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304 Chapter 15 Chemical Equilibrium -b ± 4ac (-1) = 2a 2(1) x = 0.618 or x = 1.618 Therefore, x = 0.618. [B] = = x = 0.618 = 0.62 M [A] = 1.0 - 0.618 = 0.382 = 0.38 M Check: Plug the values into the equilibrium expression: = (0.62)(0.62) (0.38) = 1.01 = 1.0, which is the equilibrium constant; so the values are correct. (b) Given: [A] = [B] = = 0.0, Kc = 0.010 Find: [A], [B], at equilibrium Conceptual Plan: Prepare an ICE table, calculate Q, compare Q and Kc, predict the direction of the reaction, represent the change with x, sum the table, determine the equilibrium values, put the equilibrium values in the equilibrium expression, and solve for x. Determine [A], [B], and Solution: A(g) B(g) + [A] [B] Initial 1.0 0.0 0.0 Change -x +x +x Equil 1.0 x x x Q = [B][C] [A] = (1.0) 0 = 0 Therefore, the reaction will proceed to the right by x. = [B][C] [A] = (1.0 (x)(x) x) = 0.010 + 0.010x - 0.010 = 0 -b ± 4ac -(0.010) 4(1)(-0.010) = 2a 2(1) x = 0.09512 or x = -0.1051 Therefore, x = 0.09512. [B] = = x = 0.09512 = 0.095 M [A] = 1.0 - 0.09512 = 0.90488 = 0.90 M Check: Plug the values into the equilibrium expression: (0.095)(0.095) Kc = = 0.01003 = 0.010, which is the equilibrium constant; the values are correct. (0.90) (c) Given: [A] = 1.0 M, [B] = [C] = 0.0, Kc = 1.0 X 10⁻⁵ Find: [A], [B], at equilibrium Conceptual Plan: Prepare an ICE table, calculate Q, compare Q and Kc, predict the direction of the reaction, represent the change with x, sum the table, determine the equilibrium values, put the equilibrium values in the equilibrium expression, and solve for x. Determine [A], [B], and Solution: A(g) B(g) + [A] [B] [C] Initial 1.0 0.0 0.0 Change -x +x +x Equil 1.0 x x x Q = [B][C] [A] = (1.0) 0 = 0 Therefore, the reaction will proceed to the right by Kc = [B][C] [A] = (1.0 (x)(x) = 1.0 X 10⁻⁵ Copyright © 2017 Pearson Education, Inc.