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To determine the hydronium ion concentration \([H_3O^+]\) in an aqueous solution of a polyprotic acid, such as oxalic acid, we must consider the successive dissociation steps. For oxalic acid (H₂C₂O₄), the two dissociation steps can be represented as: 1. First dissociation: \[ \text{H}_2\text{C}_2\text{O}_4 \rightleftharpoons \text{H}^+ + \text{HC}_2\text{O}_4^- \] \( K_1 = 5.9 \times 10^{-2} \) 2. Second dissociation: \[ \text{HC}_2\text{O}_4^- \rightleftharpoons \text{H}^+ + \text{C}_2\text{O}_4^{2-} \] \( K_2 = 6.4 \times 10^{-5} \) ### Steps to solve: #### Step 1: Set up the equilibrium expressions for both dissociation steps. For the first dissociation: \[ K_1 = \frac{[H^+][HC_2O_4^-]}{[H_2C_2O_4]} = 5.9 \times 10^{-2} \] For the second dissociation: \[ K_2 = \frac{[H^+][C_2O_4^{2-}]}{[HC_2O_4^-]} = 6.4 \times 10^{-5} \] #### Step 2: Approximate the initial conditions. Let’s assume the concentration of oxalic acid is \( [\text{H}_2\text{C}_2\text{O}_4] = 1.0 \times 10^{-3} \, \text{M} \). Initially: - \( [H_2C_2O_4] = 1.0 \times 10^{-3} \, \text{M} _____ ______ _________ ___ ______ __________.
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