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Mass percent calculator: % w/w, g/L, mol/L and ppm

Calculate the mass percent of a solution and convert it to mass concentration, molarity, molality and ppm using the solution density.

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Results

Mass percent (w/w)

10 %

Mass concentration

107 g/L

Molarity

1.831 mol/L

Molality
1.901 mol/kg
Parts per million (by mass)
100,000 ppm
Volume of solution
93.46 mL

Many ways to express concentration

The same solution can be described as 10% by mass, 107 g/L, 1.83 mol/L or 100,000 ppm. Each unit suits a different job: mass percent for commercial reagents and food labels, g/L and mol/L for lab work, ppm for traces in water and air. This calculator starts from masses and converts to all of them.

The formulas

  • Mass percent (w/w) = mass of solute ÷ mass of solution × 100
  • Mass concentration (g/L) = mass fraction × density (g/mL) × 1000
  • Molarity (mol/L) = mass concentration ÷ molar mass
  • Molality (mol/kg) = moles of solute ÷ kg of solvent
  • ppm (by mass) = mass fraction × 1,000,000

The density of the solution is the bridge between mass-based and volume-based units.

Worked example

Dissolve 10 g of sodium chloride in 90 g of water. The solution has a density of 1.07 g/mL.

  1. Mass percent = 10 ÷ 100 × 100 = 10% w/w.
  2. Mass concentration = 0.10 × 1.07 × 1000 = 107 g/L.
  3. Molarity = 107 ÷ 58.44 = 1.831 mol/L.
  4. Molality = (10 ÷ 58.44) ÷ 0.090 = 1.901 mol/kg.
  5. The 100 g of solution occupy 100 ÷ 1.07 = 93.46 mL.

Concentrated reagents

Commercial acids are labeled in mass percent. Converting them is a classic calculation:

Reagent Mass percent Density (g/mL) Molarity
Hydrochloric acid 37% 1.18 about 12 mol/L
Sulfuric acid 96% 1.84 about 18 mol/L
Nitric acid 70% 1.41 about 16 mol/L
Ammonia solution 28% 0.90 about 15 mol/L
Hydrogen peroxide 30% 1.11 about 9.8 mol/L

w/w, w/v and v/v

  • w/w (weight per weight): grams per 100 g of solution, used here.
  • w/v (weight per volume): grams per 100 mL of solution; normal saline is 0.9% w/v, or 9 g/L.
  • v/v (volume per volume): mL per 100 mL, as for alcohol by volume.

They match only when the solution’s density is 1 g/mL, so always check which one a label or protocol means.

ppm and ppb

For traces, 1 ppm (part per million) is 1 mg of solute per kg of solution, close to 1 mg/L in water. 1 ppb (part per billion) is 1 µg/kg, so 15 ppb of lead in tap water means about 15 micrograms per liter.

Frequently asked questions

How do you calculate mass percent?

Mass percent = mass of solute ÷ (mass of solute + mass of solvent) × 100. Dissolving 10 g of salt in 90 g of water gives 10% w/w.

How do you convert mass percent to molarity?

Molarity = mass percent ÷ 100 × density (g/mL) × 1000 ÷ molar mass. A 10% NaCl solution with a density of 1.07 g/mL is 107 g/L, or 1.83 mol/L.

What is the difference between w/w, w/v and v/v?

w/w compares masses, w/v gives grams per 100 mL of solution, and v/v compares volumes, as for alcohol by volume. They are only equal when the density is 1.

What does ppm mean?

Parts per million: grams of solute per million grams of solution. For dilute aqueous solutions, 1 ppm is about 1 mg/L.

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Results are estimates provided for information purposes. They do not replace professional advice.

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