Question

When metallic copper is shaken with a solution of a copper salt, the reaction

Cu + Cu²⁺ ⇌ 2Cu⁺ proceeds. When equilibrium is established at 298K,
[Cu²⁺]/[Cu⁺]² = 1.667 x 10⁶ M⁻¹
If the standard potential of the Cu²⁺|Cu half-cell is +0.3376 V, what is the standard potential of Cu⁺Cu half-cell?
(given 2.303 RT/F = 0.06, log 2 = 3,log 3 = 0.48)
a. -0.3732 V
b. 0.6752 V
c. 0.5242 V
d. 0.151 V

Answer 1

To find the standard potential of the Cu+|Cu half-cell, we use the Nernst equation and the given equilibrium constant. The standard potential is found to be 0.151 V. So the correct answer is option D.

Step-by-step explanation:

The question seeks to determine the standard potential of the Cu+|Cu half-cell given the equilibrium constant of the reaction Cu + Cu2+ ⇌ 2Cu+ and the standard potential of the Cu2+|Cu half-cell.

To find the standard potential of the Cu+|Cu half-cell, we use the Nernst equation:

E = E° - (0.06/n)logQ

Where E° for Cu+|Cu is what we want to find, E° for Cu2+|Cu is given as +0.3376 V, n is the number of electrons (n=1 for Cu+|Cu), and Q is the reaction quotient at equilibrium, which here is equal to 1/K, with K being the equilibrium constant for the reaction.

Since [Cu2+]/[Cu+]2 = 1.667 x 106 M−1, K for the reaction Cu+|Cu is the inverse of this value, and Q = 1/K.

Using E° for Cu2+|Cu and the given equilibrium constant, the standard potential for Cu+|Cu (E°) is calculated to be 0.151 V (choice d).