Chemistry 2e · Composition of Substances and Solutions
Other Units for Solution Concentrations
On this page 9 sections
In 30 seconds
Molarity (previous topic) is the workhorse concentration unit, but it is not always the most convenient — or even the most meaningful — way to report how much solute is in a mixture. This topic surveys the other concentration units chemists actually use, each suited to a different job: mass percent and volume percent (ratios scaled to 100), mass/volume percent (grams per 100 mL, common in medical labeling), parts per million/billion (tiny concentrations for environmental reporting), mole fraction (unitless mole ratio), and molality (m) (moles per kilogram of solvent, temperature-independent).
The unifying idea: every concentration unit is a ratio of solute to solution (or solvent), and you can convert between units whenever you know the relevant masses, volumes, and molar masses.
Why this matters
Real-world concentration labels rarely say "molar." A bottle of household hydrogen peroxide says "3% H₂O₂" (mass/volume). A hospital saline bag is "0.9% NaCl" (mass/volume, i.e., 0.9 g NaCl per 100 mL). Industrial hydrochloric acid is sold as "37% HCl" (mass percent, with a Density Mass per unit volume (g/mL) Full entry → that lets you convert to molarity). Drinking-water regulations are written in parts per million or billion — the U.S. EPA's enforceable limit for lead in public drinking water, for example, is commonly cited as 15 ppb. Antifreeze labels report ethylene glycol by mass percent, while chemists studying freezing-point depression (colligative properties, Chapter 11) switch to molality because it does not change when temperature shifts the solution's volume. Knowing which unit is being used — and how to convert it — is the difference between reading a label correctly and mis-dosing a solution.
The college version
Core Concepts
Mass percent (% m/m)
Mass percent is the mass of solute divided by the total mass of the solution, multiplied by 100:
% (m/m) = mass of solutemass of solute + mass of solvent × 100
Because it uses masses, it is temperature-independent. A "5% (m/m) glucose solution" means 5 g of glucose per 100 g of total solution — that is, 5 g glucose + 95 g water.
Volume percent (% v/v) and mass/volume percent (% m/v)
Volume percent is used when both components are liquids:
% (v/v) = volume of solutevolume of solution × 100
Alcoholic beverages ("40% ABV") and mixed solvents use this unit. Mass/volume percent — grams of solute per 100 mL of solution — is the unit behind medical and consumer labels:
% (m/v) = mass of solute (g)volume of solution (mL) × 100
"0.9% NaCl" therefore means 0.9 g NaCl per 100 mL of solution. This unit is convenient (it needs only a balance and a graduated cylinder), but it is not a true ratio of like units, so converting it to molarity requires extra data.
Parts per million and parts per billion
For very dilute systems, chemists scale the mass ratio by powers of ten:
ppm = mass of solutemass of solution × 106 ppb = mass of solutemass of solution × 109
For aqueous solutions at ordinary concentrations, 1 ppm ≈ 1 mg solute per liter and 1 ppb ≈ 1 µg per liter — approximations that work because 1 L of dilute water solution has a mass near 1 kg. These units dominate environmental chemistry — nutrient levels, drinking-water limits, and trace-metal analyses are all reported in ppm/ppb.
Mole fraction
The mole fraction of component A is the ratio of its moles to the total moles of all components:
XA = nAntotal
Mole fractions are unitless, always sum to 1 over all components, and are the natural variable in Raoult's law and gas-mixture problems (Chapters 9 and 11). For a two-component solution of A in B, XA + XB = 1.
Molality
Molality is moles of solute per kilogram of solvent:
m = moles of solutekilograms of solvent
Because both numerator and denominator are mass-based, molality is unaffected by temperature — a crucial property for colligative-property calculations such as freezing-point depression and boiling-point elevation (Chapter 11), which depend on the number of solute particles per mass of solvent.
How It Works / Step-by-Step Process
- Read the label or problem: identify which unit is being used (look for "m/m," "v/v," "m/v," "ppm," mole fraction, or molality).
- Identify what the ratio's denominator includes — total solution mass, solution volume, total moles, or solvent mass.
- Convert everything to consistent units (grams, liters, moles) using molar masses and densities as needed.
- Convert between units when asked: mass percent → molarity needs density and molar mass; molarity → molality needs solvent mass; mole fraction needs molar masses of all components.
Common Confusions
| Do Not Confuse | With | Difference |
|---|---|---|
| Mass percent denominator | Solvent mass | Denominator is total solution mass (solute + solvent) |
| Mass/volume percent (g/100 mL) | Mass percent (g/100 g) | One is per 100 mL of solution, the other per 100 g of solution — numerically close only when density ≈ 1 g/mL |
| ppm | ppb | ppm = ×10⁶, ppb = ×10⁹ — ppb is 1000× smaller, used for trace contaminants |
| Mole fraction | Molality | Mole fraction is unitless moles/total moles; molality is mol solute per kg solvent |
| Molality (m) | Molarity (M) | m uses kg of solvent and is temperature-independent; M uses L of solution and varies with temperature |
| 1 ppm ≈ 1 mg/L | Exact equality | The mg/L equivalence is an approximation valid for dilute aqueous solutions where 1 L ≈ 1 kg |
Eli explains
The same idea, in plain words
Explain it like I’m 10
There are many ways to say how much chocolate is in a chocolate-milk recipe. You could say "one spoon of chocolate per glass of milk," or "10% chocolate," or "one chocolate per every nine milks," or even "one tiny chocolate bit in a million drops." All of them describe the same drink using different rulers — cups, percentages, ratios, or super-tiny amounts. Chemists do the same thing: molarity, mass percent, ppm, mole fraction, and molality are just different rulers for measuring "how much stuff is in the mixture," and each ruler is best for a particular job.
Worked example
Example 1: Mass percent from measured masses
Problem: 25.0 g of glucose is dissolved in 175.0 g of water. What is the mass percent of glucose?
Total solution mass = 25.0 g + 175.0 g = 200.0 g. Apply the formula:
% (m/m) = 25.0 g200.0 g × 100 = 12.5%
Answer: The solution is 12.5% glucose by mass. Note the denominator is the total mass, not the water mass.
Example 2: Molality from a weighed solute
Problem: 36.0 g of glucose (molar mass 180.16 g/mol) is dissolved in 250 g of water. Find the molality.
Step 1 — Convert grams of solute to moles:
n = 36.0 g × 1 mol180.16 g = 0.200 mol glucose
Step 2 — Convert solvent mass to kilograms:
250 g × 1 kg1000 g = 0.250 kg water
Step 3 — Divide moles by kilograms of solvent:
m = 0.200 mol0.250 kg = 0.80 mol/kg = 0.80 m
Answer: The molality is 0.80 m. The solvent (water), not the solution, goes in the denominator.
Example 3: Mole fraction
Problem: A mixture contains 0.100 mol of NaCl and 5.00 mol of water. What is the mole fraction of NaCl?
Total moles = 0.100 + 5.00 = 5.10 mol.
XNaCl = 0.100 mol5.10 mol = 0.0196
Answer: XNaCl = 0.0196 (unitless), and XH2O = 1 - 0.0196 = 0.980. The two fractions must sum to 1.
Key takeaways
- Mass percent = (mass solute ÷ total mass solution) × 100 — temperature-independent, needs only a balance.
- Volume percent = (volume solute ÷ volume solution) × 100 — for liquid-liquid mixtures.
- Mass/volume percent = (g solute ÷ mL solution) × 100 — the "0.9% saline" style of label; not convertible to molarity without extra data.
- ppm = mass ratio × 10⁶; ppb = mass ratio × 10⁹; for dilute water solutions, 1 ppm ≈ 1 mg/L and 1 ppb ≈ 1 µg/L.
- Mole fraction XA = nA/ntotal is unitless; all mole fractions in a mixture sum to 1.
- Molality m = mol solute / kg solvent — the temperature-independent unit for colligative properties.
- Converting mass percent → molarity requires the solution density and the solute's molar mass.
Check yourself
6 review questions from the chapter. Try each one, then open the answer.
What is the difference between 5% (m/m) and 5% (m/v) glucose solutions?
Show answer
5% (m/m) = 5 g glucose per 100 g total solution; 5% (m/v) = 5 g glucose per 100 mL solution. They coincide only when solution density is 1 g/mL.
Why is molality preferred over molarity in colligative-property calculations?
Show answer
Molality uses masses (mol solute per kg solvent), which do not change with temperature; molarity uses volume, which expands/contracts with temperature.
0.9% (m/v) NaCl: how many grams of NaCl are in 100 mL? In 500 mL?
Show answer
0.9 g per 100 mL, so 500 mL contains 0.9 × 5 = 4.5 g NaCl.
A lake sample contains 3 ppb of a contaminant. Is that a larger or smaller concentration than 3 ppm?
Show answer
Much smaller — ppb is 1000× more dilute than ppm (10⁹ vs 10⁶ scale factor).
In a two-component solution, XA = 0.30. What is XB?
Show answer
XB = 1 - XA = 0.70.
Why can't you convert a mass/volume percent to molarity using only the label?
Show answer
% (m/v) mixes grams and milliliters; converting to molarity needs moles (requires molar mass) and liters, plus the solution density to relate volume to mass.
Study tools & related lessonsKey vocabulary · Related
Key vocabulary
- Mass percent (% m/m)
- Grams of solute per 100 g of total solution
- Volume percent (% v/v)
- mL of solute per 100 mL of solution
- Mass/volume percent (% m/v)
- Grams of solute per 100 mL of solution
- Parts per million (ppm)
- 1 part solute per 10⁶ parts solution by mass
- Parts per billion (ppb)
- 1 part solute per 10⁹ parts solution by mass
- Mole fraction (X)
- Moles of one component ÷ total moles of all components
- Molality (m)
- Moles of solute per kilogram of solvent
- Density
- Mass per unit volume (g/mL)
Sources & references
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