What Is Mass Fraction?
When you dissolve salt in water, the resulting liquid contains two substances: the solute (salt, the substance that dissolved) and the solvent (water, the liquid it dissolved in). Together they form a solution.
The mass fraction (also called weight fraction) tells us what proportion of the total mass of the solution is made up of the solute. It answers the question: "Of every gram (or kilogram) of this solution, how much is the dissolved substance?"
Mass fraction is written as the symbol w and can be expressed either as:
- A decimal between 0 and 1 (e.g. 0.05)
- A percentage between 0 % and 100 % (e.g. 5 %)
A mass fraction of 0.05 (or 5 %) means that in every 100 g of solution, 5 g is the dissolved substance (solute) and 95 g is the solvent.
The Formula
The formula for mass fraction is:
w = m(solute) ÷ m(solution)
Where:
- w = mass fraction (as a decimal, between 0 and 1)
- m(solute) = mass of the dissolved substance (in grams or kilograms)
- m(solution) = total mass of the solution = mass of solute + mass of solvent
To convert to a percentage, multiply by 100:
w% = [m(solute) ÷ m(solution)] × 100 %
Important: the mass of the solution is not the same as the mass of the solvent. When you dissolve 10 g of salt in 90 g of water, the solution has a mass of 100 g — not 90 g.
| Symbol | Meaning | Units |
|---|---|---|
| w | Mass fraction | Dimensionless (0 to 1) |
| w% | Mass fraction as percentage | % |
| m(solute) | Mass of dissolved substance | g or kg |
| m(solvent) | Mass of dissolving liquid | g or kg |
| m(solution) | Total mass of solution | g or kg |
A Simple Example
Suppose you dissolve 20 g of sugar in 180 g of water.
Step 1: Find the total mass of the solution. m(solution) = 20 g + 180 g = 200 g
Step 2: Apply the formula. w = 20 ÷ 200 = 0.10
Step 3: Convert to percentage. w% = 0.10 × 100 % = 10 %
This means the sugar solution is 10 % sugar by mass. In every 100 g of solution, 10 g is sugar and 90 g is water.
Real world: Reading food labels
When you pick up a bottle of fruit juice, the label lists the percentage of ingredients. "Sugar content: 12 g per 100 ml" means the mass fraction of sugar is approximately 12 %. Food manufacturers are legally required to list these mass fractions so consumers can compare products. A sports drink labelled "6 % carbohydrates" contains 6 g of carbohydrate in every 100 g of drink.
Mass Fraction vs. Concentration
Mass fraction and concentration are both ways of describing how much solute is in a solution, but they express different things:
| Property | Mass Fraction (w) | Concentration (c) |
|---|---|---|
| What it measures | Mass of solute per mass of solution | Amount of solute per volume of solution |
| Units | None (decimal) or % | g/L, g/mL, mol/L |
| Depends on temperature? | No | Yes (volume changes with temperature) |
| Useful for | Comparing recipes, food labels, industrial mixtures | Laboratory measurements, reactions |
Mass fraction is more practical for everyday use because it does not depend on temperature. The mass of a solution stays the same whether it is hot or cold. The volume, however, expands when heated — so concentration (expressed per litre) changes with temperature.
Mass fraction is especially useful when mixing or diluting solutions by mass, as in cooking or pharmacy. Concentration is preferred in laboratory settings where you measure volumes with pipettes and burettes.
More Real-World Examples
Salt in Seawater
The average salt content of seawater is about 3.5 %, meaning a mass fraction of 0.035. In every kilogram of seawater, approximately 35 g is dissolved salts. This is why seawater tastes so strongly salty — your body is not designed to handle such high salt concentrations.
Sugar in Syrup
Simple syrup used in cooking is often made by dissolving equal masses of sugar and water (e.g. 200 g sugar in 200 g water). The mass fraction would be: w = 200 ÷ 400 = 0.50, or 50 % sugar.
Blood Alcohol Content
Blood alcohol content (BAC) is sometimes expressed as a mass fraction (mass of alcohol per mass of blood). Legal driving limits in most European countries are around 0.05 % (w/w), meaning 0.05 g of alcohol per 100 g of blood.
Real world: Making saline solution for contact lenses
Contact lens saline solution typically contains 0.9 % sodium chloride (salt) by mass. This is called physiological saline — it matches the salt concentration of human tears. If the solution were more concentrated, it would draw water out of your eyes. If less concentrated, water would flow into the cells. The precise mass fraction is critical for safety and comfort.
Always use total solution mass in the denominator — not just solvent mass. A common mistake is to divide the solute mass by the solvent mass instead of the solution mass. Remember: m(solution) = m(solute) + m(solvent).
Practice Problems
A chemist dissolves 15 g of sodium chloride in 285 g of water. What is the mass fraction of sodium chloride in the solution? Express your answer as both a decimal and a percentage.
Show answer
Explain the difference between mass fraction and concentration, and state one advantage of using mass fraction.