The three percents, and which base each one uses
"Percent" solution can mean three different things. Each divides the dissolved substance by a different measure of the whole solution, so check which one a recipe or label means before you weigh anything.
| Type | Formula | Units | Where you see it |
|---|---|---|---|
| w/v (mass/volume) | g solute ÷ mL solution × 100 | g / mL | Pharmacy, saline, lab standards |
| w/w (mass/mass) | g solute ÷ g solution × 100 | g / g | Brines, food, industrial acids |
| v/v (volume/volume) | mL solute ÷ mL solution × 100 | mL / mL | Alcohol, spirits, solvents |
w/v is the practical shortcut: percent = grams per 100 mL. So 0.9% saline is 0.9 g of salt in 100 mL, and 3% hydrogen peroxide is 3 g in 100 mL.
Working out the mass to weigh
Weigh the solute, dissolve it in a little solvent, then make the solution up to its final volume in a graduated flask. Adding the solute to a full measure of water overshoots the volume and dilutes the concentration.
Converting between w/w and w/v needs the density
w/w never changes with temperature; w/v does, because the volume shifts as the liquid warms. To move between them you need the solution's density.
- Equal only at 1 g/mL. Pure water is 1.00 g/mL, so dilute aqueous solutions have w/w and w/v that nearly match.
- Denser solution, higher w/v. A 10% w/w brine at 1.075 g/mL is 10.75% w/v.
- ppm is just small percent. 1% w/w equals 10,000 ppm, so 0.001% is 10 ppm.
Common questions
What is the difference between w/v and w/w percent?
Both put the dissolved substance on top. w/w divides its mass by the mass of the whole solution; w/v divides its mass in grams by the volume of the solution in mL. They only match when the solution has a density of 1 g/mL. A 10% w/w solution at 1.2 g/mL is 12% w/v.
How many grams do I need for a given percent?
For w/v, grams equals percent times volume in mL divided by 100. A 5% w/v solution in 100 mL needs 5 g; in 250 mL it needs 12.5 g. Then top up to the final volume, do not just add that much water.
Can I add the volumes of two liquids to get the total?
No. 50 mL of ethanol plus 50 mL of water gives about 96 mL, not 100, because the molecules pack together. For v/v percent always make up to the final volume in a graduated flask rather than adding volumes.
