Question

Explain why the volume of \(0.100 \mathrm{M} \mathrm{NaOH}\) required to reach the equivalence point in the titration of \(25.00 \mathrm{mL}\) of \(0.100 \mathrm{M}\) HA is the same regardless of whether HA is a strong or a weak acid, yet the \(\mathrm{pH}\) at the equivalence point is not the same.

Short answer

The volume of NaOH required to reach the equivalence point is the same whether HA is a strong or weak acid because this volume is determined by the number of H+ ions in solution, which are present in equal quantities for a given concentration and volume of any acid. However, the pH at the equivalence point varies because a strong acid will have all its H+ ions neutralized by NaOH, giving a neutral pH of 7, while a weak acid will have residual unmolested acid molecules that yield H+ ions, making the solution acidic and hence the pH at the equivalence point will be less than 7.

Step-by-step solution

Understanding Titration

Titration is a technique in chemistry used to determine the concentration of an unknown substance by adding a solution of known concentration (titrant) until the reaction between them is just complete. The point at which this occurs is known as the equivalence point.

Understanding Reactions of Strong and Weak Acids with Bases

Strong acids fully ionize in water, producing H+ ions. Weak acids only partially ionize, producing fewer H+ ions. When a strong base like NaOH is added, it removes H+ ions from the solution by turning them into water (H2O). The base will do this whether the acid is strong or weak, thus the volume of NaOH needed to react with all the H+ ions (i.e., reach the equivalence point) is the same for a given volume and concentration of any acid.

Differentiating the pH at the Equivalence Point

While the volume of NaOH to reach the equivalence point is the same for strong and weak acids, the pH at the equivalence point is different. This is due to the reaction of the strong base with the dissociated (for strong acid) or residual, non-dissociated (for weak acid) acid particles. For strong acid, all particles are H+ ions and all are neutralized by the base, leaving only water at the equivalence point, which has a pH of 7. For weak acid, besides H+ ions, there are also residual non-dissociated acid molecules that react with water to establish an equilibrium yielding H+ ions and making the solution acidic and hence the pH of the solution at the equivalence point is less than 7.

Key concepts

Equivalence Point

During a titration, the goal is to add enough of the titrant—here it's sodium hydroxide (NaOH)—to completely react with the substance whose concentration you're measuring. The equivalence point is crucial in this process. It's the exact moment where the amount of titrant added equals the amount needed for a complete chemical reaction with the analyte, often resulting in the formation of a neutral compound.

In our case, we're examining a titration involving a fixed volume (25.00 mL) and concentration (0.100 M) of an acid (HA), with a titrant that is 0.100 M NaOH. Whether HA is a strong or weak acid, the equivalence point—in terms of volume—remains constant. This is because, for both types of acids, the number of moles of H+ ions needing neutralization remains the same. The stoichiometry of the reaction dictates that the same volume of NaOH will completely react with these ions, irrespective of the strength of the acid. Thus, the volume of NaOH needed is identical for both strong and weak acids under these conditions.

Strong vs Weak Acids

One of the primary distinctions between strong and weak acids lies in their ability to ionize in water.

• Strong Acids: They almost completely dissociate in water. This means that strong acids release a large number of hydrogen ions (H+), making them very efficient at lowering the pH of a solution. Examples include hydrochloric acid (HCl) and sulfuric acid (H₂SO₄).
• Weak Acids: They only partially dissociate in water. Thus, in a solution, a significant amount of the acid remains undissociated, and the amount of H+ ions is less than what you'd find in an equimolar solution of a strong acid. Examples include acetic acid (CH₃COOH) and formic acid (HCOOH).

In titrations involving strong acids, the complete dissociation means a direct and immediate neutralization by the base. Meanwhile, for weak acids, only the dissociated portion reacts promptly. The remaining non-dissociated acid can slowly contribute to the equilibrium by further dissociating as the titration progresses.

pH Differences in Titration

At the equivalence point in a titration, the pH can vary based on the acid's strength. This difference can be explained by the behavior of residual substances post-reaction.

For the titration of strong acids with a strong base like NaOH, the hydrogen ions and hydroxide ions completely neutralize each other to form water, resulting in a pH close to 7. Because there are no additional acidic or basic ions left in solution, the environment is neither acidic nor basic.

In contrast, when a weak acid is titrated, even at the equivalence point, the solution can remain slightly acidic. This happens because any remaining acid molecules, which haven't already dissociated, can react with water to produce additional H+ ions. This process slightly shifts the pH below 7, indicating a slight acidity remains. Therefore, the pH at the equivalence point for weak acids will be less than 7.

To summarize:

• For strong acids, the equivalence point results in a neutral pH (~7).
• For weak acids, the equivalence point reflects a mildly acidic environment, with pH < 7.

This distinction is a fundamental aspect of acid-base titration and highlights the need to understand both the concentration and the intrinsic characteristics of the acids involved.