What pH is needed for a buffer to achieve a Mg2+ concentration of 3.0 × 10^-2 M in equilibrium with solid magnesium oxalate?

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Identify the relevant chemical equilibrium: The dissolution of magnesium oxalate, MgC2O4, in water can be represented by the equation: MgC2O4(s) \rightleftharpoons Mg^{2+}(aq) + C2O4^{2-}(aq).

Use the solubility product constant (K_sp) for magnesium oxalate: The K_sp expression is K_{sp} = [Mg^{2+}][C2O4^{2-}]. You will need the K_sp value for magnesium oxalate from a reference source.

Relate the pH to the concentration of oxalate ions: The oxalate ion (C2O4^{2-}) is the conjugate base of oxalic acid (H2C2O4). The pH will affect the concentration of C2O4^{2-} through the acid dissociation equilibria of oxalic acid.

Set up the equilibrium expression: Substitute the given [Mg^{2+}] = 3.0 \times 10^{-2} M into the K_sp expression to solve for [C2O4^{2-}].

Determine the pH: Use the relationship between [C2O4^{2-}] and the pH, considering the dissociation constants (K_a1 and K_a2) of oxalic acid, to find the pH that results in the calculated [C2O4^{2-}].

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Buffer Solutions

A buffer solution is a system that resists changes in pH upon the addition of small amounts of acid or base. It typically consists of a weak acid and its conjugate base or a weak base and its conjugate acid. Understanding how buffers work is essential for maintaining the desired pH in chemical reactions, especially when dealing with metal ions like Mg2+.

Solubility Product Constant (Ksp)

The solubility product constant (Ksp) is an equilibrium constant that applies to the solubility of sparingly soluble ionic compounds. It is defined as the product of the molar concentrations of the ions, each raised to the power of their coefficients in the balanced equation. For magnesium oxalate, knowing its Ksp allows us to determine the concentration of Mg2+ ions in equilibrium with the solid phase.

pH and Metal Ion Solubility

The pH of a solution can significantly affect the solubility of metal ions. In the case of magnesium oxalate, the pH influences the equilibrium between the solid and dissolved forms of the compound. A higher pH can lead to decreased solubility of certain metal oxalates, thus affecting the concentration of Mg2+ ions in solution, which is crucial for achieving the desired equilibrium concentration.

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