Chemistry: Atoms First 2e · Composition of Substances and Solutions

Other Units for Solution Concentrations

9 min read

Reference-values note: EPA arsenic MCL (10 ppb) and lead action level (15 ppb) are commonly cited regulatory values; verify against current EPA regulations before citing in professional work.

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In 30 seconds
Why this matters
The college version
Eli explains
Worked example
Key takeaway
Check yourself
Study tools
Sources & references

In 30 seconds

Molarity is the most familiar concentration unit, but it is not always the most convenient. Molarity is defined per liter of solution, and because liquid volumes expand and contract with temperature, a molarity value drifts when the temperature changes. Chemists therefore keep a toolbox of units that describe the same mixture in different ways: mass percentage, volume percentage, mass-volume percentage, , , mole fraction, and molality. Each answers a slightly different question — "how much solute per 100 parts of mixture," "how many solute particles per 1,000,000 parts," or "how many moles of solute per kilogram of solvent" — and each fits a particular setting, from IV fluid labels to trace-contaminant reports. The key skill is not memorizing seven formulas, but knowing which unit fits which question and converting fluently between mass, moles, and solution composition.

Why this matters

Real chemistry happens in mixtures, and the concentration unit you choose shapes the calculation. In health care, IV solutions are labeled in (e.g., 5% dextrose means 5 g of dextrose per 100 mL of solution), while blood tests report glucose in milligrams per deciliter. Environmental agencies regulate trace contaminants in parts per billion — the EPA's maximum contaminant level for arsenic in U.S. drinking water is 10 ppb — because molarity would be unwieldy for such tiny amounts. Physical chemists prefer molality for colligative properties (freezing-point depression, boiling-point elevation) because it depends only on masses, which do not change with temperature. Mole fraction is essential for gas mixtures and Raoult's law. Mastering these units lets you read any concentration label, convert between units, and predict how a solution behaves — a skill used in every later chapter, from reaction stoichiometry to acid-base equilibria.

The college version

Core Concepts

Mass percentage: parts per hundred by mass

Mass percentage compares the mass of one component to the total mass of the mixture:

$mass percent = mass of component total mass of mixture \times 100 %$

For a solution, the total mass is solute plus solvent. Because it uses masses, is temperature-independent. It appears on commercial labels ("2% milk" means 2 g of milk fat per 100 g of milk) and in alloy specifications. A useful conversion: in any mass percentage, the percentage figure itself gives grams of component per 100 g of mixture — 2% milk has 2 g fat per 100 g total.

Volume percentage and mass-volume percentage

When both solute and solvent are liquids, concentration is often reported as volume percentage:

$volume percent = volume of solute volume of solution \times 100 %$

Ethanol in alcoholic beverages and isopropanol in rubbing alcohol are labeled this way (70% isopropanol means 70 mL isopropanol per 100 mL solution). Note that the denominator is the solution volume, not the sum of the separate liquid volumes — liquids can contract or expand slightly on mixing.

Mass-volume percentage mixes the two ideas: grams of solute per 100 mL of solution, standard in medicine and pharmacy (5% dextrose = 5 g per 100 mL).

$mass-volume percent = mass of solute (g) volume of solution (mL) \times 100 %$

Parts per million and parts per billion: tiny amounts, big consequences

For trace analysis, percentages are too coarse. Parts per million (ppm) and parts per billion (ppb) express the ratio of component mass to total mixture mass on enormous scales:

$ppm = mass of component total mass of mixture \times 106$

$ppb = mass of component total mass of mixture \times 109$

A convenient shortcut for dilute aqueous solutions: since 1 L of water has a mass of about 1 kg (10⁶ mg), 1 ppm ≈ 1 mg/L and 1 ppb ≈ 1 µg/L — which is why water-quality reports switch freely between "10 ppb arsenic" and "10 µg/L arsenic." Both units are temperature-independent because they are mass ratios.

Mole fraction: counting particles

Mole fraction X is the ratio of moles of one component to total moles of all components:

$X A = n A n A + n B + n C + \dots$

Mole fractions are dimensionless, between 0 and 1, and all mole fractions in a mixture sum to exactly 1. For ideal gas mixtures, a gas's mole fraction equals the ratio of its partial pressure to total pressure — the foundation of Dalton's law. In solution chemistry, mole fraction appears in Raoult's law, which relates vapor pressure to the mole fraction of solvent.

Molality: moles per kilogram of solvent

Molality (symbol m, lowercase) is moles of solute per kilogram of solvent — not solution:

$m = moles of solute kilograms of solvent$

Because it uses only masses, molality is unaffected by temperature, which makes it the unit of choice for colligative-property calculations (Chapter 11). Do not confuse it with molarity (M), which is moles of solute per liter of solution. For dilute aqueous solutions the numerical values are close — 1 L of water ≈ 1 kg — but they are not identical and diverge as concentration rises.

Common Confusions

Do Not Confuse	With	Difference
Molarity (M)	Molality (m)	Molarity = moles ÷ liters of solution; molality = moles ÷ kg of solvent. Only molality is temperature-independent
Mass percent	Mass-volume percent	Mass percent uses total mass (g/g); mass-volume percent uses grams solute per 100 mL solution
ppm	ppb	A factor of 1000: ppm is 10⁶ scale, ppb is 10⁹ scale. 1 ppm = 1000 ppb
Volume percent using added liquid volumes	Volume percent using final solution volume	Liquids can contract/expand on mixing; always use the final solution volume as the denominator
Mole fraction (mol/mol)	Mass fraction (g/g)	Mole fraction counts particles (moles); mass fraction counts mass. Same mixture gives different values for each
"1 ppm = 1 mg/L" as an exact rule	As a dilute-water approximation	The shortcut assumes solution density ≈ 1 g/mL; it fails for concentrated or non-aqueous solutions

Eli explains

The same idea, in plain words

Explain it like I’m 10

Imagine you made lemonade and want to tell a friend how sweet it is. You could say "5 spoonfuls of sugar in every 100 spoonfuls of drink" (percent), "5 spoonfuls of sugar in a million spoonfuls" (ppm), or "5 spoonfuls of sugar for every kilogram of water" (molality). They all describe the same lemonade — just in ways that are handy for different situations, like medicine, pollution, or freezing point.

Worked example

Example 1: Mass percent of a saline solution

A pharmacy technician dissolves 4.50 g of sodium chloride (NaCl) in 95.50 g of water. What is the mass percent of NaCl in the resulting solution?

Step 1 — Write the formula before substituting:

$mass percent = mass of solute total mass of solution \times 100 %$

Step 2 — Find the total mass: total mass = 4.50 g + 95.50 g = 100.00 g.

Step 3 — Substitute and solve:

$mass percent = 4.50 g 100.00 g \times 100 % = 4.50 %$

The solution is 4.50% NaCl by mass.

Example 2: Converting mass to ppm — trace lead in water

A water sample contains 2.50 × 10^-4 g of lead dissolved in 500.0 g of water. Express the lead concentration in ppm.

Step 1 — Write the formula:

$ppm = mass of component total mass of mixture \times 106$

Step 2 — Total mass: 500.0 g + 2.50 × 10^-4 g ≈ 500.0 g (the solute mass is negligible).

Step 3 — Substitute with units canceling:

$ppm = 2.50 \times 10 -4 g 500.0 g \times 106 = 0.500 ppm$

Using the dilute-water shortcut, 0.500 ppm ≈ 0.500 mg/L. The sample is well above the EPA action level for lead in drinking water (15 ppb = 0.015 mg/L), so this water would require treatment.

Example 3: Molality — moles per kilogram of solvent

What is the molality of a solution made by dissolving 8.00 g of NaOH (molar mass 40.00 g/mol) in 250.0 g of water?

Step 1 — Write the formula:

$m = moles of solute kilograms of solvent$

Step 2 — Convert solute mass to moles (dimensional analysis):

$8.00 g NaOH \times 1 mol NaOH 40.00 g NaOH = 0.200 mol NaOH$

Step 3 — Convert solvent mass to kilograms: 250.0 g = 0.2500 kg.

Step 4 — Substitute:

$m = 0.200 mol 0.2500 kg = 0.800 mol/kg = 0.800 m$

Note: if the solution's density were 1.00 g/mL, the molarity would be 0.200 mol0.258 L ≈ 0.775 M — close to, but not equal to, the molality, because one uses solution volume and the other solvent mass.

Example 4: Mole fraction in a mixture

A solution contains 2.00 mol of glucose and 55.5 mol of water. What is the mole fraction of glucose?

Step 1 — Write the formula:

$X glucose = n glucose n glucose + n water$

Step 2 — Substitute:

$X glucose = 2.00 mol 2.00 mol + 55.5 mol = 2.00 57.5 = 0.0348$

The mole fraction of glucose is 0.0348 (unitless), and the mole fraction of water is 1 - 0.0348 = 0.9652. The two sum to 1, as they must.

Key takeaways

Mass percent and volume percent both use "per 100 parts of the whole mixture," and both use solution mass/volume in the denominator.
Mass-volume percent is grams of solute per 100 mL of solution — the standard for IV fluids and pharmacy labels.
ppm and ppb are mass ratios scaled by 10⁶ and 10⁹; for dilute water, 1 ppm ≈ 1 mg/L and 1 ppb ≈ 1 µg/L.
Molality m = moles solute ÷ kilograms solvent; molarity M = moles solute ÷ liters solution. Only molality is temperature-independent.
Mole fraction X is dimensionless, ranges 0–1, and all mole fractions in a mixture sum to 1; for gases, X_A = P_A/P_total (Dalton's law).
To convert between units, always route through moles: mass → moles (via molar mass) → moles of other component (via ratio) → desired unit.

Check yourself

6 review questions from the chapter. Try each one, then open the answer.

A solution is prepared by dissolving 12.0 g of KCl in 188.0 g of water. What is the mass percent of KCl?
Show answer
Total mass = 12.0 g + 188.0 g = 200.0 g; mass percent = (12.0/200.0) × 100% = 6.00%.
Why is molality preferred over molarity for colligative-property calculations?
Show answer
Molality uses kilograms of solvent, a mass, which does not change with temperature; molarity uses liters of solution, and liquid volumes expand/contract with temperature, so molarity changes.
A drinking-water test reports nitrate at 8.0 ppm. Express this concentration in ppb and in mg/L (dilute-water approximation).
Show answer
8.0 ppm × 1000 = 8000 ppb; using 1 ppm ≈ 1 mg/L, the concentration is 8.0 mg/L.
What is the mole fraction of water in a solution containing 1.00 mol of sucrose and 9.00 mol of water?
Show answer
X_water = 9.00/(1.00 + 9.00) = 9.00/10.00 = 0.900.
What mass of glucose is needed to prepare 250.0 mL of a 5.0% (m/v) glucose solution?
Show answer
5.0% (m/v) means 5.0 g glucose per 100 mL; for 250.0 mL: 5.0 g × (250.0/100) = 12.5 g glucose.
Explain the difference between the denominators in molarity and molality, and why that difference matters when temperature changes.
Show answer
Molarity's denominator is liters of solution; molality's is kilograms of solvent. When temperature rises, the solution expands (volume increases) so molarity falls, while the solvent mass is unchanged so molality stays constant.

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Study tools & related lessonsKey vocabulary · Related

Key vocabulary

Mass percent: Grams of one component per 100 g of total mixture
Volume percent: mL of liquid solute per 100 mL of solution
Mass-volume percent: Grams of solute per 100 mL of solution
Parts per million (ppm): Mass ratio scaled by 10⁶
Parts per billion (ppb): Mass ratio scaled by 10⁹
Mole fraction (X): Moles of one component ÷ total moles of all components
Molality (m): Moles of solute ÷ kilograms of solvent

Sources & references

openstax.org — Chemistry Atoms First 2e

This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.

Educational content only. It is not medical, legal or professional advice. Found an error? Tell us.

In 30 seconds

Why this matters

The college version

Core Concepts

Mass percentage: parts per hundred by mass

Volume percentage and mass-volume percentage

Parts per million and parts per billion: tiny amounts, big consequences

Mole fraction: counting particles

Molality: moles per kilogram of solvent

Common Confusions

The same idea, in plain words

Worked example

Example 1: Mass percent of a saline solution

Example 2: Converting mass to ppm — trace lead in water

Example 3: Molality — moles per kilogram of solvent

Example 4: Mole fraction in a mixture

Key takeaways

Check yourself

Keep learning

Key vocabulary

Related lessons

Sources & references