For the electrochemical cell, $M g (s) | M g^{2 +} (a q . 1 M) | | C u^{2 +} (a q, 1 M) | C u (s)$ the standard emf of the cell is $2.70$ V at $300$ K. When the concentration of $M g^{2 +}$ 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, $l n (10) = 2.30$ )

Open in App

Solution

Cell reaction,

$M g (s) + C u^{2 +} (a q) \to M g^{2 +} (a q) + C u (s)$

$E_{c e l l}^{o} = 2.70$ ; $E_{C e l l} = 2.67$ ; $M g^{2 +} = x M$ ; $C u^{2 +} = 1 M$

$E_{c e l l} = E_{c e l l}^{o} - \frac{R T}{n F} l n x$

$2.67 = 2.70 - \frac{R T}{2 F} l n x$

$- 0.03 = - \frac{R \times 300}{2 F} \times l n x$

$l n x = \frac{0.03 \times 2}{300} \times \frac{F}{R}$

$l n x = \frac{0.03 \times 2 \times 11500}{300 \times 1}$

$l n x = 2.30 = l n (10)$

$∴ x = 10$ .

Suggest Corrections

Similar questions

Q. If the standard electrode potential constant for a cell is

2 V

300 K

the equilibrium constant (K) for the reaction:

Z n (s) + C u^{2 +} (a q) ⇌ Z n^{2 +} (a q) + C u (s)

300 K

is approximately.

(R = 8 J K^{- 1} m o l^{- 1}, F = 96000 C m o l^{- 1})

Q. The cell reaction of a cell is:

M g (s) + c u^{2 +} (a q) ⇌ C u (s) + M g^{2 +} (a q)

If the standard reduction potentials of

M g

and

C u

are

- 2.37

and

+ 0.34 V

respectively. The emf of the cell is:

Q. For the following electrochemical cell at 298 K,

P t (s) | H_{2} (g, 1 b a r) | H^{+} (a q, 1 M) | | M^{4 +} (a q), M^{2 +} (a q) | P t (s)

E_{c e l l} = 0.092 V w h e n \frac{[M^{2 +} + (a q)]}{[M^{4 +} (a q)]} = 10^{x}

G i v e n : E_{M^{4 +} / M^{2 +}}^{\circ} = 0.151 V; 2.303 \frac{R T}{F} = 0.059 V

The value of x is

Q. For the following electrochemical cell at 298 K,

P t (s) | H_{2} (g, 1 b a r) | H^{+} (a q, 1 M) | | M^{4 +} (a q), M^{2 +} (a q) | P t (s) E_{c e l l} = 0.092 V w h e n \frac{[M^{2 +} (a q)]}{[M^{4 +} (a q)]} = 10^{x} G i v e n : E_{M^{4 +} / M^{2 +}}^{0} = 0.151 V; 2.303 \frac{R T}{F} = 0.059 V

The value of x is:

For a cell, the cell reaction is $M g (s) + C u^{2 +} (a q) \to M g^{2 +} (a q) + C u (s)$ . If the S.R.P. values of $M g$ and $C u$ are $- 2.37 V$ and $+ 0.34 V$ respectively, the EMF of the cell is:

Join BYJU'S Learning Program

Cell reaction,Mg(s)+Cu2+(aq)→Mg2+(aq)+Cu(s)Eocell=2.70; ECell=2.67; Mg2+=x M; Cu2+=1 MEcell=Eocell−RTnFlnx2.67=2.70−RT2Flnx−0.03=−R×3002F×lnxlnx=0.03×2300×FRlnx=0.03×2×11500300×1lnx=2.30=ln(10)∴ x=10.