 # Hydrogen Ion Concentration of Strong Acids Calculations Tutorial

## Key Concepts

• Concentration of hydrogen ions in an aqueous solution can be calculated if the pH of the solution is known:
[H+] = 10-pH
where pH is the pH of the aqueous solution
and [H+] = concentration of hydrogen ions1 in mol L-1
Square brackets, [ ], are Chemist's short-hand for concentration in mol L-1 (molarity or molar concentration).
• A strong acid is one that dissociates completely in water to form hydrogen ions:

 acid → hydrogenions + anions HA → H+ + A-

• For a strong monoprotic acid, an acid that contains only 1 hydrogen atom that can dissociate, the concentration of hydrogen ions in solution is only dependent on the concentration of the original acid.

 monoproticacid → hydrogenions + anion HA → H+ + A- [HA] = [H+] = [A-]

This means that the concentration of hydrogen ions in solution is the same as the concentration of the monoprotic strong acid.

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## Calculating the Hydrogen Ion Concentration of Strong Monoprotic Acids

pH is measure of the hydrogen ion concentration in a solution:

pH = -log10[H+(aq)]

We can rearrange this equation to find the concentration of hydrogen ions in a solution given its pH:

[H+] = 10-pH

There are 2 steps for calculating the concentration of hydrogen ions (or oxonium or oxidanium or hydronium ions H3O+) in a solution if you have been given the pH of the solution:

Step 1. Write the equation for finding [H+]:

[H+] = 10-pH

Step 2. Substitute in the value for pH and solve to give the concentration of H+ in mol L-1

## Calculating the Concentration of Strong Monoprotic Acids

If we know the pH of a solution of strong acid, we can use this to calculate the concentration of the acid.

Step 1. Write the equation for finding [H+]:

[H+] = 10-pH

Step 2. Substitute in the value for value for pH and solve to give the concentration of H+ in mol L-1

Step 3. Write the equation for the complete dissociation of the strong monoprotic acid:

 monoproticacid → hydrogenions + anion hydrochloric acid HCl → H+ + Cl- hydrobromic acid HBr → H+ + Br- hydroiodic acid HI → H+ + I- nitric acid HNO3 → H+ + NO3- perchloric acid HClO4 → H+ + ClO4-
Strong Monoprotic Acids
hyrochloric acidHCl
hydrobromic acidHBr
hyroiodic acidHI
nitric acidHNO3
perchloric acidHClO4

Step 4. Use the concentration of the hydrogen ions in solution to determine the concentration of the acid :

For a monoprotic acid, the stoichiometric ratio (mole ratio) of the acid, HA, to the hydrogen ions, H+, is 1 : 1

 general monoprotic acid : HA → H+ + A- for 1 mole of acid : 1 mole HA → 1 mole H+ + 1 mole A- for 0.1 mole of acid : 0.1 mole HA → 0.1 mole H+ + 0.1 mole A- for 0.5 mole of acid : 0.5 mole HA → 0.5 mole H+ + 0.5 mole A- for 2.3 mole of acid : 2.3 mole HA → 2.3 mole H+ + 2.3 mole A- so for n mole of acid : n mole HA → n mole H+ + n mole A-

Concentration in mol L-1 (molarity or molar concentration) is calculated by dividing moles by volume in litres:

molarity = moles ÷ volume

The volume of the solution is the same for both the undissociated acid, HA, and for the hydrogen ions, H+, it produces.

 general monoprotic acid : HA → H+ + A- for n mole of acid in 1 L of solution: [HA]=n/1 → [H+]=n/1 + [A-]=n/1 for n mole of acid in 2 L of solution: [HA]=n/2 → [H+]=n/2 + [A-]=n/2 for n mole of acid in 0.4 L of solution: [HA]=n/0.4 → [H+]=n/0.4 + [A-]=n/0.4 for n mole of acid in 1.3 L of solution: [HA]=n/1.3 → [H+]=n/1.3 + [A-]=n/1.3 so for n mole of acid in V L of solution: [HA]=n/V → [H+]=n/V + [A-]=n/V

We can see that the concentration of the hydrogen ions produced by the strong monoprotic acid will be the same as the concentration of the acid.

[HA] = [H+] = 10-pH

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## Worked Examples

(based on the StoPGoPS approach to problem solving in chemistry.)

Question 1. Find the concentration of hydrogen ions in an aqueous solution of hydrochloric acid with a pH of 2.0

1. What have you been asked to do?
Calculate the concentration of hydrogen ions
[H+] = ? mol L-1
2. What information (data) have you been given?
Extract the data from the question:
pH = 2.0
3. What is the relationship between what you know and what you need to find out?
Write the equation (formula) for finding [H+]:
[H+] = 10-pH
4. Substitute in the value for pH and solve:
[H+] = 10-pH
[H+] = 10-2.0
= 0.010 mol L-1
Use your calculated value for [H+] to find pH and compare it to that given in the question:
pH = -log10[H+] = -log10[H+] = 2
Since this value is the same as that given in the question we are confident our answer is correct.
6. State your solution to the problem:
[H+] = 0.010 mol L-1

Question 2. An aqueous solution of hydrochloric acid has a pH of 3.6
Calculate the concentration of the acid in mol L-1.

1. What have you been asked to do?
Calculate the concentration of the hydrochloric acid
[HCl(aq)] = ? mol L-1
2. What information (data) have you been given?
Extract the data from the question:
pH = 3.6
3. What is the relationship between what you know and what you need to find out?
Write the equation (formula) for finding the concentration of hydrogen ions in solution:
[H+] = 10-pH

Substitute in the pH value and solve:
[H+] = 10-3.6 = 2.5 × 10-4 mol L-1

Write the balanced chemical equation for the dissociation of the acid:
HCl → H+(aq) + Cl-(aq)

Find the mole ratio (stoichiometric ratio) :
H+ : HCl
1 : 1

4. Determine the concentration of the acid using the mole ratio (stoichiometric ratio):
1 mole per litre H+ is produced by 1 mole per litre HCl
So, 2.5 × 10-4 mol L-1 H+ is produced by 2.5 × 10-4 mol L-1 HCl

Concentration of the acid is 2.5 × 10-4 mol L-1

Use your calculated value for [HCl(aq)] to find pH and compare it to that given in the question:
HCl(aq) → H+(aq) + Cl-(aq)
[HCl(aq)] = [H+] = 2.5 × 10-4 mol L-1
pH = -log10[H+] = -log10[2.5 × 10-4] = 3.6
Since this value is the same as that given in the question we are confident our answer is correct.
6. State your solution to the problem:
[HCl(aq)] = 2.5 × 10-4 mol L-1

3. 0.25 L of an aqueous solution of hydrochloric acid has a pH of 3.5
Calculate the moles of hydrogen ions present in the solution.

1. What have you been asked to do?
Calculate the moles of hydrogen ions
n(H+) = ? mol
2. What information (data) have you been given?
Extract the data from the question:
pH = 3.5
volume = V = 0.25 L
3. What is the relationship between what you know and what you need to find out?
Write the equation (formula) for finding the concentration of hydrogen ions in solution:
[H+] = 10-pH

Substitute in the pH value and solve:
[H+] = 10-3.5 = 3.2 × 10-4 mol L-1

Write the equation (formula) for finding moles given concentration and volume
moles = concentration (mol L-1) × volume (L)
concentration of hydrogen ions = [H+] = 3.2 × 10-4 mol L-1
volume of solution = 0.25 L

4. Substitute the values into the equation and solve:
moles = concentration (mol L-1) × volume (L)
moles(H+) = 3.2 × 10-4 mol L-1 × 0.25
= 8.0 × 10-5 mol

Use your calculated value for moles of H+ to find pH and compare it to that given in the question:
[H+] = n(H+) ÷ V(solution) = 8.0 × 10-5 mol ÷ 0.25 L = 3.2 × 10-4 mol L-1
pH = -log10[H+] = -log10[3.2 × 10-4] = 3.5
Since this value is the same as that given in the question we are confident our answer is correct.
6. State your solution to the problem:
n(H+) = 8.0 × 10-5 mol

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1. A hydrogen ion is a hydrogen atom that has lost an electron.
Given that the most common naturally occurring isotope of hydrogen contains just 1 proton and NO neutrons in its nucleus, and 1 "orbiting" electron, then, when this isotope loses an electron it is just a proton!
Because naturally occuring hydrogen is also made up of very tiny amount of other isotopes of hydrogen, the term hydron is preferred by IUPAC to represent H+, but most Chemists will still use the term proton when referring to H+.
Most hydrogen ions, H+, are just a naked proton!
A naked proton is very reactive, so, in practice an H+ ion "jumps" onto a water molecule to form the hydronium (or oxidanium or oxonium) ion, H3O+.
For this reason H3O+ is also known as a hydrated hydrogen ion or hydrated proton.
When Chemists refer to hydrogen ions, hydrons, or H+ in aqueous solutions, they really mean H3O+.
Should you write H+ or H3O+ when talking about aqueous solutions?
Generally speaking, it doesn't matter, but it would be better to refer to H+(aq), rather than H+, so that there is no confusion about the nature of the proton.
We use H+ and H+(aq) here because it highlights the fact that pH relates to H+ concentration.
If you decide to use H3O+ instead of H+(aq), then the equation for finding H3O+ concentration becomes:
[H3O+] = 10-pH