Solution mass percent:
how much of the liquid's weight is the dissolved part

What a mass-percent label tells you

A bottle labelled 5% w/w means that for every 100 g of liquid in the bottle, 5 g is the dissolved substance and 95 g is solvent. The 'w/w' stands for weight by weight, so both parts are measured on a balance, not with a measuring cylinder.

The advantage of mass-based percent is that it does not change with temperature. Volumes expand when heated, but a gram stays a gram, so w/w strengths are stable and are used for reagents, food formulations and pharmaceutical preparations where accuracy is important.

Do not confuse it with w/v (grams per 100 mL) or v/v (millilitres per 100 mL). Those are different bases, and the same label number can describe quite different amounts of solute.

The formula and the denominator trap

The most frequent error is dividing by the solvent mass alone. That gives a number slightly higher than the true percentage, and the gap grows as the solution gets stronger. For dilute solutions it hardly matters; for 20 or 30 percent solutions it matters a great deal.

Solute and solution masses must be in the same unit. Weigh in grams, or convert milligrams and kilograms first.

Worked example: 15 g in 300 g of solution

A technician weighs a finished solution and finds a total mass of 300 g, of which 15 g is dissolved solute. What strength is it?

To make a fresh batch of 250 g at the same strength: solute needed is 5% of 250 = 12.5 g, and solvent is 250 − 12.5 = 237.5 g. Weigh the solute first, then add solvent until the total reads 250 g on the balance.

A percentage-of-a-number tool does the first step directly, since 5% of 250 is the same operation as 0.05 × 250.

Preparation reference for common batch sizes

The 0.9% row is the familiar saline strength. It is quoted here as an arithmetic illustration only; any solution for medical use must be prepared and checked under proper pharmaceutical procedures.

When the solvent is water, 1 g of water is close to 1 mL, so solvent masses can be measured by volume for rough work. Use a balance for anything that needs accuracy.

Moving between mass percent and other units

• To ppm: multiply percent by 10,000. A 5% w/w solution is 50,000 ppm.
• To grams per 100 mL: multiply the mass percent by the solution density in g/mL. A 5% solution with a density of 1.03 g/mL holds about 5.15 g per 100 mL.
• To molarity: grams of solute per litre divided by the molar mass, which needs the density of the solution.

The density step is the one people skip. Without it, the number of grams in a litre of a 5% solution cannot be found exactly; assuming the density is 1.00 g/mL is acceptable only for dilute solutions.

Mixing, diluting and evaporating by mass

Mass percent behaves nicely because masses add. To combine solutions, add the solute masses and the solution masses separately and divide once at the end.

Mix 200 g of a 10% solution with 300 g of a 5% solution. Solute is 20 + 15 = 35 g and the total is 500 g, so the blend is 35 ÷ 500 = 7%. Averaging 10 and 5 without weighting would wrongly give 7.5%.

To dilute 200 g of the 10% solution down to 4%, the solute stays at 20 g, so the final mass must be 20 ÷ 0.04 = 500 g. Add 500 − 200 = 300 g of solvent.

Evaporation works in reverse. If 100 g of 5% solution loses 40 g of water, the 5 g of solute now sits in 60 g, so the strength rises to 5 ÷ 60 = 8.3%.

• Track solute mass through each step; it is the quantity that does not change in dilution or evaporation.
• Convert any volumes to mass with density before blending.
• Recompute from the final masses, not from rounded percentages.

Checking a finished batch

A quick check on any prepared solution is to rebuild the percentage from the masses you actually recorded. If the total reads 251.3 g and you added 12.5 g of solute, the true strength is 12.5 ÷ 251.3 = 4.97 percent, close enough to 5 for most purposes but worth noting if accuracy matters.

Record the solute purity, the balance used and the date. Strengths of volatile or hygroscopic solutes drift, and a note on the bottle makes the label trustworthy later.

If you need a result to a tighter tolerance, weigh to at least one more decimal place than the tolerance requires, since a balance reading is itself uncertain by its last digit.

Errors to avoid when making up solutions

• Adding the solvent first and then weighing the solute against a total target. Zero the vessel, add solute, then bring the total up to the final mass.
• Measuring solvent by volume while the target is by mass, which hides the density difference.
• Forgetting the purity of the solute. A 95 percent pure reagent needs 12.5 ÷ 0.95 = 13.2 g to supply 12.5 g of active substance.
• Rounding too early. Keep full figures until the final weighing.