Mass percent concentration:
formula and worked example

Concentration you can read off a balance

Mass percent expresses how much of a mixture, by weight, is the substance of interest. Because it only needs a balance, it is the concentration of choice on product labels, for alloys and for industrial blends. There are no volumes to read and no density to look up, so it is also the least error-prone way to state a recipe.

It is a pure ratio. Whether the batch is a few grams or several tonnes, a 6% solution has the same proportion of solute in it, and a measured share of any total can be calculated by simple multiplication.

The unit is easy to extend. Parts per million and parts per billion are the same idea scaled to very small fractions, and a percentage can always be converted to them by multiplying by ten thousand or ten million. Once the mass fraction is clear, moving between these ways of stating it is only a matter of shifting the decimal point.

Formula, inputs and units

Mass percent is the mass of solute as a fraction of the total mass of the solution, multiplied by 100.

• Solute mass: the mass of the dissolved component, in any mass unit.
• Solution mass: the mass of solute plus solvent, in the same unit as the solute mass.
• Result: a percentage, written as % w/w, meaning weight by weight.

Because both masses use the same unit, it cancels. You can enter grams, kilograms or tonnes, as long as both are the same.

Worked example: 15 g of solute in 250 g of solution

1. 1Solute mass: 15 g.
2. 2Total solution mass: 250 g, which already includes the 15 g.
3. 3Take the ratio: 15 / 250 = 0.06.
4. 4Convert to percent: 0.06 x 100 = 6 % w/w.

By subtraction, the solvent is 250 - 15 = 235 g. If you had divided by 235 you would have got 6.38%, which is the sort of subtle overstatement this formula's wording is designed to avoid.

What the percentage means in use

The percentage tells you the share of the solution that is solute, so a 6% solution is 94% solvent. Strength is judged against the purpose: a few percent is typical for many dilute working solutions, while concentrated stocks may be tens of percent. Ranges depend on the substance and its solubility, so there is no universal good or bad value.

To turn the percentage into a usable quantity, multiply by the batch size. A 6% solution in a 2 kg batch contains 0.12 kg of solute. To go the other way, divide the required solute by the percentage as a fraction to find the batch size.

Mass percent is independent of temperature, since mass does not expand. It cannot, however, be converted to molarity without the solution's density and the solute's molar mass.

How more solute shifts the percentage

A 10% larger solute mass moved the figure from 6% to 6.6%, a proportional increase of 10% in the percentage but only 0.6 percentage points. The distinction between percent change and percentage-point change matters when reporting results. Note also that in this scenario the solution mass was held at 250 g; in practice, adding solute to a fixed amount of solvent also increases the total, so the real percentage rises slightly less than in a naive calculation.

Errors that skew a mass percent

• Dividing by the solvent mass rather than the total solution mass.
• Mixing units, for example solute in milligrams against solution in grams, which gives a result a thousand times too small.
• Confusing % w/w with % w/v. A w/v percentage uses millilitres of solution in the denominator and depends on density.
• Forgetting that a hydrated solid brings its water along, so the solute mass should be the anhydrous component if that is what the percentage refers to.

Rounding can also hide a problem. A result like 6.0% quoted from 15.4 g in 250 g actually reflects 6.16%, and in a formulation with a tight tolerance that difference matters. Keep the unrounded fraction through the calculation and round only when reporting.

Making a solution to a target percentage

Decide the total batch mass, multiply by the percentage as a fraction to get the solute mass, weigh that, then add solvent until the total reaches the batch mass. For a 250 g batch at 6%, that is 15 g of solute and 235 g of solvent.

Consider a practical case: a cleaning solution is specified as 6% w/w of an active ingredient and the batch is to be 2 kg. The active ingredient required is 0.06 x 2000 g = 120 g, and the remaining 1880 g is the carrier. Checking that 120 divided by 2000 returns 0.06 confirms the batch before anything is mixed, which is far cheaper than discovering an error afterwards.