Concentration units — mass %, volume %, ppm, ppb, molarity (M), molality (m), mole fraction: Question bank

Every item below tests a why or a boundary, never arithmetic. Companion prerequisites live in The Mole and Avogadro's Number, Molar Mass and Formula Mass, Density, and the temperature reasoning shows up again in Colligative Properties.

True or false — justify

Heating a 1 M solution to 60 °C keeps it exactly 1 M.

False. Warming expands the volume of solution, so the same moles now sit in more litres → molarity drops. Molarity carries volume in its denominator, and volume is temperature-sensitive.

Heating a 1 m solution keeps it exactly 1 m.

True. Molality divides moles by mass of solvent in kg, and mass never changes when you heat something — no atoms leave. Temperature has no handle on it.

Mole fraction of the solvent can equal 1.

True at the limit — pure solvent with zero solute gives

x_{solvent} = n_{solvent} / n_{solvent} = 1

. Adding any solute pushes it below 1 because the total moles in the denominator grow.

Adding 100 mL water to 100 mL ethanol gives 200 mL of solution.

False. Volumes are not additive — the smaller ethanol-water clusters pack together, so the total is slightly less than 200 mL. This is exactly why molarity is fixed after mixing in a volumetric flask, never by adding volumes.

For any solution, 1 ppm equals 1 mg/L.

False. ppm is a mass/mass ratio; mg/L is mass/volume. They coincide only when density

\approx 1

g/mL (water), because then 1 L weighs ≈ 1000 g so mass and volume basis line up.

Two mole fractions in a two-component solution must sum to 1.

True.

x_{A} + x_{B} = (n_{A} + n_{B}) / n_{total} = n_{total} / n_{total} = 1

. Mole fractions are just each part's slice of the whole pie of moles.

Doubling the solute always doubles the mass percent.

False. The added solute is also in the denominator (mass of solution = solute + solvent). Going from 20 g in 100 g solution to 40 g of solute makes it

40/120 = 33.3%

, not

40%

A very dilute aqueous solution has molarity ≈ molality.

True. When solute is tiny, the term

M \cdot M_{w}

m = \frac{1000 M}{1000 ρ - M M _{w}}

is negligible, and if

ρ \approx 1

then

m \approx M

. Both conditions — dilute and water-like density — are required.

Spot the error

"Mass % = mass of solute ÷ mass of solvent × 100."

Wrong denominator. It must be mass of solution (solute + solvent). Using solvent alone overstates concentration for anything but the most dilute cases.

"Molarity = moles of solute ÷ volume of solvent in litres."

Wrong denominator. Molarity uses volume of solution (the final total in the flask), not the solvent you started with. The mnemonic: molarity → solution.

"To make 0.5 M salt water, dissolve 0.5 mol salt in exactly 1 L of water."

Error. You dissolve 0.5 mol in enough water to reach 1 L of solution — the salt occupies space too, so you add water up to the mark, not a full litre first.

"ppm and % differ only by which element you're measuring."

Error. They differ only by the base of the scale — % is per 100, ppm is per

1 0^{6}

. Same fraction, bigger scaling factor, chosen so trace amounts read as tidy numbers instead of

0.0001%

"Volume % is the safest unit because volumes are precise."

Error. Volume-based units (volume %, molarity) change with temperature because liquids expand. For temperature-safe work you want mass- or mole-based units (molality, mole fraction).

"Since molality uses solvent mass, molarity must use solvent volume."

False symmetry. The two units deliberately break symmetry: molality is built on solvent mass (T-independent), molarity on solution volume (T-dependent). Don't assume one mirrors the other.

"1 M is a stronger solution than 1 m, always."

Error. Neither is universally stronger; their ratio depends on density and molar mass. For a dense heavy-solute solution

m

can exceed

M

(e.g. concentrated H₂SO₄), because the solvent mass drops below 1 kg.

Why questions

Why does a physical chemist studying freezing points prefer molality over molarity?

Because freezing/boiling shifts are measured at varying temperatures, and molarity's volume would drift with T. Molality stays fixed, so the concentration you plug in is honest at every temperature. See Colligative Properties.

Why multiply by 100 in mass % but by

1 0^{6}

in ppm?

The multiplier just rescales the same fraction to a convenient base — "per hundred" for ordinary amounts, "per million" for trace amounts so the number isn't a string of leading zeros.

Why is mole fraction dimensionless?

It divides moles by moles, so the units cancel completely. This makes it clean for theory (Raoult's law, partial pressures) where you want a pure ratio, not something tied to grams or litres.

Why does molarity need Density to convert into molality but mass % does not?

Molarity gives you a volume basis; to reach the mass basis molality needs, you must turn litres of solution into grams — that bridge is density. Mass % already lives in mass units, so no density is needed.

Why can't you convert molarity to molality without knowing the solute's molar mass?

You must subtract the solute's mass from the solution's mass to isolate solvent mass, and getting solute grams from moles requires molar mass (

grams = n \times M_{w}

). See Molar Mass and Formula Mass.

Why do reactions and stoichiometry favor molarity despite its temperature flaw?

Reactions count particles, and molarity delivers moles directly per convenient litre measured with lab glassware. The temperature drift is small and tolerable for room-temperature bench work. See Stoichiometry and Dilution.

Edge cases

What is the molality of pure solvent (no solute)?

Zero. With

n_{solute} = 0

, the numerator is 0 regardless of solvent mass, so

m = 0

. There is nothing dissolved.

What happens to mole fraction as you approach infinite dilution of solute A?

x_{A} \to 0

and

x_{solvent} \to 1

, because

n_{A}

becomes negligible in the total. The solvent's fraction approaches 1 but never quite reaches it while any solute remains.

If the solute is the solvent (a pure liquid), what is its mole fraction?

1 — there is only one component, so it is 100% of the moles. Concentration language collapses; there's nothing to be dissolved in.

Can mass % exceed 100%?

No. Solute mass can never exceed solution mass (solution = solute + solvent, both non-negative), so the ratio is capped at 1, i.e. 100% at pure solute.

For a gas-in-gas mixture, which "volume %" quirk should you watch?

Gas volumes are nearly additive and, at fixed T and P, volume fraction equals mole fraction (from Ideal Gas Law,

V \propto n

). So for ideal gases volume % and mole fraction ×100 agree — unlike liquids.

What does

M \approx m

break down first as you concentrate a solution?

The subtracted term

M \cdot M_{w}

grows, shrinking the solvent mass below 1 kg, so

m

climbs above

M

. Heavy solutes and high densities break the approximation fastest.

If two liquids mix with volume contraction, is the final molarity higher or lower than a naive "add-the-volumes" estimate?

Higher. The true solution volume is smaller than the sum, so the same moles divided by a smaller volume give a larger molarity than the additive guess predicted.

Recall One-line self-test

Which single property splits every unit into "T-safe" vs "T-drifts"? ::: Whether its denominator contains volume (drifts with temperature) or only mass/moles (safe). Volume%, molarity → drift; mass%, molality, mole fraction, ppm → safe.