Dilution and pH Change

Introduction

Squash from a bottle is far too strong to drink neat, so you add water. The flavour is still there, but it is weaker because the same amount of flavouring is spread through more liquid. Acids and alkalis behave in the same way. Adding water does not destroy the hydrogen ions in an acid or the hydroxide ions in an alkali, but it spreads them out, and that changes the pH in a predictable way. This page explains which way the pH moves and by how much.

Core explanation

Dilution spreads ions out. A solution of hydrochloric acid contains H⁺(aq) ions. When water is added, the number of H⁺ ions stays the same, but the volume increases. The concentration of H⁺ ions — the number of ions per cubic decimetre — therefore falls. Because pH measures hydrogen ion concentration, the pH changes.

Diluting an acid raises its pH. A lower concentration of H⁺ means a less acidic solution, and a less acidic solution has a higher pH. For example, an acid at pH 1 might become pH 2 or pH 3 after dilution. Its pH moves upwards, towards 7.

Diluting an alkali lowers its pH. An alkali contains OH⁻(aq) ions. Adding water lowers the OH⁻ concentration, so the solution becomes less alkaline and its pH falls — for example from pH 13 to pH 12. Its pH moves downwards, towards 7.

The tenfold rule. The pH scale is logarithmic : each whole unit represents a tenfold change in H⁺ concentration. So for a strong acid, a solution diluted ten times (a dilution factor of 10) has one-tenth of the H⁺ concentration and a pH about one unit higher . A hundredfold dilution raises the pH by about two units; a thousandfold dilution by about three units. The same rule works in reverse for strong alkalis: each tenfold dilution lowers the pH by about one unit.

Dilution factor [H⁺] in mol/dm³ (starting at 0.1) pH --- --- --- 1 (undiluted) 0.1 1 10 0.01 2 100 0.001 3 1000 0.0001 4

Dilution never crosses pH 7. However much water you add to an acid, you cannot make it alkaline. Pure water itself has pH 7, so adding more and more water brings an acid closer and closer to 7 but never beyond it. To go past 7 you need to add a base, which removes H⁺ ions chemically by neutralisation. Dilution only spreads the ions out; neutralisation actually uses them up.

Weak acids. For a weak acid, such as ethanoic acid, dilution also raises the pH, but by less than one unit per tenfold dilution. This is because dilution encourages more of the weak acid molecules to ionise, partly replacing the H⁺ ions that were spread out. The direction is the same; the size of the change is smaller.

Step-by-step reasoning

To predict the pH of a diluted strong acid:

1. Note the starting pH. 2. Work out the dilution factor (final volume ÷ starting volume). 3. Count how many factors of ten the dilution contains: 10 → one, 100 → two, 1000 → three. 4. Add that number of units to the pH of an acid (or subtract it for an alkali). 5. Check that your answer has not passed 7; if it would, the answer is simply "very close to 7".

Visual explanation

In the pH simulation, picture a beaker with twenty red H⁺ dots in 100 cm³ of solution. Pour it into a larger beaker and top it up to 1000 cm³. There are still twenty dots, but now they are scattered through ten times the space. The indicator colour shifts from red towards orange as the dots thin out.

Real-world analogy

Think of a drop of food colouring in a glass of water, then the same drop in a bath. The amount of dye is identical, but in the bath it is so spread out that the colour is barely visible. The dye has not gone; its concentration has fallen.

Real-world example

Spilled acid or alkali on skin is washed with plenty of running water. The water dilutes the chemical, shifting its pH towards 7 and lowering the concentration of the damaging ions, while also carrying it away. Large volumes are used because each tenfold dilution only moves the pH by about one unit.

Why?

Why does a tenfold dilution change pH by exactly one unit for a strong acid? Because pH is defined as the negative logarithm of the H⁺ concentration, and the logarithm of 10 is 1. Dividing the concentration by ten therefore adds exactly one to the pH.

Common misconception

"If you add enough water to an acid it becomes neutral and then alkaline." Dilution can only bring an acid closer to pH 7. It cannot remove H⁺ ions, so it can never make the solution alkaline. Only a base can do that.

Worked example

Question: 10 cm³ of a strong acid of pH 2 is diluted with water to a total volume of 1000 cm³. What is the new pH?

Reasoning: Dilution factor = 1000 ÷ 10 = 100. A factor of 100 is two factors of ten, so the pH rises by two units: 2 + 2 = 4.

Answer: pH 4.

Quick check

1. Does diluting sodium hydroxide solution raise or lower its pH? Answer: It lowers the pH, moving it down towards 7, because the OH⁻ concentration falls.

Exam focus

State clearly that dilution lowers the concentration of H⁺ (or OH⁻) ions, not the number of them. Use the tenfold rule only for strong acids and alkalis, and always say that the pH moves "towards 7". Examiners reward the phrase "a tenfold dilution changes the pH by one unit".

Advanced insight

When a strong acid is diluted to extremely low concentrations, around 10⁻⁷ mol/dm³, the H⁺ ions produced by water itself become significant. The simple rule would then predict a pH above 7, which is impossible; the true pH levels off just below 7. This is a good reminder that simple rules have limits.

Summary

Diluting a solution spreads the same number of ions through a larger volume, lowering their concentration. Diluting an acid raises its pH; diluting an alkali lowers its pH; both move towards 7 but never past it. For strong acids and alkalis, each tenfold dilution changes the pH by about one unit, because the pH scale is logarithmic. Weak acids change by less.

Practice questions

1. A strong acid has pH 1. What is its pH after a tenfold dilution? Answer: pH 2, because a tenfold dilution raises the pH of a strong acid by one unit. 2. A strong alkali has pH 13. It is diluted 1000 times. What is the new pH? Answer: A thousandfold dilution is three factors of ten, so the pH falls by three units to pH 10. 3. Explain why adding water to vinegar can never produce a solution of pH 8. Answer: Water only spreads out the H⁺ ions; it does not remove them. Water itself has pH 7, so dilution can only bring the pH closer to 7, never above it. 4. By what factor must a strong acid of pH 3 be diluted to reach pH 5? Answer: The pH must rise by two units, so it must be diluted 100 times.