# Hydrogen Ion Concentration Calculations Chemistry Tutorial

## Key Concepts

• The hydrogen ion concentration in a solution, [H+], in mol L-1, can be calculated if the pH of the solution is known.
• pH is defined as the negative logarithm (to base 10) of the hydrogen ion concentration in mol L-1
pH = -log10[H+]
where [H+] is the concentration of hydrogen ions in mol L-1 (mol/L or M)
• [H+] in mol L-1 can be calculated using the equation (formula):
[H+] = 10-pH
• As the pH increases, the concentration of hydrogen ions in the solution decreases.

As the pH decreases, the concentration of hydrogen ions in the solution increases.

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## [H+] Calculations Using a Calculator

You will need to locate the 10x button on your calculator.

This button will probably be labelled 10x and be above the button labelled log or LOG

For calculations involving pH, do NOT use the button labelled ex (above the button labelled ln or LN)

On AUS-e-TUTE's calculator the 10x button is above the log button positioned in the top left hand corner of the calculator.

To use the 10x button to calculate [H+] you will need to:

1. Enter the number (the pH value) in the textbox
2. Multiply the pH by -1 to find -pH
3. Click the INV button
4. Click the log button

On the calculator shown below, we have disabled all the buttons except the INV and log button.

 To find the [H+] in mol L-1 of a solution given the pH of the solution: First, we need to multiply the pH value by -1. Enter a pH value between 0 and 14 in the textbox: pH = Click the -pH button: = -1 × pH = -1 × = Now click the INV button on the calculator shown on the right Then click the log button on the calculator shown on the right [H+] = 10-pH = 10 = mol L-1 Click the Reset button to clear these numbers and start a new calculation:

Check the calculations below:

 pH [H+] mol L-1 trend 3 2.3 2 1.3 1 0.3 0 -0.7 -1 1 × 10-3 5 × 10-3 1 × 10-2 5 × 10-2 1 × 10-1 5 × 10-1 1 × 100 5 × 100 1 × 101 (= 0.001) (= 0.005) (= 0.01) (= 0.05) (= 0.1) (0.5) (= 1) (= 5) (= 10) decreasing pH → increasing hydrogen ion concentration →

• Decreasing pH increases [H+]
• Increasing pH decreases [H+]

Notice that a change of 1 pH unit results in a tenfold change in the concentration of hydrogen ions results:

 pH = 3 - 1 = pH = 2 - 1 = pH = 1 - 1 = pH = 0 - 1 = pH = -1 [H+]=1 × 10-3 M x10= [H+]=1 × 10-2 M x10= [H+]=1 × 10-1 M x10= [H+]=1 × 100 M x10= [H+]=1 × 101 M

 pH = 2.3 - 1 = pH = 1.3 - 1 = pH = 0.3 - 1 = pH = -0.7 [H+]=5 × 10-3 M x10= [H+]=5 × 10-2 M x10= [H+]=5 × 10-1 M x10= [H+]=5 × 100 M

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## pH - [H+] Graphs

Using the formula (equation) [H+] = 10-pH we can calculate the [H+] in mol L-1 of solutions with varying pH values and plot these values on a graph.

An example is shown below:

Data Graph Trends
pH 10-pH = [H+]
mol L-1
0.00 100.00 = 1.00
0.05 10-0.05 = 0.89
0.10 10-0.10 = 0.79
0.15 10-0.15 = 0.71
0.20 10-0.20 = 0.63
0.25 10-0.25 = 0.56
0.30 10-0.30 = 0.50
0.35 10-0.35 = 0.45
0.40 10-0.40 = 0.40
0.45 10-0.45 = 0.35
 [H+] mol L-1 Relationship Between [H+] and pHpH
Increasing pH decreases [H+].

Higher pH gives a lower [H+].

Decreasing pH increases [H+].

Lower pH gives a higher [H+].

If you place your mouse over any of the points in the graph, a small box should appear to show you the values of the hydrogen ion concentration and the pH at that point.

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## Worked Examples

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

Question 1. The pH of an aqueous solution of an acid is determined to be 5.8
What is the concentration of hydrogen ions in mol L-1 in this acidic solution?

1. What have you been asked to do?
Calculate concentration of hydrogen ions
[H+] = ? mol L-1
2. What information (data) have you been given?
Extract the data from the question:
pH = 5.8
3. What is the relationship between what you know and what you need to find out?
Write the equation (formula) for finding [H+] given the pH:
[H+] = 10-pH
4. Substitute in the values and solve:
[H+] = 10-5.8
= 1.6 × 10-6 mol L-1
Use the value for the concentration of H+ to calculate the pH and compare this value to the value given in the question:
pH = -log10[H+] = log10[1.6 × 10-6] = 5.8
Since this value is the same as the one given in the question, we are confident our answer is correct.
6. State your solution to the problem:
[H+] = 1.6 × 10-6 mol L-1

Question 2. The pH of an aqueous solution of hydrochloric acid is 3.2
Calculate the moles of hydrogen ions in 0.20 L of this solution.

1. What have you been asked to do?
Calculate moles of hydrogen ions
n(H+) = ? mol
2. What information (data) have you been given?
Extract the data from the question:
pH = 3.2
volume = 0.20 L
3. What is the relationship between what you know and what you need to find out?
Find the concentration of hydrogen ions:
[H+] = 10-pH
= 10-3.2
= 6.3 × 10-4 mol L-1

Write the equation (formula) that relates moles, volume and concentration (molarity):
molarity = moles ÷ volume (L)

Rearrange this equation (formula) to find moles:
moles = molarity (mol L-1) × volume (L)

4. Calculate moles of H+:
molarity = 6.3 × 10-4 mol L-1
volume = 0.20 L

moles H+ = molarity (mol L-1) × volume (L)
= 6.3 × 10-4 × 0.20
= 1.3 × 10-4 mol

Use the value for the moles of H+ to calculate the pH and compare this value to the value given in the question:
[H+] = moles ÷ volume = 1.3 × 10-4 mol ÷ 0.20 L = 6.5 × 10-4 mol L-1
pH = -log10[H+] = log10[6.5 × 10-4] = 3.2
Since this value is the same as the one given in the question, we are confident our answer is correct.
6. State your solution to the problem:
n(H+) = 1.3 × 10-4 mol

Question 3. An aqueous solution of citric acid has a pH of 6.0
Calculate the number of hydrogen ions present in 100 mL of this solution.

1. What have you been asked to do?
Calculate number of hydrogen ions
N(H+) = ?
2. What information (data) have you been given?
Extract the data from the question:
pH = 6.0
volume = 100 mL
3. What is the relationship between what you know and what you need to find out?
Find the concentration of hydrogen ions:
[H+] = 10-pH = 10-6.0 mol L-1

Find the moles of H+:
Write the equation (formula) that relates moles, volume and concentration (molarity):
molarity = moles ÷ volume (L)

Rearrange this equation (formula) to find moles:
moles = molarity (mol L-1) × volume (L)

Calculate moles of H+:
molarity = 10-6 mol L-1
Convert volume in mL to L by dividing by 1000:
volume = 100 mL = 100 × 10-3 = 0.10 L

moles H+ = 10-6 × 0.10 = 10-7 mol

4. Calculate moles of H+:
Calculate the number of hydrogen ions:
1 mole = Avogadro's Number of particles = 6.02 × 1023 particles
10-7 mol H+ = 10-7 × 6.02 × 1023
= 6.0 × 1016 hydrogen ions
Use the value for the number of H+ to calculate the pH and compare this value to the value given in the question:
moles(H+) = N(H+) ÷ NA = (6.0 × 1016) ÷ (6 × 1023) = 10-7 mol
[H+] = moles ÷ volume =10-7 mol ÷100/1000 = 10-6 mol L-1
pH = -log10[H+] = log10[10-6] = 6
Since this value is the same as the one given in the question, we are confident our answer is correct.
6. State your solution to the problem:
N(H+) = 6.0 × 1016

Question 4. An aqueous solution of hydrochloric acid contains 0.005 moles of hydrogen ions and has a pH of 4.3.
Calculate the volume of the solution in litres.

1. What have you been asked to do?
Calculate volume of solution
V(HCl(aq)) = ? L
2. What information (data) have you been given?
Extract the data from the question:
pH = 4.3
moles H+ = 0.005 mol
3. What is the relationship between what you know and what you need to find out?
Find the concentration of hydrogen ions:
[H+] = 10-pH
= 10-4.3
= 5.0 × 10-5 mol L-1

Write the equation (formula) that relates moles, volume and concentration (molarity):
molarity = moles ÷ volume (L)

Rearrange this equation (formula) to find volume:
volume= moles ÷ molarity (mol L-1)

4. Calculate volume of solution:
moles H+ = 0.005 mol
molarity = 5.0 × 10-5 mol L-1

volume of solution = 0.005/5.0 × 10-5
= 100 L