Chemistry · General chemistry II · Concept
Molality, mass percent, mole fraction and ppm
Concentration can be stated several ways, each with its own denominator. Molarity counts moles of solute per liter of solution, and molality counts moles of solute per kilogram of solvent. Mass percent and parts per million compare the solute’s mass with the solution’s, and mole fraction compares a component’s moles with the total moles. Converting between them takes molar masses and, whenever a volume meets a mass, the solution’s density.
Five ways to state a concentration
The name of each unit tells you its denominator: the solution’s volume, the solvent’s mass, the solution’s mass or the total moles.
| Unit | Definition | Changes with temperature? |
|---|---|---|
| Molarity, M | mol of solute per L of solution | Yes: the volume expands |
| Molality, m | mol of solute per kg of solvent | No |
| Mass percent | g of solute per g of solution, × 100% | No |
| Mole fraction, χ | mol of one component per total mol | No |
| ppm and ppb | g of solute per g of solution, × 10⁶ or × 10⁹ | No |
Why chemists use molality
Molality is built from masses, which do not change with temperature, while a solution’s volume does. That is why freezing-point depression and boiling-point elevation are calculated with molality.
Solvent or solution?
Molality divides by the solvent’s mass alone, while mass percent divides by the whole solution’s mass, solute included. Mixing the two up is the most common error.
Converting molarity and molality
Take 1 L of solution. Its density gives the solution’s mass; subtract the solute’s mass to get the solvent’s mass. Then divide the moles of solute by the kilograms of solvent.
Parts per million and billion
For trace amounts, multiply the mass fraction by 10⁶ for ppm or by 10⁹ for ppb. A liter of a dilute water solution weighs about 1 kg, so 1 ppm is about 1 mg of solute per liter.
Two meanings of mass percent
The mass percent of a solution compares the solute with the whole solution. Percent composition compares one element with a whole compound; the page on empirical formulas covers it.
Common mistakes
- Dividing by the solution’s mass for molality instead of the solvent’s mass.
- Leaving the solvent in grams: molality needs kilograms.
- Converting molarity to molality without the solution’s density.
- Leaving the solvent’s moles out of the mole-fraction denominator.
Key terms
- Molality
- Moles of solute per kilogram of solvent (mol/kg). Unlike molarity, it uses the solvent’s mass rather than the solution’s volume, so it doesn’t change with temperature.
- Mass percent
- mass percent = (mass of the component ÷ total mass of the solution) × 100%. Use the same mass units on the top and the bottom.
- Mole fraction
- mole fraction of A = (moles of A) ÷ (total moles of everything in the mixture). It has no units, and all the mole fractions in a mixture add up to 1.
- Parts per million
- Parts by mass multiplied by 10⁶: 1 ppm means 1 g of solute per 10⁶ g of solution. For dilute aqueous solutions, 1 ppm ≈ 1 mg/L.
- Parts per billion
- Parts by mass multiplied by 10⁹: 1 ppb means 1 g of solute per 10⁹ g of solution, about 1 μg/L for dilute aqueous solutions.
- Molarity
- Moles of solute per liter of solution (mol/L, or M). The volume is that of the whole finished solution, not just the solvent you started with.
- Density
- Mass per unit volume, such as g/mL. It converts between the mass and the volume of a sample, and it changes with temperature.
Work through an example
A solution is made by dissolving 10.0 g of NaCl in 250.0 g of water. Find its molality, its mass percent of NaCl and the mole fraction of NaCl.
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