By Claire Gillespie
Updated Mar 24, 2022
When you combine solutions that differ in concentration, the resulting mixture’s strength is not simply the arithmetic mean of the original percentages. Instead, the final concentration depends on both the volume and the strength of each component.
Concentration is usually expressed as a percentage of the solute relative to the total volume of the solution, though it can also be given in units such as molarity, molality, or mass percent.
For example, mixing 100 ml of a 10 % solution of compound A with 250 ml of a 20 % solution of the same compound requires a basic volume‑weighted calculation to determine the new concentration.
Convert the percentage to a decimal by dividing by 100, then multiply by the total volume. For the first component: (10 ÷ 100) × 100 ml = 10 ml of compound A. For the second: (20 ÷ 100) × 250 ml = 50 ml of compound A.
Sum the solute volumes: 10 ml + 50 ml = 60 ml of compound A in the final mixture.
Add the component volumes: 100 ml + 250 ml = 350 ml total solution volume.
Use the formula x = (c ÷ V) × 100, where c is the solute volume and V is the total volume. Here, c = 60 ml and V = 350 ml, so x = (60 ÷ 350) × 100 ≈ 17.14 %. Thus the final solution is 17.14 % compound A.
You can express concentration in any consistent unit—percent, molarity, mass percent, etc. The key is to use volume‑weighted averages. For instance, a 100 g salt solution containing 20 g salt has a mass‑percent concentration of 20 %: (20 g ÷ 100 g) × 100. If you only know the amount of solute and the volume, calculate molarity as moles ÷ liters (e.g., 0.6 mol NaCl in 0.45 L gives 1.33 M).
