Mass Percent, Volume Percent, and PPM/PPB
Mass percent, volume percent, ppm and ppb are ways of expressing the concentration of a solution as a fraction of the whole: parts of solute per 100 parts, per million parts or per billion parts of solution. In brief: mass percent = (mass of solute / mass of solution) × 100, so 12.0 g of NaCl in 88.0 g of water (100.0 g of solution) is a 12.0 % solution, and 1 % equals 10,000 ppm.
These units are easy to use because they do not require molar masses. They appear on food labels, in medicines, in environmental regulations and in the specifications of alloys. This article defines each unit, shows the conversion between them and solves typical problems with worked examples.
What is mass percent?
Mass percent, also called weight percent or percent by mass (w/w), tells how many grams of solute are in 100 g of solution:
mass % = (mass of solute / mass of solution) × 100
The mass of solution is the mass of solute plus the mass of solvent. Mass percent does not change with temperature, because mass is constant, which is an advantage over molarity. A bottle of concentrated hydrochloric acid labeled “37 %” contains 37 g of HCl in every 100 g of solution.
What is volume percent?
Volume percent (v/v) is used when both the solute and the solvent are liquids, as in alcoholic drinks:
volume % = (volume of solute / volume of solution) × 100
It is expressed as a percentage, often abbreviated “% v/v” or, on drinks, “ABV” (alcohol by volume). Volumes of liquids are not exactly additive, so the volume of the solution must be measured and not calculated as the sum of the volumes of the components. When 50 mL of ethanol is mixed with 50 mL of water, the volume is only about 96 mL.
What are ppm and ppb?
For very dilute solutions, percentages become awkward, so concentrations are expressed in parts per million (ppm) and parts per billion (ppb):
ppm = (mass of solute / mass of solution) × 106
ppb = (mass of solute / mass of solution) × 109
For dilute aqueous solutions the density is close to 1.00 g/mL, so 1 L of solution has a mass of about 1 kg. Thus 1 ppm is roughly 1 mg of solute per liter, and 1 ppb is roughly 1 µg per liter. Gas concentrations are often given in ppm by volume, for example 420 ppm of CO2 in air.
Conversion table for concentration units
| Fraction | Percent | ppm | ppb |
|---|---|---|---|
| 0.1 | 10 % | 100,000 | 100,000,000 |
| 0.01 | 1 % | 10,000 | 10,000,000 |
| 0.0001 | 0.01 % | 100 | 100,000 |
| 0.000001 | 0.0001 % | 1 | 1,000 |
| 0.000000001 | 0.0000001 % | 0.001 | 1 |
To convert from percent to ppm, multiply by 10,000. To convert from ppm to ppb, multiply by 1000.
How do you solve concentration problems?
Example 1: finding mass percent
A solution is made by dissolving 12.0 g of NaCl in 88.0 g of water. The mass of the solution is 12.0 + 88.0 = 100.0 g, so the mass percent is (12.0 / 100.0) × 100 = 12.0 %.
Example 2: finding the mass of solute
How many grams of sugar are in 750 g of a 3.5 % sugar solution? Mass = 0.035 × 750 = 26 g (26.25 g before rounding). The mass of water is 750 − 26.25 = 723.75 g.
Example 3: volume percent
A solution is prepared by diluting 50.0 mL of ethanol with water to a total volume of 250.0 mL. Volume percent = (50.0 / 250.0) × 100 = 20.0 % v/v.
Example 4: parts per million
A 1.00 L sample of drinking water, with a mass of about 1.00 kg, contains 2.5 mg of fluoride. Concentration = 2.5 × 10−3 g / 1000 g × 106 = 2.5 ppm. The World Health Organization sets a guideline value of 1.5 mg/L (1.5 ppm) for fluoride in drinking water, so this sample is above the guideline.
Example 5: converting units
Seawater contains about 3.5 % dissolved salts by mass. In ppm that is 3.5 × 10,000 = 35,000 ppm. A trace contaminant of 0.0025 % is 0.0025 × 10,000 = 25 ppm.
Example 6: ppb in a large volume
A lake contains 8.0 ppb of mercury, and its volume is 2.0 × 109 L. The mass of water is about 2.0 × 109 kg, so the mass of mercury is 8.0 × 10−9 × 2.0 × 109 kg = 16 kg. Even a very small concentration can add up to a considerable mass.
Where are these units used?
- Mass percent: commercial acids and bases, bleach, saline solutions (0.9 % NaCl) and alloy compositions.
- Volume percent: alcoholic beverages, rubbing alcohol and gas mixtures.
- ppm: water quality, soil chemistry, air pollutants and food additives.
- ppb: trace contaminants such as lead, arsenic and pesticides.
Where does the notation come from?
Percentage composition was used in analytical chemistry from the early days of quantitative analysis in the 18th and 19th centuries, when results were reported as grams of a component per 100 g of sample. Parts per million and billion became common in the 20th century with the development of sensitive analytical instruments, which made it possible to detect traces of substances in water, air and food. Note that the “billion” in ppb is the American billion, 109, which in some older British usage meant 1012. Scientific papers therefore often prefer µg/L or mg/kg, which are unambiguous.
Which mistakes are common?
- Dividing by the mass of the solvent: the denominator is the mass of the whole solution.
- Adding volumes of liquids: measure the final volume for volume percent.
- Treating ppm as mg/L for non-aqueous solutions: the equivalence holds only when the density is close to 1 g/mL.
- Confusing ppm by mass with ppm by volume: for gases, ppm usually refers to volume.
- Mixing percent and fraction: 5 % is 0.05, not 5.