What is the mathematical relationship between $pH$ and $pK_a$ at the half-equivalence point of a weak acid titration?

At the half-equivalence point, $pH = pK_a$. This occurs because the concentration of the weak acid $[HA]$ equals the concentration of its conjugate base $[A^-]$, causing them to cancel out in the $K_a$ expression.

How does the uncertainty of a volumetric pipette differ from that of a burette in a titration experiment?

A pipette has a single uncertainty because it involves only one volume delivery. A burette has double the uncertainty because the total volume delivered is calculated from two separate readings: the initial and final levels.

Why must a pH probe be calibrated before finding $K_a$?

pH probes can lose accuracy over time or due to storage conditions. Calibration against standard buffers ensures the voltage readings from the probe correctly correspond to known pH values, providing reliable data for $pK_a$ calculation.

What is the difference between the equivalence point and the end-point in a titration?

The equivalence point is the theoretical point where the moles of acid and base are stoichiometrically equal. The end-point is the physical point where the indicator changes color, which is used as an estimate for the equivalence point.

Define $pK_a$ in terms of $K_a$.

$pK_a$ is defined as the negative base-10 logarithm of the acid dissociation constant: $pK_a = -\log_{10}(K_a)$. It is a measure of acid strength where smaller values indicate stronger acids.

In the 'half-volume' method, why do we add a second equal portion of acid after reaching the end-point?

Adding an equal volume of the original acid to the neutralized salt solution creates a mixture where the moles of $HA$ (added) equal the moles of $A^-$ (produced during titration). This creates the specific condition needed for $pH = pK_a$.

What is a common source of human error when determining the equivalence point volume?

The judgement of the color change in the indicator is subjective. If the student stops the titration too early or too late (over-titrating), the volume recorded will be inaccurate, leading to an incorrect half-equivalence point.

How do you calculate $K_a$ if the measured pH at half-equivalence is $3.80$?

Since $pK_a = pH$ at this point, $pK_a = 3.80$. To find $K_a$, use the inverse log: $K_a = 10^{-3.80} \approx 1.58 \times 10^{-4} \, mol \, dm^{-3}$.

Why does the total volume of the solution not affect the $pK_a$ value determined at half-equivalence?

The $K_a$ expression depends on the ratio $\frac{[A^-]}{[HA]}$. Since both species are in the same total volume, the volume terms in their concentration formulas cancel out, making the ratio dependent only on the moles of each species.

What is 'two-point calibration' for a pH meter?

It is the process of adjusting the pH meter using two different standard buffer solutions, typically one acidic (pH 4.0) and one neutral or basic (pH 7.0 or 9.0), to ensure the meter is accurate across a range of values.

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Finding Ka

Summary

The acid dissociation constant ( $K_a$ ) of a weak acid can be experimentally determined by measuring the pH at the half-equivalence point of a titration. At this specific point, the concentrations of the weak acid and its conjugate base are equal, simplifying the equilibrium expression such that $pK_a$ equals the measured $pH$ .

1. Definition & Core Concepts

2. Underlying Principles

Titration curve of a weak acid with a strong base, highlighting the half-equivalence point where pH equals pKa.

3. Methods & Techniques

The Half-Volume Method: A precise volume of weak acid is titrated to the equivalence point using a strong base and an indicator. Once the end-point is reached, an identical volume of the original weak acid is added to the mixture.
pH Probe Calibration: Before measurements, the pH probe must undergo a two-point or three-point calibration using standard buffer solutions (e.g., pH 4.0 and pH 9.0). This ensures the accuracy of the $pK_a$ determination.
Measurement Procedure: After adding the second portion of acid, the solution is effectively half-neutralized. The pH of this final mixture is measured directly using the calibrated probe to find the $pK_a$ .

4. Key Distinctions

5. Exam Strategy & Tips

6. Common Pitfalls & Misconceptions