Use standard potentials to calculate the equilibrium constant

Question

Use standard potentials to calculate the equilibrium constant for the following cell and cell reaction at 298 K:

           

Cr(s) + Zn2+(aq) → Cr2+(aq) + Zn(s)

Answer 1

There are 2 half reactions here:

1. The oxidation of Cr(s) --> Cr²⁺(aq) + 2e-
2. The reduction of Zn²⁺(aq) + 2e- --> Zn(s)

Note that this equation is already balanced, so we are ready to look up the standard potentials for each half reaction. You can usually find the standard potential values in the back of your textbook. I found these values on an open source resource online:

1. Cr²⁺ + 2e⁻ ⇌ Cr(s) –0.90 volts
2. Zn²⁺(aq) + 2e^– ⇌ Zn(s) –0.7618 volts

Now we plug the standard potentials into the formula:

E_cell = E_reduction - E_oxidation

= -0.7618 volts - (-0.90 volts)

= 0.1382 volts

Conceptually, the positive value for E_cell means that this reaction is progressing spontaneously in the direction it is written in your problem.

Now that we have E_cell, we can calculate the equilibrium constant using the Nernst equation at standard conditions: E⁰_cell = 0.0257volts/n * (lnK)

Now we can just plug in the numbers.

0.1382volts = 0.0257volts/2 * ln(K)

lnK = (2/0.0257)(0.1382)

e^lnK= e^{(2/0.0257)(0.1382)}

K = 4.69 x 10⁴

I hope this helps!

Note: Be sure that you use any values for standard potentials from your textbook and significant figures you are given for the constants in this formula to solve the problem. Because it's exponential, even small differences in the values you use can make the final answer come out pretty differently.