Suppose 'Solution A' has a pH of 3, 'Solution B' has a pH of 7, and 'Solution C' has a pH of 10. If solution B contains 10,000,000 H + ions in a given volume, how many ions will each of solution A and solution C have in equal volumes?

Solution A: 100,000,000,000 Solution C: 10,000

Explanation:

The definition of pH is pH = - log [H⁺], i. e. pH is the negative of the base 10 logarithm of the conentration of H⁺ ions.

Since you have the number of H⁺ ions in the solution B and its pH, you can calculate the volume, V:

pH = 7 = - log [H⁺] = - log { 10,000,000 / V)

Apply antilogarithm: (10,000,000 / V) = 10⁻⁷

Solve for V: V = 10,000,000 / 10⁻⁷ = 10¹⁴ liter

That is the same volume of the solutions A and C, so you can use the formula to calculate the pH of the solutions A and C.

Solution A:

pH = 3 V = 10¹⁴ liter

3 = - log { n / 10¹⁴ } n / 10¹⁴ = 10⁻³ n = 10⁻³ * 10¹⁴ = 10¹¹ = 100,000,000,000

Solution C:

pH = 10 V = 10¹⁴ liter

10 = - log { n / 10¹⁴ } n / 10¹⁴ = 10⁻¹⁰ n = 10⁻¹⁰ * 10¹⁴ = 10⁴ = 10,000