Calculate the equilibrium constant for the reaction between Ni2+(aq) and Cd(s) at 25 °C.

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1. Identify the half-reactions involved in the redox process. For the reaction between Ni^{2+}(aq) and Cd(s), the half-reactions are: Ni^{2+}(aq) + 2e^- \rightarrow Ni(s) and Cd(s) \rightarrow Cd^{2+}(aq) + 2e^-.
2. Look up the standard reduction potentials (E^\circ) for each half-reaction from a standard reduction potential table. The standard reduction potential for Ni^{2+}/Ni is typically around -0.25 V, and for Cd^{2+}/Cd, it is around -0.40 V.
3. Calculate the standard cell potential (E_{cell}^\circ) for the overall reaction by subtracting the anode potential from the cathode potential: E_{cell}^\circ = E_{cathode}^\circ - E_{anode}^\circ.
4. Use the Nernst equation to relate the standard cell potential to the equilibrium constant (K). The equation is: E_{cell}^\circ = \frac{RT}{nF} \ln K, where R is the gas constant, T is the temperature in Kelvin, n is the number of moles of electrons transferred, and F is Faraday's constant.
5. Rearrange the Nernst equation to solve for the equilibrium constant (K): K = e^{\frac{nFE_{cell}^\circ}{RT}}. Substitute the known values (R, T, n, F, and E_{cell}^\circ) to find K.