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Chapter 19 Electrochemistry 431 19.67 Given: overall reactions from Problem 19.65 Find: K Conceptual Plan: °C K then T = K K = 273.15 + °C = In Solution: T = 273.15 + 25 °C = 298 K then (a) = RT In K. Rearrange to solve for K. K = e = = = 5.31 X 10⁷⁵ (b) = -RT In K. Rearrange to solve for K. K = e = = = 7.77 X 10⁻¹⁰ (c) = RT K. Rearrange to solve for K. K = e = = 68,616 = 6.3 X Check: The units (none) are correct. If the voltage is positive, the reaction is spontaneous, the free energy change is negative, and the equilibrium constant is large. 19.69 Given: Ni²⁺ (aq) + Cd(s) Find: K Conceptual Plan: Write two half-cell reactions and add electrons as needed to balance the reactions. Look up half-reactions in Table 19.1. Calculate the standard cell potential by subtracting the electrode potential of the anode from the electrode potential of the cathode: E°cell = - then °C K then n, K = 273.15 + = RT In K = F Ecell Solution: Ni²⁺ (aq) + Ni(s) and Cd(s) Cd²⁺ (aq) + Look up cell potentials. Cd is oxidized, so = -0.40 V = Ni²⁺ is reduced, = -0.23 V = Then = = -0.23 V (-0.40 = +0.17 V. The overall reaction is Ni²⁺ + Ni + (aq). n = 2 and T = 273.15 + 25 °C = 298 K then = RT In K = -n F Ecell. Rearrange to solve for K. = 5.6 X 10⁵ Check: The units (none) are correct. If the voltage is positive, the reaction is spontaneous and the equilibrium con- stant is large. 19.71 Given: n = 2 and K = 25 Find: and Conceptual Plan: K, and = Solution: = RT In K = 8.314 K) In 25 = -7.97500 X 10³ J = -8.0kJ and = -n F Rearrange to solve for mole Check: The units (kJ and V) are correct. the voltage is positive and the free energy change is negative. Copyright © 2017 Pearson Education, Inc.