CHM110H5 Chap.3 Solution Concentration Units
Solution Concentration Units
Five ways to say how much is dissolved
CHM110H5 expects you to define and know when to use five concentration measures: molarity (M), molality (m), normality (N), mole fraction (X) and percent. Each is a ratio of solute to some size of the mixture. Molarity is moles of solute per litre of solution. Molality is moles of solute per kilogram of solvent.
Normality counts equivalents per litre, so 1 M sulfuric acid is 2 N in hydrogen ions. Mole fraction divides the moles of one component by the total moles of everything present, and percent by mass gives grams of solute in 100 g of solution.
Volume and volume-mass percentages exist as well, but mass percent is the version that appears on bottles of concentrated acids and bases.
Why temperature matters
Solutions expand when warmed, so any unit with litres on the bottom drifts with temperature. Molarity and normality behave this way.
Molality, mole fraction and percent by mass are built only from masses and moles, so they hold steady as a sample heats or cools. That is the practical reason chemists switch to molality for boiling point and freezing point calculations, where the temperature is the very thing being changed. Normality carries a second subtlety: its value depends on the reaction, because it counts the ions that actually react.
In acid-base titrations the equivalence condition is equal moles of H+ and OH-, which is why normality times volume balances on both sides even when molarity times volume does not.
Density is the bridge
Most exam problems give a concentration on one basis and ask for another.
When the given unit uses mass and the target uses volume, density is the conversion factor between grams of solution and millilitres of solution. The reliable approach is to fix a convenient basis first: 100 g of solution for a percent problem, 1 L for a molarity problem, or 1 mol of total particles for a mole fraction problem.
Every other quantity then follows by one conversion at a time, with units written beside each number. For mole fraction, remember to convert the solvent into moles as well, using 18.02 g/mol for water.
Molarity versus molality
For aqueous solutions, molarity usually comes out smaller than molality. Dividing the two definitions shows that M/m equals the kilograms of solvent inside one litre of solution.
Pure water is close to 1 kg per litre, and dissolved solute takes up some of that space, so the ratio normally falls below 1. The two values agree in very dilute solutions and drift apart as solute builds up, especially when the solution is not much denser than water. Learning to predict which one is bigger, and by roughly how much, is a fast check on any calculated answer.
What this chapter covers
- 01
Molarity, molality and normality definitions
- 02
Mole fraction and percent by mass
- 03
Temperature dependence of volume-based units
- 04
Density as the mass to volume bridge
- 05
Choosing a calculation basis
- 06
Why molality usually exceeds molarity
Worked example · free
Concentrated nitric acid in three units
- 1Basis: 100 g of solution contains 65.0 g HNO3 and 100 - 65.0 = 35.0 g water.
- 2Moles: n(HNO3) = 65.0 / 63.01 = 1.032 mol; n(water) = 35.0 / 18.02 = 1.942 mol.
- 2Volume: 100 g / 1.39 g/mL = 71.94 mL = 0.07194 L, so M = 1.032 / 0.07194 = 14.3 M.
- 2Molality: m = 1.032 mol / 0.0350 kg water = 29.5 m.
- 1Mole fraction: X(HNO3) = 1.032 / (1.032 + 1.942) = 0.347.
Key terms
- Molarity
- Moles of solute per litre of solution, written M; it changes slightly with temperature because the solution volume expands or contracts as it warms or cools.
- Molality
- Moles of solute per kilogram of solvent, written m; built from masses only, so it stays constant when temperature changes and suits colligative property calculations.
- Normality
- Equivalents of solute per litre of solution, written N; it counts reactive units such as H+ ions, so 1 M sulfuric acid is 2 N in H+.
- Mole fraction
- Moles of one component divided by total moles of all components, written X; it has no units and all fractions in a mixture sum to one.
- Percent by mass
- Grams of solute in 100 grams of solution, written % w/w; it needs no molar mass and is common on labels of concentrated commercial acids and bases.
- Solution density
- Mass of solution per unit volume, usually in g/mL; it converts between a mass basis and a volume basis when switching between percent, molality and molarity.
Solution Concentration Units FAQ
Why is molarity usually smaller than molality for a water-based solution?
Molarity divided by molality equals the kilograms of solvent in one litre of solution. Dissolved solute occupies part of each litre, so less than about 1 kg of water remains, and the litre-based number comes out lower.
When should I use molality instead of molarity?
Choose molality whenever temperature changes during the problem, such as freezing point depression or boiling point elevation. Volume expands on heating and shifts molarity, while solvent mass and solute moles stay fixed.
Do I need the density to convert percent by mass into molarity?
Yes. Percent by mass relates grams of solute to grams of solution, but molarity needs litres of solution. Density turns that 100 g basis into millilitres, which completes the conversion.
Exam move
Memorise the five definitions by their denominators: litres of solution, kilograms of solvent, total moles, 100 g of solution. Then practise conversions in pairs, always fixing a basis first (100 g for percent, 1 L for molarity, 1 mol total for mole fraction). After each answer, check that mole fractions sum to one and that molality exceeds molarity for a concentrated aqueous solution.
Rework the lecture problems on concentrated hydrochloric acid and on the sulfuric acid solution with your own changed numbers until each takes under five minutes.
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