This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.
ScanSolve AI Answer
Step 1: Calculate the pK_a of benzoic acid. The K_a for benzoic acid (C_6H_5COOH) is 6.3 × 10^-5. pK_a = -(K_a) pK_a = -(6.3 × 10^-5) pK_a ≈ 4.201 Step 2: Use the Henderson-Hasselbalch equation to find the ratio of the conjugate base to the weak acid. The target pH is 4.25. pH = pK_a + ([C_6H_5COO^-][C_6H_5COOH]) 4.25 = 4.201 + ([C_6H_5COO^-][C_6H_5COOH]) 4.25 - 4.201 = ([C_6H_5COO^-][C_6H_5COOH]) 0.049 = ([C_6H_5COO^-][C_6H_5COOH]) [C_6H_5COO^-][C_6H_5COOH] = 10^0.049 [C_6H_5COO^-][C_6H_5COOH] ≈ 1.119 Step 3: Calculate the initial moles of sodium benzoate (C_6H_5COO^-). The volume of sodium benzoate solution is 5.0 L and its concentration is 0.05 M. Moles of C_6H_5COO^- = Concentration × Volume Moles of C_6H_5COO^- = 0.05 M × 5.0 L Moles of C_6H_5COO^- = 0.25 mol Step 4: Calculate the required moles of benzoic acid (C_6H_5COOH). Since the volume is the same for both components in the buffer, the ratio of concentrations is equal to the ratio of moles. Moles of C_6H_5COO^-Moles of C_6H_5COOH = 1.119 Moles of C_6H_5