Question

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?

Answer 1

Answer:

• 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