70

E_{cell} = 2.67

n = 2

[Cu^{2 +}] = 1

2.67 = 2.70 - \frac{300}{2 \times 11500} ln x

0.03 = \frac{300}{23000} ln x

ln x = \frac{0.03 \times 23000}{300} = \frac{690}{300} = 2.3

Since

ln (10) = 2.30

x = 10

Answer: 10

JEE Advanced · 2018 · 20 May 2018 · Paper 1 · Numerical answer