How to calculate H+ or H3O+ concentration from pH?, [pH to Hydrogen ion (H+) concentration]

HCl is a strong acid that completely ionizes in water. 1 H⁺ ion is released per HCl molecule in its aqueous solution.

As the pH of the solution is given in the question statement (i.e., pH = 1.3), so we can easily find its H⁺ concentration by substituting the known value into equation (iii), as shown below.

[H⁺] = 10^-pH ………. Equation (iii)

[H⁺] = 10^-1.3 = 0.050 mol/L

Result: The H⁺ concentration of the given HCl solution of pH 1.3 is 0.050 mol/L.

As the pH of the solution is given in the question statement (i.e., pH = 5.8), so we can easily find its H⁺ concentration by substituting the known value into equation (iii), as shown below.

[H⁺] = 10^-pH ………. Equation (iii)

[H⁺] = 10^-5.8 = 1.58 x 10^-6 mol/L

Result: The H⁺ concentration of the given acidic solution is 1.58 x 10^-6 mol/L.

A lower H⁺ concentration is obtained in Example 2 as compared to that in example 1.

This reaffirms what we discussed earlier in the article, i.e., strongly acidic solutions have low pH values as they possess a greater H⁺ concentration and vice versa. 

As the pH of the solution is given in the question statement (i.e., pH = 13.2), so we can easily find its H⁺ or H₃O⁺ concentration by applying equation (ii).

pH = -log₁₀ [H₃O⁺] …………. Equation (ii)

Making [H₃O⁺] the subject of the formula by taking the antilog of pH gives us equation (iv).

[H₃O⁺] = 10^-pH ………. Equation (iv)

Now substitute the given pH value into equation (iv) to find the required H₃O⁺ concentration;

[H₃O⁺] = 10^-13.2 = 6.31 x 10^-14 mol/L

Result: The H₃O⁺ concentration of the given aqueous solution is 6.31 x 10^-14 mol/L.

Such a low H₃O⁺ concentration while a high pH value implies that the given solution is very weakly acidic, aka strongly basic in nature.

Example # 4: Which of the following options gives the correct hydrogen (H⁺) ion concentration in mol/L in a solution of pH = 5.4?

A) 3.98 x 10⁸   B) 3.88 x 10⁶   C) 3.68 x 10^-6   D) 3.98 x 10^-6

Answer: Option D (3.98 x 10^-6) is the correct H⁺ concentration of the given solution of pH 5.4.

Explanation:

As the pH of the solution is given in the question statement (i.e., pH = 5.4), so we can easily find its H⁺ concentration by applying equation (iii) as follows:

[H⁺] = 10^-pH ………. Equation (iii)

[H⁺] = 10^-5.4

[H⁺] = 3.98 x 10^-6 mol/L.  

What is [H⁺]?

What is [H₃O⁺]?

[H₃O⁺] represents the concentration of hydronium ions. An acid is defined as a chemical substance that breaks down to release H⁺ ions in water.

The hydrogen ions combine with water molecules to form hydronium ions. The greater the H⁺ concentration in an aqueous solution, the more the H₃O⁺ ions formed in it.

What is pH?

pH stands for the power of hydrogen. It is measured by taking the negative logarithm of H⁺ concentration, as shown below.

pH = -log₁₀ [H⁺]

pH is measured in numbers on a scale of 0-14. It tells us whether a solution is acidic or basic in nature.

Acidic solutions have a pH below 7, while basic solutions have a pH above 7. The pH of a purely neutral solution such as water is exactly equal to 7.

How is pH related to the acidity of an aqueous solution?

pH is inversely related to acidity while directly related to the basicity of an aqueous solution.

The lower the pH of an aqueous solution, the more acidic it is, and vice versa.

What is the formula that relates pH to H⁺ or H₃O⁺ concentration?

pH is related to [H⁺] or [H₃O⁺] by the formulae given below.

pH = -log₁₀ [H⁺]

or

pH = -log₁₀ [H₃O⁺]

How to find H⁺ or H₃O⁺ concentration from pH?

As we know; pH = -log₁₀ [H⁺]; if we apply antilog on both sides of the equation and make [H⁺] the subject of the formula;

∴ [H⁺] = 10^-pH

Thus, if we know the pH of an aqueous solution, we can easily find its H⁺ or H₃O⁺ concentration by substituting the known value into the above formula.