Following Neutralisation with pH Curves

Introduction

When alkali is added to an acid, you might expect the pH to rise smoothly and steadily, a little for each drop. In fact it does something much more dramatic. For a long time the pH barely moves; then, within a single drop or two, it leaps by six or more units. A graph of pH against the volume of alkali added — a pH curve — captures this behaviour. Reading these curves is essential for understanding titrations and for choosing indicators.

Core explanation

Setting up the measurement. A fixed volume of acid is placed in a flask with a pH probe connected to a meter or data logger. Alkali is added from a burette in small steps, and the pH is recorded after each addition. The results are plotted with pH on the y-axis and volume of alkali added on the x-axis.

The shape for a strong acid and a strong alkali. Consider 25 cm³ of 0.10 mol/dm³ hydrochloric acid with 0.10 mol/dm³ sodium hydroxide added:

Volume of NaOH added (cm³) Approximate pH --- --- 0 1.0 10 1.4 20 2.0 24 2.7 24.9 3.7 25.0 7.0 25.1 10.3 26 11.3 35 12.2

Region 1: slow rise. At first, the flask contains lots of H⁺ ions. Each portion of alkali removes some of them, but plenty remain. Because pH is a logarithmic scale, the pH rises by only 1 unit when the H⁺ concentration falls to one tenth. Removing even 90% of the acid raises the pH by only about one unit.

Region 2: the vertical section. Near the end point, only a tiny amount of H⁺ is left. One more drop of alkali removes almost all of it, and the next drop leaves a small excess of OH⁻. The pH jumps from about 3 to about 11 in less than half a cubic centimetre. The middle of this vertical section is the equivalence point , where the moles of OH⁻ added exactly equal the moles of H⁺ originally present. For a strong acid and strong alkali it is at pH 7.

Region 3: levelling off. After the end point, the solution contains excess OH⁻. Further alkali increases the OH⁻ concentration only slowly in logarithmic terms, so the curve flattens towards the pH of the alkali itself, about 13.

Reversing the process. If acid is added to alkali, the curve is the mirror image: high and flat, a steep fall at the end point, then low and flat.

Why this matters. The steep section tells us that one drop decides whether the solution is acidic or alkaline. That is why a titration can find the end point so precisely, and why an indicator that changes colour anywhere within that steep range works well.

Step-by-step reasoning

To read the end point volume from a pH curve:

1. Find the steep, nearly vertical part of the curve. 2. Locate its midpoint. 3. Draw a line straight down to the x-axis. 4. Read the volume; this is the volume of alkali needed for exact neutralisation.

Visual explanation

Picture a stretched letter S lying on its side: a long, gently rising floor on the left, a near-vertical cliff in the middle, and a high, flat plateau on the right. In the titration simulation, watch the pH trace crawl along the floor and then shoot up the cliff as the last drops are added.

Real-world analogy

Think of emptying a full swimming pool with a bucket. For hours the water level seems unchanged. Only when the last few bucketfuls are removed does the pool suddenly go from "some water" to "empty". The logarithmic pH scale behaves in the same way near the end point.

Real-world example

Water treatment works and food manufacturers use automatic pH probes to add acid or alkali to process streams. Engineers design the controls with the steep part of the pH curve in mind: near neutral, tiny dosing errors cause large pH swings, so additions must be slow and carefully controlled.

Why?

Why is the vertical section so steep? Near the end point, the concentration of H⁺ changes by factors of ten with each tiny addition, for example from 10⁻⁴ to 10⁻¹⁰ mol/dm³. Every tenfold change is one pH unit, so the pH changes by many units very quickly.

Common misconception

"Adding half the alkali makes the pH halfway between the acid and 7." At half neutralisation, the pH of a strong acid has risen only by about half a unit, because half the H⁺ ions still remain.

Worked example

Question: A pH curve for adding sodium hydroxide to 20.0 cm³ of nitric acid has its vertical section centred at 16.4 cm³. What volume of alkali neutralises the acid, and what is the pH at that point?

Reasoning: The middle of the vertical section is the equivalence point. For a strong acid and strong alkali, the salt solution formed is neutral.

Answer: 16.4 cm³; pH 7.

Quick check

1. What is the approximate pH at the end point when a strong alkali neutralises a strong acid? Answer: pH 7.

Exam focus

Be able to sketch the curve for alkali added to acid and for acid added to alkali, labelling the starting pH, the vertical section, the end point and the final pH. Explain the slow initial change using the logarithmic nature of the pH scale.

Advanced insight

When a weak acid such as ethanoic acid is titrated with a strong alkali, the curve starts higher (about pH 3), the vertical section is shorter, and the equivalence point is above 7, around pH 8–9, because the ethanoate ion formed is slightly basic. With a weak base and strong acid, the equivalence point falls below 7. These differences decide which indicator is suitable.

Summary

A pH curve plots pH against volume added during neutralisation. For a strong acid with a strong alkali, pH rises slowly, then jumps steeply around the end point, then levels off near 13. The end point is the middle of the vertical section, at pH 7 for strong acid–strong alkali. The shape arises because pH is logarithmic.

Practice questions

1. Describe the three regions of the pH curve when sodium hydroxide is added to hydrochloric acid. Answer: A slow rise from about pH 1, a steep vertical rise from about 3 to 11 at the end point, then a levelling off near pH 13. 2. Why does the pH change very little during the first 20 cm³ of alkali added to 25 cm³ of acid of the same concentration? Answer: Plenty of H⁺ ions remain, and the pH rises by only one unit each time the H⁺ concentration falls tenfold. 3. How would the curve differ if acid were added to alkali instead? Answer: It would start high near pH 13, fall slowly, drop steeply at the end point and level off at a low pH. 4. What is meant by the equivalence point? Answer: The point at which the moles of alkali added exactly match the moles of acid, as required by the equation.