Consider an electrochemical cell with a copper electrode immersed in 1.0 M Cu²⁺ and a silver electrode immersed in 1.0 M Ag⁺.
If [Cu²⁺]₀ is 0.0038 M and [Ag⁺]₀ is 0.27 M, calculate E.

Question

Consider an electrochemical cell with a copper electrode immersed in 1.0 M Cu²⁺ and a silver electrode immersed in 1.0 M Ag⁺. If [Cu²⁺]₀ is 0.0038 M and [Ag⁺]₀ is 0.27 M, calculate E.

Quizplus · Accepted Answer

To calculate the cell potential, we need to use the equation:
Ecell = Ecathode - Eanode

The reduction half-reaction occurring at the cathode is:

Cu2+(aq) + 2e- -> Cu(s)

The reduction half-reaction occurring at the anode is:

Ag(s) -> Ag+(aq) + e-

The standard reduction potential for the Cu2+/Cu half-reaction is +0.34 V, and for the Ag+/Ag half-reaction is +0.80 V.

Using the Nernst equation, the cell potential at non-standard conditions can be calculated as:

Ecell = E°cell - (RT/nF) ln(Q)

where E°cell is the standard cell potential, R is the gas constant, T is the temperature in Kelvin, n is the number of electrons transferred in the balanced chemical equation, F is the Faraday constant, and Q is the reaction quotient.

For this problem, n = 2 because 2 electrons are transferred in the balanced half-reaction at the cathode. The temperature is not given, so we can assume it to be standard (298 K).

At the cathode, Cu2+ ions are reduced to Cu metal:
Cu2+(aq) + 2e- -> Cu(s)
This has an electrode potential of +0.34 V at standard conditions.
At a concentration of [Cu2+] = 0.0038 M:
Cu2+(aq) + 2e- -> Cu(s) E = E° - (RT/2F)ln([Cu2+]) = 0.34 - (0.0257/2)ln(0.0038) = 0.30 V

At the anode, the Ag metal oxidizes:
Ag(s) -> Ag+(aq) + e-
This has an electrode potential of -0.80 V at standard conditions.
At a concentration of [Ag+] = 0.27 M:
Ag(s) -> Ag+(aq) + e- E= E° - (RT/F)ln([Ag+]) = -0.80 - (0.0257/1)ln(0.27) = -0.59 V

Plugging these values into the first equation, we get:

Ecell = Ecathode - Eanode = 0.30 - (-0.59) = 0.89 V

However, this is the cell potential at standard conditions, and the question is asking for the cell potential at non-standard conditions.

Plugging the concentrations into the Nernst equation gives:

Ecell = E°cell - (RT/nF) ln(Q) 
Ecell = 0.34 - (0.0257/2) ln([Cu2+]/[Ag+])
Ecell = 0.34 - (0.0257/2) ln(0.0038/0.27)
Ecell = 0.50 V

Therefore, the answer is B, 0.50 V.

Consider an Electrochemical Cell with a Copper Electrode Immersed in 1.0