Tartaric acid is found in many fruits, including grapes, and is partially responsible for the dry texture of certain wines. Calculate the pH and the tartrate ion C4H4O6²⁻ concentration for a 0.250 M solution of tartaric acid, for which the acid-dissociation constants are listed in Table 16.3. Did you have to make any approximations or assumptions in your calculation?

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1. Identify the relevant acid-dissociation constants (Ka1 and Ka2) for tartaric acid from Table 16.3, as tartaric acid is a diprotic acid.
2. Write the balanced chemical equations for the stepwise dissociation of tartaric acid: \( \text{H}_2\text{C}_4\text{H}_4\text{O}_6 \rightleftharpoons \text{H}^+ + \text{HC}_4\text{H}_4\text{O}_6^- \) and \( \text{HC}_4\text{H}_4\text{O}_6^- \rightleftharpoons \text{H}^+ + \text{C}_4\text{H}_4\text{O}_6^{2-} \).
3. Set up the equilibrium expressions for each dissociation step using the acid-dissociation constants: \( K_{a1} = \frac{[\text{H}^+][\text{HC}_4\text{H}_4\text{O}_6^-]}{[\text{H}_2\text{C}_4\text{H}_4\text{O}_6]} \) and \( K_{a2} = \frac{[\text{H}^+][\text{C}_4\text{H}_4\text{O}_6^{2-}]}{[\text{HC}_4\text{H}_4\text{O}_6^-]} \).
4. Assume that the first dissociation is the primary contributor to the \([\text{H}^+]\) concentration, and use the initial concentration of tartaric acid (0.250 M) to solve for \([\text{H}^+]\) using \( K_{a1} \).
5. Use the \([\text{H}^+]\) concentration from the first dissociation to calculate the \([\text{C}_4\text{H}_4\text{O}_6^{2-}]\) concentration from the second dissociation using \( K_{a2} \), and then calculate the pH as \( \text{pH} = -\log[\text{H}^+] \).