A 0.1$moldm^{-3}$ solution of sodium hydroxide was diluted with distilled water to 0.001$moldm^{-3}$. What is the dilution factor?

Analyze the question: A solution of NaOH is diluted from 0.1 mol/dm³ to 0.001 mol/dm³. We need the dilution factor.

Concept: The dilution factor is how many times more dilute the solution becomes. It is the ratio of the initial concentration to the final concentration (equivalently, final volume ÷ initial volume):

Dilution factor = C₁ / C₂ = V₂ / V₁

This follows from the dilution equation C₁V₁ = C₂V₂, since the amount of solute (moles) stays the same when you add water.

Solution:

• C₁ = 0.1 mol/dm³
• C₂ = 0.001 mol/dm³

Dilution factor = 0.1 / 0.001 = 100

This means the final volume is 100 times the initial volume. For example, 10 cm³ of the original solution would be topped up with water to 1000 cm³.

Option A (1000) would be correct if the concentration fell from 1.0 to 0.001, and option D (0.01) is the inverse of the factor, not the factor itself.

Answer: B, 100.00

Exam tip: Always divide the larger concentration by the smaller one to get the dilution factor. Count the decimal places too: 0.1 is 10⁻¹ and 0.001 is 10⁻³, so the factor is 10⁻¹ ÷ 10⁻³ = 10², which is 100.