Concentration Calculator: Molarity, Molality, ppm

What is a solution concentration calculator?

A solution concentration calculator finds how much solute is dissolved in a solution, expressed in a chosen unit. A solute is the substance being dissolved, such as salt or sugar. This tool converts a solute's mass, a solution's volume, and a solution's density into five common concentration units: molarity, molality, percent by mass, percent by volume, and parts per million (ppm).

Concentration describes the strength of a mixture. The same solution can be described in several ways, and each unit suits a different purpose. A chemist mixing a reaction uses molarity. A physical chemist studying freezing points uses molality. An environmental lab testing water uses ppm.

Concentration units explained

• Molarity (M) — moles of solute per liter of solution. Common in general chemistry.
• Molality (m) — moles of solute per kilogram of solvent. Does not change with temperature.
• Percent by mass (% w/w) — mass of solute divided by mass of solution, times 100.
• Percent by volume (% v/v) — volume of solute divided by volume of solution, times 100. Used for liquid mixtures such as alcoholic drinks.
• Parts per million (ppm) — mass of solute per million parts of solution by mass. Used for very small (trace) amounts.

A mole is a fixed number of particles (about 6.022 × 10²³), used to count atoms or molecules by weighing them.

How to calculate molarity

Molarity is the number of moles of solute divided by the volume of the solution in liters:

$M = \frac{\text{moles of solute}}{\text{volume of solution (L)}}$

Since moles equal mass divided by molecular weight, the formula becomes:

$M = \frac{\text{mass of solute (g)}}{\text{molecular weight (g/mol)} \times \text{volume of solution (L)}}$

Example. Dissolve 5.85 g of sodium chloride (NaCl, molecular weight 58.44 g/mol) in enough water to make 0.1 L of solution:

$M = \frac{5.85}{58.44 \times 0.1} = 1.00 \text{ mol/L}$

The final volume must be measured after the solute is fully dissolved, not before. Adding a solid to a fixed volume of water increases the total volume slightly.

How to calculate molality

Molality divides moles of solute by the mass of the solvent, in kilograms, instead of the volume of the solution:

$m = \frac{\text{mass of solute (g)}}{\text{molecular weight (g/mol)} \times \text{mass of solvent (kg)}}$

Example. Dissolve 5.85 g of NaCl in exactly 100 g (0.1 kg) of water:

$m = \frac{5.85}{58.44 \times 0.1} = 1.00 \text{ mol/kg}$

Because mass does not change with temperature, molality stays constant when a solution is heated or cooled. Molarity does not, because volume expands with heat. This is why molality is used to study freezing point depression and boiling point elevation.

How to calculate percent by mass

Percent by mass is the mass of solute divided by the total mass of the solution, multiplied by 100:

$\%\text{ w/w} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 100$

Example. Dissolve 10 g of sugar in 90 g of water, for a total solution mass of 100 g:

$\%\text{ w/w} = \frac{10}{100} \times 100 = 10\%$

Hydrogen peroxide sold for household use is commonly labeled "3%," meaning 3 g of hydrogen peroxide per 100 g of solution.

How to calculate percent by volume

Percent by volume divides the volume of solute by the total volume of the solution:

$\%\text{ v/v} = \frac{\text{volume of solute}}{\text{volume of solution}} \times 100$

Example. Mix ethanol with water to make 100 mL of solution, using 15 mL of ethanol:

$\%\text{ v/v} = \frac{15}{100} \times 100 = 15\%$

This is the unit used for alcohol content in drinks. Wine is usually 12-14% v/v; distilled spirits are 40% v/v or higher. Liquid volumes do not always add up exactly when mixed, so a precise solution is measured to a final volume rather than assumed from the sum of its parts.

How to calculate parts per million (ppm)

Parts per million is used for very dilute solutions. It divides the mass of solute by the mass of the solution and multiplies by one million:

$\text{ppm} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 1{,}000{,}000$

Example. A water sample of 1,000 g contains 0.002 g of dissolved lead:

$\text{ppm} = \frac{0.002}{1000} \times 1{,}000{,}000 = 2 \text{ ppm}$

For dilute water-based solutions, 1 ppm is close to 1 milligram of solute per liter of solution.

Worked example: physiological saline

Physiological saline is a 0.9% salt solution used in medicine because it matches the salt concentration of blood plasma. To check a batch made from 9 g of NaCl dissolved to a final volume of 1 L, with a solution density of 1.005 g/mL:

First, find the total solution mass from its volume and density:

$\text{mass} = 1 \text{ L} \times 1.005 \text{ g/mL} \times 1000 = 1{,}005 \text{ g}$

• Percent by mass: 9 ÷ 1,005 × 100 = 0.90%
• Molarity: 9 ÷ (58.44 × 1) = 0.154 mol/L
• Molality: solvent mass is 1,005 − 9 = 996 g (0.996 kg); 9 ÷ (58.44 × 0.996) = 0.155 mol/kg
• Parts per million: 9 ÷ 1,005 × 1,000,000 ≈ 8,955 ppm

The ppm figure is not exactly 9,000 because the solution mass is 1,005 g, not 1,000 g. The extra 5 g comes from the solution's density being slightly higher than pure water.

Other concentration units

Some fields use units beyond the five above. Normality (N) counts reactive units instead of moles; a solution of sulfuric acid (H₂SO₄) that is 1 M is 2 N, because each molecule can donate two hydrogen ions. Mole fraction divides the moles of one component by the total moles of everything in the mixture, and is used in distillation calculations. For extremely dilute solutions, chemists switch from ppm to parts per billion (ppb) or parts per trillion (ppt).

Common sources of error

A calculated concentration can differ from the real one for several reasons. Dissolving a solid changes the total volume of a solution, so the final volume must be measured after mixing, not assumed to equal the starting solvent volume. Lab chemicals are rarely 100% pure; a reagent labeled "98.5% assay" needs its mass increased to compensate. Some compounds include water bound in their crystal structure, called hydration water; copper sulfate pentahydrate (CuSO₄·5H₂O, 249.68 g/mol) weighs more per mole than anhydrous copper sulfate (159.61 g/mol), and using the wrong molecular weight changes the result. Temperature changes the volume of a solution, which changes molarity but not molality.

Frequently asked questions

What is the difference between molarity and molality? Molarity divides by the volume of the solution, in liters. Molality divides by the mass of the solvent, in kilograms. Volume changes with temperature; mass does not. For dilute water-based solutions at room temperature, the two values are close.

How do I convert ppm to percent? Divide the ppm value by 10,000. For example, 5,000 ppm equals 0.5%.

Is 1 ppm always equal to 1 mg/L? Only approximately, and only for dilute solutions where the solution's density is close to 1 g/mL, such as most water samples. For denser liquids the two values diverge.

Why doesn't my measured concentration match my calculation? Common causes include an impure reagent, water bound in the solute's crystal structure, a solution volume measured before full mixing, or a temperature different from the one used to prepare the solution.

What is the maximum concentration a solute can reach? The limit is the solute's solubility in that solvent at that temperature. Table salt dissolves up to about 36 g per 100 mL of water at room temperature; beyond that, undissolved solid remains at the bottom of the container.

Does temperature affect concentration? Yes, for units based on volume. Water expands as it warms, so a solution's molarity decreases slightly on heating even though the amount of solute has not changed. Percent by mass and molality, which are based on mass, are not affected.

References

1. Harris, D. C. (2015). Quantitative Chemical Analysis (9th ed.). W. H. Freeman.
2. Chang, R., & Goldsby, K. A. (2015). Chemistry (12th ed.). McGraw-Hill Education.
3. International Union of Pure and Applied Chemistry. (1997). Compendium of Chemical Terminology (the "Gold Book").
4. National Institute of Standards and Technology. NIST Chemistry WebBook. https://webbook.nist.gov/chemistry/