JEE Advanced · 2010 · 11 Apr 2010 · Paper 1 · Redox Reactions and Electrochemistry

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The concentration of potassium ions inside a biological cell is at least twenty times higher than the outside. The resulting potential difference across the cell is important in several processes such as transmission of nerve impulses and maintaining the ion balance. A simple model for such a concentration cell involving a metal M is:

M (s) ∣ M^{+} (aq; 0.05

molar

) ∣∣ M^{+} (aq; 1

molar

) ∣ M (s)

For the above electrolytic cell the magnitude of the cell potential

∣ E_{cell} ∣ = 70 mV

.

For the above cell

(A) $E_{cell} < 0; Δ G > 0$
(B) $E_{cell} > 0; Δ G < 0$ ✓ Correct
(C) $E_{cell} < 0; Δ G^{0} > 0$
(D) $E_{cell} > 0; Δ G^{0} < 0$

Answer: (B)

Solution

The cell reaction is:

M^{+} (1 M) \to M^{+} (0.05 M)

Using the Nernst equation:

E_{cell} = E_{cell}^{\circ} - \frac{2.303 R T}{F} lo g \frac{[ M ^{+} ] _{dilute}}{[ M ^{+} ] _{conc}}

Since

E_{cell}^{\circ} = 0

for a concentration cell:

E_{cell} = - \frac{2.303 R T}{F} lo g \frac{0.05}{1} = - \frac{2.303 R T}{F} lo g (0.05) > 0

Since

E_{cell} > 0

, the reaction is spontaneous, and

Δ G = - n F E_{cell} < 0

JEE Advanced · 2010 · 11 Apr 2010 · Paper 1 · Single correct option

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JEE Advanced · 2010 · 11 Apr 2010 · Paper 1 · Redox Reactions and Electrochemistry

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