A solution contains 20 g of solute in 180 g of solvent. If the solvent is water, what is the concentration of the solution in terms of mass by mass percentage?
- (a)11.1%
- (b)22.2%
- (c)10%
- (d)20%
Correct — C, 10%. Mass by mass percentage is the mass of solute expressed as a percentage of the mass of the whole solution, and the whole solution is solute plus solvent. Here the solute is 20 g and the solvent 180 g, so the solution weighs 20 + 180 = 200 g. The concentration is (20 ÷ 200) × 100 = 10%. The single step that decides the question is remembering to add the two masses before dividing. Every wrong option in the list is what comes out of dividing by the wrong quantity.
- (a)11.1% — This is 20 ÷ 180, the solute divided by the solvent alone rather than by the solution. It is the answer to a mass-by-mass ratio, not to a mass percentage.
- (b)22.2% — Twice the previous figure — it comes from 40 ÷ 180, or from doubling the solute by mistake. Nothing in the stem supports 40 g of anything.
- (d)20% — This reads the 20 g figure straight off as a percentage, which would only be right if the solution weighed exactly 100 g.
Concentration says how much solute a given quantity of solution holds. Mass by mass percentage takes the mass of solute over the mass of solution, times a hundred; mass by volume percentage takes the mass of solute over the volume of solution; volume by volume percentage is used when both are liquids. The denominator is always the solution, never the solvent on its own.
The mention of water in the stem is there to reassure rather than to be used — no density is needed and no volume is asked for, so 'if the solvent is water' changes nothing in the arithmetic. Work in three steps and the traps disappear: add the masses to get the solution, divide the solute by that, multiply by a hundred. Option (a) is the one to watch, because 11.1% is exactly what an examinee gets by dividing by the solvent, and it looks like a properly worked figure rather than a guess.
- Mass by mass percentage = (mass of solute ÷ mass of solution) × 100.
- The mass of the solution is the mass of the solute plus the mass of the solvent.
- 20 g in 180 g of water gives a 200 g solution and a concentration of 10%.
- Mass by volume percentage divides the mass of solute by the volume of the solution instead.
- The solvent is the component present in the larger amount; the solute is dissolved in it.
Every distractor here is a division by the wrong denominator, so naming the denominator first settles the item.
- Dividing by the mass of solvent instead of the mass of solution.
- Reading the extra information about water as a signal that a density or volume calculation is needed.
- Confusing mass percentage with molality, which does use the solvent mass in its denominator.
As a one-step numerical with the solute and solvent masses given separately, so that the candidate has to form the solution mass.
20 g of common salt is dissolved in 180 g of water. What is the mass percentage of the salt in the solution ?
- (a) 5%
- (b) 9%
- (c) 10%
- (d) 15%
Answer(c) 10%
The same sum with the same two numbers, four years earlier and with common salt named as the solute. Both give a 200 g solution and both answer 10 per cent, and both offer the divide-by-the-solvent figure among the options.
- practice — not a real PYQ
A solution is made by dissolving 5 g of sugar in 45 g of water. Its concentration by mass by mass percentage is
- (a)5%
- (b)10%
- (c)11.1%
- (d)20%
Answer(b) 10% — the solution weighs 5 + 45 = 50 g, and 5 ÷ 50 × 100 gives 10 per cent.
- practice — not a real PYQ
In expressing the concentration of a solution as mass by mass percentage, the denominator used is the mass of the
- (a)solute
- (b)solvent
- (c)solution
- (d)container
Answer(c) solution — that is, the solute and the solvent taken together, which is why the two masses must be added first.