Mass fraction of solute
Mass fraction tells what part of a solution's total mass comes from a chosen solute. It is a ratio, so it has no unit; multiplying by 100% expresses the same composition as a percentage.
Learning goals
- Calculate solution mass from solute and solvent masses.
- Calculate mass fraction and mass percent.
- Rearrange the formula to find an unknown mass.
- Predict how adding solvent, adding solute, or evaporating solvent changes composition.
- Check answers with units and reasonable bounds.
1. The part-whole relationship
$m_{solution}=m_{solute}+m_{solvent}$
$w_{solute}=\dfrac{m_{solute}}{m_{solution}}$
$w_{solute}(\%)=\dfrac{m_{solute}}{m_{solution}}\times100\%$
The numerator and denominator must use the same mass unit. For example, 20 g solute plus 80 g water gives 100 g solution, so $w=20/100=0.20=20\%$.
Analogy: mass fraction is a part-whole bar. The solute is one segment; the entire bar is solute plus solvent.
2. A reliable calculation routine
- Write the known masses with units.
- Find total solution mass if necessary.
- Choose the required form: decimal fraction or percent.
- Substitute values with matching units.
- Calculate and label the result.
- Check that a mass fraction is from 0 to 1 and a percent from 0% to 100%.
Warning: divide by the mass of the whole solution, not by solvent mass alone.
3. Rearranging the formula
| Unknown | Useful form |
|---|---|
| Solute mass | $m_{solute}=w\,m_{solution}$ |
| Solution mass | $m_{solution}=m_{solute}/w$ |
| Solvent mass | $m_{solvent}=m_{solution}-m_{solute}$ |
Convert percent to decimal before multiplication or division: 15% = 0.15.