If you remove part of a well-mixed solution and replace that volume with pure water, the volume returns to its starting value but the moles of solute decrease. Repeating the process removes part of what remains after the first round.
Work out the fraction of solution left after one withdrawal. Because the refill restores the original volume, the concentration after that round is the previous concentration multiplied by that fraction.
- Make sure the solution is mixed before each withdrawal.
- Find the fraction that remains after withdrawing the sample.
- Apply that fraction once for each refill.
Worked example | Replace 50 cm³ twice
Start with 250 cm³ of a 0.800 mol/dm³ solution. Remove 50 cm³, then add pure water until the total volume is back to 250 cm³. Mix thoroughly and repeat the same steps.
Each withdrawal leaves 200/250 = 0.800 of the solute present at that point. The first refill gives 0.800 × 0.800 = 0.640 mol/dm³. The second gives 0.640 × 0.800 = 0.512 mol/dm³.
Check with the actual amount of solute
The original 0.250 dm³ contains 0.800 × 0.250 = 0.200 mol. The first withdrawal removes 0.040 mol, leaving 0.160 mol. The second withdrawal removes 0.032 mol, leaving 0.128 mol.
After the second refill, 0.128 mol occupies 0.250 dm³. That gives 0.512 mol/dm³ again. The second sample contains fewer moles because its concentration is lower.
Change the starting concentration
A well-mixed 200 cm³ solution has concentration 1.20 mol/dm³. Remove 50 cm³, restore the volume with pure water and mix. Repeat once. Find the final concentration.
Answer. Each round leaves 150/200 = 0.75 of the solute. The final concentration is 1.20 × 0.75² = 0.675 mol/dm³.
Frequently asked questions
Does taking a sample change the concentration of the liquid left behind immediately?
Taking a representative sample removes solute and solvent in the same proportion. The concentration changes when you add pure water.
Is withdrawing 100 cm³ once equivalent to two 50 cm³ withdrawals with a refill in between?
A single 100 cm³ withdrawal in the worked example leaves 60% of the original solute. Two 50 cm³ withdrawals with refills leave 64%.
Official information
SEAB, 2027 SEC G3 Chemistry syllabus (K324), Stoichiometry and the Mole Concept, solution concentration. Syllabus checked 11 November 2026. The examples are original.