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334 Chapter 16 Acids and Bases (b) Given: 0.350 M = 6.0 X 10⁻², Kₐ₂ = 6.0 X 10⁻⁵ Find: [H₃O⁺], pH Conceptual Plan: is much larger than use Kₐ₁ to calculate [H₃O⁺]. Write a balanced reaction. Prepare an ICE table, represent the change with x, sum the table, determine the equilibrium values, put the equilibrium values in the equilibrium expression, and solve for x. Solution: H₂C₂O₄(aq) + + Initial 0.350 0.0 0.0 Change -x +x +x Equil 0.350 x x x = [H₂C₂O₄] = (0.350 (x)(x) x) = 6.0 X 10⁻² + 6.0 X 10⁻² 0.021 = 0 x = 0.1179 = 0.12 M [H₃O⁺] pH = log(0.1179) = 0.93 Check: The units (none) are correct. We expect pH slightly above -log((0.350 = 0.84. 16.113 Given: 0.500 M H₂SO₃ = 1.6 X 10⁻², = 6.4 X 10⁻⁸ Find: concentration of all species Conceptual Plan: is much larger than use to calculate [H₃O⁺]. Write a balanced reaction. Prepare an ICE table, represent the change with x, sum the table, determine the equilibrium values, put the equilibrium values in the equilibrium expression, and solve for x. Repeat this process by preparing a second ICE table using these values and representing the change with Solution: H₂SO₃(aq) + 11 + Initial 0.500 0.0 0.0 Change -x +x +x Equil 0.500 x x x = [H₂SO₃] = (0.500 (x)(x) x) = 1.6 X 10⁻² + 1.6 X 10⁻² 0.0080 = 0 x = 0.0818 = 0.082 M [H₃O⁺] = Use the values from reaction 1 in reaction 2. + + (aq) Initial 0.0818 0.0818 0.0 Change -y +y +y Equil 0.0818 y y = [HSO₃⁻] = (0.0818 (0.0818 + y)(y) = 6.4 X 10⁻⁸ Assume that y is small. y = 6.4 X 10⁻⁸ [H₂SO₃] = 0.500 0.0818 = 0.418 M [HSO₃⁻] = = 0.0818 = 0.082 M [SO₃²⁻] = y = 6.4 X 10⁻⁸ M [H₃O⁺] = x = 0.0818 M + 6.4 X 10⁻⁸ M = 0.082 M [OH⁻] = [H₃O⁺] Kw = 1.0 0.0818 X 10⁻¹⁴ = 1.2 X 10⁻¹³ M Check: The units (Ms) are correct. We expect to be the highest at just under 0.500 M and to be much lower than [HSO₃] and near We expect [H₃O⁺] near (0.500 X = 0.089 M. 16.115 (a) Given: [H₂SO₄] = 0.50 M = 0.012 Find: [H₃O⁺], pH Conceptual Plan: The first ionization step is strong. Use and reaction 2. Write a balanced reaction. Prepare an ICE table, represent the change with x, sum the table, determine the equilibrium values, put the equilibrium values in the equilibrium expression, and solve for x. Copyright © 2017 Pearson Education, Inc.