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302 Chapter 15 Chemical Equilibrium Kc = [N₂O₄] = (0.0500 = 0.513 + 0.513x 0.02565 = 0 -b ± 4ac -0.513 ± 4(4)(-0.02565) -0.513 ± V0.6735 = = 2a 2(4) 2(4) x = -0.1667 or x = 0.0385 Therefore, x = 0.0385. [N₂O₄] = 0.0500 0.0385 = 0.0115 [NO₂] = 2x = 2(0.0385) = Check: Plug the values into the equilibrium expression: Kc = 0.0115 = 0.516. 15.55 Given: = 0.20 M, [CO₂] = 0.0, Kc = 4.0 X 10³ Find: [CO₂] 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 and Solution: NiO(s) + CO(g) Ni(s) + [CO] [Cl₂] Initial 0.20 0.0 Change -x +x Equil x Q = [CO₂] [CO] = (0.20) 0 = 0 Therefore, the reaction will proceed to the right by Kc = [CO₂] [CO] = (0.20 x = 4.0 X 10³ 4.0 X 10³(0.20 - x) = x x = 0.199 [CO₂] = 0.199 M Check: Because the equilibrium constant is large, the reaction goes essentially to completion; therefore, it is rea- sonable that the concentration of the product is 0.199 M. 15.57 Given: [HC₂H₃O₂] = [H₃O⁺] = 0.0, = 0.0, = 1.8 X 10⁻⁵ Find: [HC₂H₃O₂], [H₂O⁺], 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 and Solution: HC₂H₃O₂(aq) + + [H₂O] [H₃O⁺] [C₂H₃O₂⁻] Initial 0.210 0.0 0.0 Change -x +x +x Equil 0.210 x x Q = [HC₂H₃O₂] = (0.210) 0 = 0 Q