Molality of a Solution Calculator: mol/kg From Masses

This calculator finds the molality of a solution, the moles of solute per kilogram of solvent. Enter the mass of solute, its molar mass and the mass of solvent in grams; you get the molality in mol/kg, the moles of solute and the mass percent of solute in the solution.

Formula

b = (m ÷ M) ÷ (m_solvent ÷ 1000), and w = m ÷ (m + m_solvent) × 100.

• b: molality in moles of solute per kilogram of solvent (mol/kg, sometimes written m)
• m: mass of solute in grams; M: its molar mass in g/mol
• m_solvent: mass of solvent in grams; 1 kg = 1000 g
• w: mass percent of solute in the whole solution

Worked Example

18.0 g of glucose (M = 180.156 g/mol) dissolved in 200 g of water.

1. Moles of solute: n = 18 ÷ 180.156 = 0.09991 mol
2. Mass of solvent in kilograms: 200 ÷ 1000 = 0.2 kg
3. b = 0.099913 ÷ 0.2 = 0.4996 mol/kg
4. Mass percent: 18 ÷ (18 + 200) × 100 = 8.26 %

Assumptions

• The solvent mass is the mass of solvent alone, not of the finished solution.
• The solute is pure and fully dissolved; a hydrate brings its water into the solvent, so use the hydrate molar mass and add that water to the solvent mass if you need high accuracy.
• Molality uses masses only, so it does not change with temperature, unlike molarity.

How to read the result

Molality is the concentration used for colligative properties such as freezing-point depression and boiling-point elevation, because it does not depend on volume or temperature. For dilute water solutions near room temperature, molality and molarity are close, since 1 L of water has a mass of about 1 kg; at higher concentration they separate. For mol/L instead, use the molarity calculator from mass.

Limits and common mistakes

• Dividing by the mass of the solution instead of the solvent gives a value that is too low.
• Leaving the solvent mass in grams without dividing by 1000 gives an answer 1000 times too small.
• For an ionic solute, the molality of ions is larger than that of the formula unit (NaCl gives about twice as many particles); this calculator reports the formula-unit molality.

Frequently Asked Questions

What is the molality of 18 g glucose in 200 g water?

About 0.4996 mol/kg.

What is the formula for molality?

Molality = moles of solute ÷ kilograms of solvent.

What is the difference between molality and molarity?

Molality is per kilogram of solvent and does not depend on temperature; molarity is per litre of solution.

Can I enter the solvent as a volume?

Convert it to a mass first with its density: mass (g) = volume (mL) × density (g/mL).

in m | Mass of solute | g | 18 | 0
in mm | Molar mass of solute | g/mol | 180.156 | 0.001
in ms | Mass of solvent | g | 200 | 0.000001
out b | Molality | mol/kg | m / mm / (ms / 1000) | 4
out n | Amount of solute | mol | m / mm | 5
out w | Mass percent of solute | % | m / (m + ms) * 100 | 2