An analyst wants to convert 1 L HCl of pH=1 to a solution of HCl of pH 2. The volume of water needed to do this dilution is __________ mL. (Nearest integer)

Solution

Chemistry ma’am · 4 steps

One pH unit up means ten times less H⁺, so the final volume must be ten times bigger.

1. Read the concentrations. HCl is a strong acid, so [H⁺] = 10^(-pH). At pH 1 it is 0.1 M, and at pH 2 it is 0.01 M.
2. Moles stay fixed. Adding water does not change the moles of H⁺, only the volume. So the product of molarity and volume is the same before and after.

   M₁V₁ = M₂V₂ ⇒ 0.1 × 1000 mL = 0.01 × V₂ ⇒ V₂ = 10000 mL

3. Subtract the start. The final volume is 10000 mL, but 1000 mL of it was already the acid. Water added = 10000 - 1000 = 9000 mL.
4. So. The analyst must add 9000 mL of water.

The common slip: 10000. Reporting the final volume instead of the water added gives 10 000, not 9000. Subtract the 1000 mL of acid you started with.

The idea to keep. For a strong acid, each rise of 1 in pH needs a tenfold dilution. Always check whether the question asks for the final volume or the water added.

Answer from the NTA final answer key. Solution by PrepWiser.