A Daniell cell Zn | Zn^2+ (1.0 M) || Cu^2+ (0.02 M) | Cu is operated at 350 K. Assume E deg_cell = 1.10 V does not change with temperature. Take R = 8.314 J mol^-1 K^-1, F = 96500 C mol^-1, ln 50 = 3.912. The cell EMF is closest to

JEE Advanced levelSingle correct optionDifficulty 3 of 3ec082

A Daniell cell $Zn ∣ Zn X^{2 +} (1.0 M) ∣∣ Cu X^{2 +} (0.02 M) ∣ Cu$ is operated at 350 K. Assume $E_{cell}^{\circ} = 1.10 V$ does not change with temperature. Take $R = 8.314 J mo l^{- 1} K^{- 1}$ , $F = 96500 C mo l^{- 1}$ , $ln 50 = 3.912$ . The cell EMF is closest to

At 350 K the factor

0.0591 V

(valid at 298 K) cannot be used; use

E = E^{\circ} - \frac{RT}{n F} ln Q

with

n = 2

and

Q = [Zn X^{2 +}] / [Cu X^{2 +}] = 1.0/0.02 = 50

\frac{RT}{2 F} = \frac{8.314 \times 350}{2 \times 96500} = 0.01508 V

, so

E = 1.10 - 0.01508 \times 3.912 = 1.10 - 0.0590 = 1.041 V

. Using 0.0591 V at 298 K would give 1.050 V, which is the common error.