3.4 Other Units for Solution Concentrations

Solution Concentration Units

Beyond molarity, chemists use several other units to describe how much solute is in a solution. The right unit depends on the situation: mass percentage works well for mixing solutions by weight, ppm is better for trace contaminants, and molality is useful when temperature changes are involved. This section covers each unit, when to use it, and how to convert between them.

Mass Percentage, Volume Percentage, and Mass-Volume Percentage

These three percentage-based units all follow the same logic: divide the amount of solute by the amount of solution, then multiply by 100%. They differ in whether you're measuring mass, volume, or a combination.

• Mass percentage (% w/w) is the mass of solute divided by the total mass of the solution, times 100%.

$\text{Mass percentage} = \frac{\text{Mass of solute}}{\text{Mass of solution}} \times 100\%$

This is most common for solid-solid or solid-liquid mixtures. For example, if you dissolve 5 g of NaCl in 95 g of water, the total solution mass is 100 g, so the mass percentage is 5%.

• Volume percentage (% v/v) is the volume of solute divided by the total volume of solution, times 100%.

$\text{Volume percentage} = \frac{\text{Volume of solute}}{\text{Volume of solution}} \times 100\%$

This is standard for liquid-liquid solutions. Rubbing alcohol labeled "70% isopropanol" means 70 mL of isopropanol per 100 mL of solution.

• Mass-volume percentage (% w/v) is the mass of solute (in grams) divided by the volume of solution (in mL), times 100%.

$\text{Mass-volume percentage} = \frac{\text{Mass of solute (g)}}{\text{Volume of solution (mL)}} \times 100\%$

You'll see this frequently in medical and pharmaceutical contexts. A "0.9% w/v saline" IV bag contains 0.9 g of NaCl per 100 mL of solution.

Parts-per-Million and Parts-per-Billion

When concentrations are extremely small, percentages become awkward (imagine writing 0.0001%). That's where ppm and ppb come in.

• Parts-per-million (ppm) uses the same ratio as mass percentage, but multiplied by 1,000,000 instead of 100.

$\text{ppm} = \frac{\text{Mass of solute}}{\text{Mass of solution}} \times 1{,}000{,}000$

For dilute aqueous solutions (where the solution density is close to 1 g/mL), 1 ppm ≈ 1 mg/L. The EPA's limit for lead in drinking water is 15 ppb, which is 0.015 ppm. Fluoride in tap water is typically around 0.7 ppm.

• Parts-per-billion (ppb) works the same way but multiplied by 1,000,000,000.

$\text{ppb} = \frac{\text{Mass of solute}}{\text{Mass of solution}} \times 1{,}000{,}000{,}000$

For dilute aqueous solutions, 1 ppb ≈ 1 μg/L. This unit is used for trace contaminants like mercury in water or pesticide residues in food.

Mole-Based Concentration Units

These units express concentration in terms of moles, which makes them especially useful for stoichiometry and thermodynamic calculations.

• Molarity (M) is moles of solute per liter of solution.

$M = \frac{\text{mol solute}}{\text{L solution}}$

This is the most common lab unit. A 1.0 M NaCl solution contains 1.0 mol of NaCl per liter of solution. One thing to watch: because volume changes with temperature, molarity is temperature-dependent.

• Molality (m) is moles of solute per kilogram of solvent (not solution).

$m = \frac{\text{mol solute}}{\text{kg solvent}}$

Because mass doesn't change with temperature, molality stays constant regardless of temperature. That's why it's preferred for colligative property calculations (boiling point elevation, freezing point depression).

• Mole fraction ($\chi$) is the moles of one component divided by the total moles of all components.

$\chi_A = \frac{\text{mol A}}{\text{mol A} + \text{mol B} + \cdots}$

Mole fractions are unitless and always add up to 1. They show up in vapor pressure calculations (Raoult's law) and gas mixture problems.

• Normality (N) is the number of equivalents of solute per liter of solution.

$N = \frac{\text{equivalents of solute}}{\text{L solution}}$

An "equivalent" depends on the reaction type. For acids, it's the moles of $\text{H}^+$ the acid can donate; for bases, it's the moles of $\text{OH}^-$ it can accept. So 1 M $\text{H}_2\text{SO}_4$ is 2 N because each mole donates 2 moles of $\text{H}^+$. Normality is less common in intro courses but appears in titration work.

Conversion of Concentration Units

Converting between units usually requires knowing the solution's density and the solute's molar mass. Here are the most common conversions.

Molarity → Mass Percentage:

1. Multiply molarity by the molar mass of the solute to get grams of solute per liter of solution (g/L).
2. Use the solution density (g/mL) to find the mass of 1 L of solution in grams: $\text{density} \times 1000 \text{ mL}$.
3. Divide the solute mass (from step 1) by the solution mass (from step 2), then multiply by 100%.

Mass Percentage → Molarity:

1. Assume a convenient amount of solution (e.g., 100 g, so the solute mass in grams equals the percentage value).
2. Use the solution density to convert that mass of solution to a volume in liters: $\text{Volume (L)} = \frac{\text{mass of solution (g)}}{\text{density (g/mL)} \times 1000}$.
3. Convert the solute mass to moles using its molar mass.
4. Divide moles of solute by volume in liters to get molarity.

Molarity → ppm or ppb:

1. Multiply molarity by the molar mass to get g/L.
2. Multiply by 1,000 to convert to mg/L (which equals ppm for dilute aqueous solutions).
3. For ppb, multiply by 1,000,000 to convert to μg/L instead.