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Question #44096

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The Question

During the titration of a weak monoprotic acid $\ce{HA}$ with a strong base $\ce{MOH}$ at $298\text{ K}$ , the equivalence point is reached. The standard textbook approximation for the pH at the equivalence point is given by $pH_{ideal} = \frac{1}{2}(pK_w + pK_a + \log C)$ , where $C$ is the concentration of the salt $\ce{MA}$ , and $pK_w$ , $pK_a$ are thermodynamic constants.

However, in real solutions, the finite ionic strength ( $I$ ) affects the activity coefficients ( $\gamma$ ) of the species. Assuming the activity coefficient of the neutral un-ionized acid $\gamma_{HA} \approx 1$ , and for the univalent ions $\gamma_{A^-} < 1$ and $\gamma_{OH^-} < 1$ .

Which of the following expressions correctly relates the true thermodynamic pH ( $pH_{true} = -\log a_{H^+}$ ) to $pH_{ideal}$ , and what is the physical consequence on the equivalence point?

Options

A.
$pH_{true} = pH_{ideal} + \frac{1}{2}\log(\gamma_{A^-}\gamma_{OH^-})$ ; the true pH is lower than predicted, meaning the solution is less alkaline than expected.
B.
$pH_{true} = pH_{ideal} - \frac{1}{2}\log\left(\frac{\gamma_{A^-}}{\gamma_{OH^-}}\right)$ ; the true pH is higher than predicted, meaning the solution is more alkaline than expected.
C.
$pH_{true} = pH_{ideal} + \frac{1}{2}\log\left(\frac{\gamma_{OH^-}}{\gamma_{A^-}}\right)$ ; the true pH remains approximately equal to $pH_{ideal}$ because the activity coefficients cancel out.
D.
$pH_{true} = pH_{ideal} - \frac{1}{2}\log(\gamma_{A^-}\gamma_{OH^-})$ ; the true pH is higher than predicted, requiring an indicator with a higher $pK_{In}$ .

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Numerical_Precision

Improve calculation stamina and avoid rounding errors in high-stakes competitive examinations.

Concepts Behind This Question

Salt Hydrolysis Logic|Titration Indicators|Concentration Units Dependency

Why This Question Is Tricky

Common Mistakes

This question tests the 'Approximation Trap' in ionic equilibrium.

Students often memorize the ideal pH formula and assume it holds universally.

A common misconception (Option C) is that because $\gamma_{A^-}$ and $\gamma_{OH^-}$ are both univalent ions and roughly equal, they cancel out in the concentration-based $K_h$ expression, leaving the pH unchanged.

However, while the concentration of $\ce{OH^-}$ might remain close to the ideal value, pH is strictly defined by the activity of $\ce{H^+}$ .

The conversion from $[OH^-]$ to $a_{H^+}$ introduces the product of the activity coefficients ( $\gamma_{A^-}\gamma_{OH^-}$ ), which strictly lowers the true thermodynamic pH of the solution.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Equilibrium - Class 11 Part 1
Concept	Salt Hydrolysis Logic
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free