What is the copper(II)-ion concentration at 25°C in the cell Zn(s)| Zn²⁺(1.0 M)|| Cu²⁺(aq)| Cu(s)if the measured cell potential is 1.08 V? The standard cell potential is 1.10 V.

Question

Quizplus · Accepted Answer

Using the Nernst equation: 
E = E° - (RT/nF)ln(Q)
where E° is the standard cell potential, R is the gas constant, T is the temperature in Kelvin, n is the number of electrons transferred, F is Faraday's constant, and Q is the reaction quotient.
First, we need to determine the reaction and the corresponding value of Q:
Zn(s) + Cu2+(aq) -> Zn2+(aq) + Cu(s)
Q = [Zn2+]/[Cu2+]
We know that [Zn2+] = 1.0 M (from the given cell diagram) and we need to find [Cu2+]. 
Substitute the given values into the Nernst equation: 
1.08 V = 1.10 V - (RT/2F)ln([Zn2+]/[Cu2+])
Solving for [Cu2+]:
[Cu2+] = [Zn2+]/exp[(1.10 V - 1.08 V)*2F/RT] 
[Cu2+] = 0.21 M (rounded to two significant figures) 
Therefore, the correct answer is C.

What Is the Copper(II)-Ion Concentration at 25°C in the Cell