20 mL of 2 M NaOH solution is added to 400 mL of 0.5 M NaOH solution. The final concentration of the solution is _________ × 10⁻² M. (Nearest integer)

Solution

Chemistry ma’am · 3 steps

Moles of NaOH just add up when you mix, and so do the volumes. Divide the total by the total.

1. Millimoles in each. Millimoles = molarity × volume in mL. The first solution has 2 × 20 = 40 mmol and the second has 0.5 × 400 = 200 mmol of NaOH.
2. Add both. Mixing does not destroy any solute, so the total is 40 + 200 = 240 mmol. The total volume is 20 + 400 = 420 mL.

   M_(final) = (M₁V₁ + M₂V₂)/(V₁ + V₂) = 240/420 = 0.5714 M

3. So. 0.5714 M = 57.14 × 10⁻² M, which rounds to 57.

The common slip: 60. Dividing 240 mmol by 400 mL instead of the full 420 mL gives 0.6 M, that is 60, not 57.

The idea to keep. When two solutions of the same solute are mixed, add the moles and add the volumes. Never average the molarities directly unless the volumes are equal.

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