The pH Value at Half-Titration of a Weak Acid by a Strong Base: Constant or Variable?

When dealing with acid-base titrations, the pH value at half-titration appears to be a matter of great significance. This article delves into the question of whether the pH at half-titration remains constant or changes with different acid concentrations, focusing on the titration of weak acids by strong bases. We will explore the underlying principles and provide experimental evidence to support our analysis.

Theoretical Background

According to the Henderson-Hasselbalch equation:

pH pKa logleft(frac{[A^-]}{[HA]}right)

At the half-titration point, half of the weak acid (HA) has been neutralized by a strong base (B), resulting in equal concentrations of the weak acid (HA) and its conjugate base (A^-). This can be mathematically represented as:

[HA] [A^-]

Substituting these equal concentrations into the Henderson-Hasselbalch equation results in:

pH pKa logleft(frac{[A^-]}{[HA]}right) pKa log(1) pKa

This relationship clearly indicates that the pH at half-titration is solely dependent on the pKa of the weak acid and is independent of its concentration. Therefore, the pH at the half-titration point is expected to remain constant regardless of the acid concentration.

Practical Verification

Despite the theoretical straightforwardness, it is instructive to conduct experimental verification to ensure that the approximations hold true under practical conditions. Let’s consider acetic acid (HOAc) with a well-known pKa of 4.75 as an example.

Experimental Data

The following table presents the calculated pH values at the half-equivalence point (pH at half-titration) for different concentrations of acetic acid and acetate ion (OAc(^-)).

Concentration (M) Predicted pH at Half-Titration 1.00 4.75001 0.100 4.75015 0.0100 4.75153 0.00100 4.76492 0.000100 4.86834

From the data, it can be observed that at concentrations close to or above [CA] [CB] geq; sqrt{K_a} (where K_a is the acid dissociation constant, approximately 0.0042 M for acetic acid), the pH at half-titration is in close agreement with the pKa value (4.75).

Influence of Indicator Selection

Theoretical considerations aside, practical determinations of the titration endpoint often rely on the selection of appropriate indicators. The choice of the indicator is crucial as it helps in identifying the pH at the half-equivalence point.

Conclusion

In summary, the pH at half-titration of a weak acid by a strong base is indeed constant, as long as the concentrations of the acid and its conjugate base are approximately equal. This constancy is dictated by the pKa of the acid, demonstrating the independence of pH at half-titration from the acid concentration. However, it is essential to consider the practical constraints and the accuracy of experimental measurements, especially at very low concentrations.

Key Takeaways:

The pH at half-titration of a weak acid by a strong base is the same for different acid concentrations. This pH value is equal to the pKa of the weak acid. Precision in titration and the selection of indicators are critical for accurate pH determination.