Chemistry · Lesson
Molar concentration, mass fractions and other concentration units
Read concentration as a ratio with a defined numerator and denominator. Compare amount concentration, mass concentration, mass fraction and molality without silently swapping solution and solvent.
Back to the Chemistry mapBy the end, you can
- Use amount divided by final solution volume for molarity.
- Distinguish mass fraction, mass concentration and molality.
- Specify the basis of percent or ppm and use density when converting mass to volume.
Molar concentration uses final solution volume
Amount concentration, often called molarity, is c = n/V: amount n of a specified solute divided by final solution volume V. For 0.0200 mol in 0.250 L of solution, c = 0.0800 mol L⁻¹. The denominator is not just the volume of solvent used before mixing.
Specify the solute entity or analytical formula being counted. An analytical salt concentration and the concentrations of the individual ions it supplies are related quantities, not interchangeable labels. In this chapter mol L⁻¹ is written explicitly so the amount and volume units remain visible.
Other ratios answer other questions
Mass concentration divides solute mass by final solution volume, for example g L⁻¹. Mass fraction w divides component mass by total mixture mass; mass percent is 100w. Molality b divides solute amount by solvent mass in kilograms. Mole fraction x divides a component amount by the total amount of the specified mixture components.
The denominator is part of the meaning. Ten grams of solute in 100 g of total solution is 10% by mass; ten grams added to 100 g of solvent gives 110 g of solution if mass is conserved, so it is about 9.09% by mass. Writing only “10%” leaves the basis unclear.
| Quantity | Numerator | Denominator | Typical expression |
|---|---|---|---|
| Amount concentration c | Solute amount | Final solution volume | mol L⁻¹ |
| Mass concentration | Solute mass | Final solution volume | g L⁻¹ |
| Mass fraction w | Component mass | Total mixture mass | Dimensionless; 100w for mass percent |
| Molality b | Solute amount | Solvent mass | mol kg⁻¹ of solvent |
| Mole fraction x | Component amount | Total specified component amount | Dimensionless |
| Mass-based ppm | Component mass | Total mixture mass | 10⁶ times mass fraction |
Symbols are defined here. Solution means the final mixture; solvent means the solvent component alone. The table compares quantities rather than presenting interchangeable concentration units.
Density connects mass and volume
To convert a mass-based ratio into a volume-based concentration, you often need the solution density and its temperature. Density ρ is total solution mass divided by solution volume. It is not solute mass concentration. Use V = m_solution/ρ when a compatible density is supplied.
Volume-based concentration can change with thermal expansion even if no material is lost or reacts. Mass fraction and molality do not acquire that volume-expansion dependence in a closed mixture of unchanged composition. Evaporation or reactions can change composition, so the unchanged-composition condition still matters.
Percent and ppm require a basis
Mass-based ppm is mass fraction multiplied by 10⁶. Thus 2.00 ppm by mass means 2.00 mg of solute per 1.000 kg of solution in an illustrative composition. A conversion to mg L⁻¹ additionally requires density. The two numerical values are approximately equal only when density is approximately 1 kg L⁻¹.
Volume percent, mass percent and grams per 100 mL describe different ratios. Do not use a concentration value in a calculation until its basis, species and units are known.
Worked examples
Use final solution volume
A solution contains 0.0200 mol of specified solute in a final volume of 0.250 L. Find c.
- Use c = n/V.
- Substitute 0.0200 mol / 0.250 L.
- Retain three significant figures from the stated inputs.
c = 0.0800 mol L⁻¹.
Convert a stipulated mass composition
A hypothetical solution has 10.0 g of solute in 100.0 g of total solution. At the stated temperature its supplied density is 1.050 g mL⁻¹. Find mass percent and mass concentration. This density is invented for the exercise, not measured material data.
- Mass fraction = 10.0/100.0 = 0.100, giving 10.0% by mass.
- Final solution volume = 100.0/1.050 = 95.238… mL = 0.095238… L.
- Mass concentration = 10.0/0.095238… = 105 g L⁻¹.
10.0% by mass and 105 g L⁻¹. The density supplies the bridge from total solution mass to final volume.
Try it yourself
In c = n/V, is V the solvent volume or final solution volume?
Show the answer and reasoning
Final solution volume.
Using solvent volume silently changes the defined ratio.
Which mass belongs in the denominator of molality?
Show the answer and reasoning
Solvent mass in kilograms.
Total solution mass belongs to a different ratio.
A conserved mixture has 10 g solute plus 90 g solvent. What is its mass fraction of solute?
Show the answer and reasoning
0.10, or 10% by mass.
Total mixture mass is 100 g, so w = 10/100.
Does a mass-based ppm value always equal the same numerical mg L⁻¹ value?
Show the answer and reasoning
No.
Converting total solution mass to volume requires density.
What to carry forward
- A concentration ratio includes its species and basis.
- Use final solution volume for c.
- Molality uses solvent mass; mass fraction uses total mixture mass.
- Density and temperature matter in mass–volume conversions.
References
Teaching resources and reference material supporting this lesson’s explanations and examples.