Relationship of pH and Diluting a Strong Acid

Strong acids dissociate completely to H+ ions and anion. When acid is diluted, concentration decreases and there is nice relationship between pH and diluting times such as diluted by 10 times, 100 times and more.


We can dilute any solution by adding distilled water. In acidic solution, when the acidic solution is diluted, H3O+ concentration decreases and pH increases



You should have an understand about how to find pH of strong acids. If you don't have please refer following tutorial.
Find pH of strong acids



Calculate pH of different strong acid solutions


There are 3 bottles which contain aqueous hydrochloric (HCl) acid solutions. These hydrochloric acids' concentrations in mol dm- are 0.1, 0.01, 0.001. Calculate pH of those solutions.


Hydrochloric acid is a strong acid. Therefore it dissociate completely in the water.

HCl(aq) + H2O(l) → Cl- (aq) + H3O+(aq)



Due to completeness dissociation,

[ HCl(aq)] = [H3O+(aq) ]

Assumption: The H3O+ receive from dissociation of water is negligible when it compares with H3O+ receive from HCl.



strong acid concentrations and pH

Relationship of pH and concentration of weak acid

We can see a pattern of pH values of solutions. pH variation against concentration of strong acids is figured below. you can see diluting 10 times will increase pH value by 1.

strong acid concentrations and pH variation against diluting

pH versus strong acid concentration

When weak acid is diluted by 10 times, concentration of it is decreased by 10 times.

When strong acid is diluted by 10 times, pH value is increased by 1

When strong acid is diluted by 100 times, pH value is increased by 2

When strong acid is diluted by 1000 times, pH value is increased by 3



Example problem:

Calculate concentration and pH of H2SO4 acid

You are provided 10cm3 of 0.1 mol dm-3 solution of H2SO4. You have to do
1. dilute the initial solution by 10 times
2. dilute the initial solution by 100 times
Find the concentration of H2SO4 and pH of every solution.

you can assume that both dissociation of H2SO4 is complete.
Sulfuric acid is strong acid and it dissociates completely in the water and gives two H3O+ (or H+) ions. Therefore concentration of H3O+ is twice as concentration of H2SO4.
[H3O+(aq)] = 2*[H2SO4(aq)]

sulfuric acid dissociation in water

In this example, at initial state,
[H2SO4(aq)] = 0.1 mol dm-3
[H3O +(aq)] = 0.2 mol dm-3

Now we can find the pH of initial solution,
pH = -log10[H3O+(aq)]
pH = -log10[0.2]
pH = 0.699


1. When initial solution is diluted by 10 times

Concentration of H2SO4(aq) is reduced by 10 times. With that H3O+(aq) concentration is also reduced by 10 times. Then,
[H2SO4(aq)] = 0.01 mol dm-3
[H3O +(aq)] = 0.02 mol dm-3

Now we can find the pH of solution,
pH = -log10[H3O+(aq)]
pH = -log10[0.02]
pH = 1.699


2. When initial solution is diluted by 100 times

Concentration of H2SO4(aq) is reduced by 100 times. With that H3O+(aq) concentration is also reduced by 100 times. Then,
[H2SO4(aq)] = 0.001 mol dm-3
[H3O +(aq)] = 0.002 mol dm-3

Now we can find the pH of solution,
pH = -log10[H3O+(aq)]
pH = -log10[0.002]
pH = 2.699



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