How Would You Explain The Apparent Discrepancy In The PH Of A Solution Of Sodium Acetate (CH3COONa) And Acetic Acid (CH3COOH) When The Ratio Of Na+ To CH3COO- Ions Is Varied, Considering The Fact That The Salt Is The Conjugate Base Of A Weak Acid, And Taking Into Account The Specific Ion Interactions And Activity Coefficients At Play?

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The apparent discrepancy in the pH of a sodium acetate and acetic acid solution when varying the Na⁺ to CH₃COO⁻ ion ratio arises from non-ideal solution behavior, specifically due to changes in ionic strength and activity coefficients. Here's a structured explanation:

  1. Buffer Solution and Henderson-Hasselbalch Equation:

    • The solution is a buffer where pH is governed by the ratio of acetate ions (A⁻) to acetic acid (HA), as described by the Henderson-Hasselbalch equation: pH=pKa+log⁡([A−][HA]){ \text{pH} = \text{pKa} + \log\left(\frac{[A^-]}{[HA]}\right) }
    • This equation assumes ideal behavior, where activity coefficients equal 1.

  2. Impact of Ionic Strength:

    • Varying the Na⁺ to CH₃COO⁻ ratio changes the solution's ionic strength. Higher ratios (more Na⁺ and CH₃COO⁻) increase ionic strength, reducing activity coefficients (γ < 1) due to ion interactions.
    • Lower ratios (more HA) result in lower ionic strength, with activity coefficients closer to 1.

  3. Activity Coefficients and Effective Concentrations:

    • At higher ionic strength, the effective concentration of A⁻ decreases (since γ < 1), while HA remains largely unaffected as a neutral molecule.
    • This reduces the effective [A⁻]/[HA] ratio, leading to a lower pH than expected from the Henderson-Hasselbalch equation.

  4. Hydrolysis and pH Effects:

    • High acetate concentrations promote hydrolysis, releasing OH⁻ and increasing basicity. However, under high ionic strength, OH⁻ activity is also reduced, complicating the pH outcome.
    • The combined effect of reduced A⁻ activity and altered OH⁻ activity results in a pH that deviates from ideal predictions.

  5. Conclusion:

    • The pH discrepancy stems from non-ideal ion behavior. The Henderson-Hasselbalch equation's assumption of ideal behavior fails when ionic strength varies, as activity coefficients significantly affect ion effectiveness, particularly at higher concentrations.

In summary, the pH deviation is due to changes in ionic strength altering activity coefficients, which the Henderson-Hasselbalch equation does not account for, highlighting the importance of considering real solution behavior.