# Percent by Mass or Weight, and, Mass or Weight Fraction (w/w or m/m)

## Key Concepts

- Mass fraction is also known as weight fraction.
mass fraction is given the symbol m/m

^{1}

weight fraction is given the symbol w/w - Percent by mass is also known as percent by weight.
percent by mass is given the symbol m/m % (or mass %)

percent by weight is given the symbol w/w % (or wt %) - Mass fraction (weight fraction) and percent by mass (percent by weight) are measurements of the concentration of a soluton.
- Mass fraction (weight fraction) is the ratio of the mass of one component of a solution to the total mass of the solution.
^{2} - Mass fraction
_{(a)}= mass_{(a)}÷ (mass_{(a)}+ mass_{(b)}+ mass_{(c)}+ ...)mass

_{(a)}= mass of component a

mass_{(b)}= mass of component b

mass_{(c)}= mass of component cFor a two component solution made up of a solute dissolved in a solvent:

mass fraction (solute) = mass

_{(solute)}÷ (mass_{(solute)}+ mass_{(solvent)}) - When added together, the mass fraction (weight fraction) of each component in the solution must equal one:
mass fraction

_{(a)}+ mass fraction_{(b)}+ mass fraction_{(c)}+ .... = 1For a two component solution made up of a solute dissolved in a solvent:

mass fraction

_{(solute)}+ mass fraction_{(solvent)}= 1 - Masses (weights) can be in any units as long as they are the same units for all components.
- Percent by mass (percent by weight) is the percent of the total mass of the solution that is one component.
Percent by mass = mass fraction × 100

OR

Percent by weight = weight fraction × 100This can also be expressed as:

mass % a = mass

_{(a)}÷ (mass_{(a)}+ mass_{(b)}+ mass_{(c)}+ ...) × 100

wt. % a = weight_{(a)}÷ (weight_{(a)}+ weight_{(b)}+ weight_{(c)}+ ...) × 100 - When added together, the percent by mass (or weight) of all components in the solution equals 100:
mass % a + mass % b + mass % c + .... = 100

OR

wt % a + wt % b + wt % c + .... = 100For a two component solution made up of a solute dissolved in a solvent:

mass % (solute) + mass % (solvent) = 100

OR

wt % (solute) + wt % (solvent) = 100