18.5 - pH Curves

Generating pH curves through titration

A pH curve is a graphical representation of how the pH of a solution changes during an acid-base titration. It is obtained by plotting the pH of the reaction mixture against the volume of the standard solution (titrant) added.

To generate a pH curve:

1. The unknown concentration of an acid or base (analyte) is determined by titration with a standard solution of a base or acid (titrant).
2. The pH of the reaction mixture is continuously monitored using a digital pH meter and a data logger as the titrant is gradually added.
3. The collected pH data is then plotted against the volume of the titrant, producing the pH curve.

The shape of the resulting pH curve depends on the strengths and concentrations of the analyte and titrant, as well as the order in which they are added.

Strong acid-strong base titration curves

When a strong acid, like hydrochloric acid (HCl), is titrated with a strong base, such as sodium hydroxide (NaOH), the pH curve has a characteristic shape:

Key features of the strong acid-strong base titration curve:

1. Low initial pH

• The initial pH is low (typically between 0-2) as the HCl_(aq) analyte is strongly acidic.
• The exact initial pH depends on the acid concentration - a higher concentration of acid will result in a lower initial pH.

1. Gradual pH rise before equivalence

• The pH rises slowly at first due to the large excess of acid present.
• For example, if [HCl] = 0.1 mol dm^-3 initially, the pH only rises from 1.0 to ~1.5 when half the acid is neutralised.
• The curve becomes progressively steeper as [HCl] decreases.

1. Equivalence point at pH 7

• At this point, the acid is completely neutralised by the base (the number of moles of H⁺ and OH^- are stoichiometrically equivalent).
• The reaction mixture contains only NaCl_(aq) at this stage: HCl_(aq) + NaOH_(aq) ➔ NaCl_(aq) + H₂O_(l).
• The pH rises very sharply to 7.0 at the equivalence point - this is because all the H⁺ ions from the acid have been neutralised by the OH^- ions from the base, resulting in a neutral solution.

1. High final pH

• The curve flattens out as the NaOH_(aq) excess becomes very large.
• The final pH is that of the NaOH_(aq) titrant (usually pH 12-14).

Strong base-strong acid titration curves

The pH curve for a strong base-strong acid titration has an inverted shape compared to a strong acid-strong base titration, but equivalence still occurs at pH 7.0. The key difference is that in a strong base-strong acid titration, the initial pH is high (12-14) due to the strong base, and the final pH is low (0-2) due to the excess strong acid.

To plot the full pH curve for both a strong acid-strong base titration and a strong base-strong acid titration, the titration must continue past the equivalence point by adding excess titrant. However, when using an acid-base indicator in either case, the titration is stopped at or near the equivalence point when the indicator colour changes.

In both cases, the concentration of the unknown acid or base is calculated from the volume of standard solution added at the equivalence point.

Summary of strong acid-base titration curves

The main characteristics of pH curves for titrations involving strong acids and bases are summarised in the table below.