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

Name: Chemistry: A Molecular Approach
Author: Tro
ISBN: 9780134874371

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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^-.

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.

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}^\(\circ\).

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.

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.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Equilibrium Constant (K)

The equilibrium constant (K) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given chemical reaction. It is temperature-dependent and provides insight into the extent of a reaction; a large K indicates a reaction that favors products, while a small K suggests reactants are favored.

Nernst Equation

The Nernst equation relates the cell potential of an electrochemical reaction to the concentrations of the reactants and products. It is crucial for calculating the equilibrium constant from standard electrode potentials, allowing us to determine how the reaction shifts under varying conditions, including concentration and temperature.

Standard Electrode Potentials

Standard electrode potentials are measured voltages that indicate the tendency of a species to be reduced, measured under standard conditions (1 M concentration, 1 atm pressure, and 25 °C). These values are essential for calculating the overall cell potential of a reaction, which can then be used to derive the equilibrium constant.

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