Molality calculator
Enter the solute and the solvent, get the molality.
What is molality?
Moles of solute per kilogram of solvent: m = mol solute ÷ kg solvent. Its unit is mol/kg, often written m (OpenStax Chemistry 2e).
Example
58.44 g of sodium chloride is 1.000 mol (molar mass 58.44 g/mol). Dissolved in 1.000 kg of water, the solution is 1.000 m.
How is molality different from molarity?
Molarity divides by liters of solution; molality divides by kilograms of solvent. Because molality uses masses, it does not change when the solution warms and expands.
What is molality used for?
Colligative properties — freezing point depression and boiling point elevation are calculated from molality.
I only know grams — what do I need?
The molar mass of the solute. The molar mass calculator adds it up from a chemical formula.
How do I convert molarity to molality?
You need the density of the solution. Take 1 L: its mass is density × 1,000 g, the solute in it is molarity × molar mass, and the solvent is the difference. For 0.556 M glucose with a density of 1.04 g/mL, 1 L weighs 1,040 g and holds 100.2 g of glucose, leaving 940 g of water, so the molality is 0.556 ÷ 0.940 = 0.59 m (OpenStax Chemistry 2e, Example 11.5).
Does molality equal molarity in dilute water solutions?
They come close only when the solution is dilute and its density is near 1 g/mL, because then 1 kg of solvent is about 1 L of solution. As the solution gets more concentrated they drift apart: the 0.556 M glucose solution above is 0.59 m. Do not interchange the two without checking the density.
Is a 1 m solution made with 1 kg of solution?
No. Molality is moles per kilogram of solvent, so for a 1 m solution you weigh the solvent first (1.000 kg of water) and then dissolve one mole of solute in it. The finished mass is larger than 1 kg, and its volume is not 1 L.
The formula and why it exists
Molality is m = moles of solute ÷ kilograms of solvent, with the solvent mass excluding the solute (OpenStax Chemistry 2e, section 11.4). Moles come from grams ÷ molar mass. Both quantities in the ratio are masses or amounts, so nothing in it depends on temperature: warming a solution changes its volume, and so its molarity, but not its molality. That is the reason molality is the unit used in boiling point elevation (ΔTb = Kb·m) and freezing point depression (ΔTf = Kf·m), where the solvent’s constants are Kb = 0.512 °C/m and Kf = 1.86 °C/m for water.
Worked example
OpenStax Example 11.3 dissolves 2.22 × 10³ g of ethylene glycol, C₂H₆O₂, in 2.00 × 10³ g of water to make antifreeze. The molar mass is 62.07 g/mol, so the amount is 2,220 ÷ 62.07 = 35.8 mol. The solvent is 2.00 kg of water, which gives m = 35.8 ÷ 2.00 = 17.9 mol/kg. With Kb = 0.512 °C/m, that solution would boil 9.2 °C higher, at 109.2 °C, which is the textbook’s practice answer. To check it here, choose “Grams and molar mass”, enter 2220 g, a molar mass of 62.07 and 2 kg of solvent.
Common mistakes
The biggest mistake is dividing by the mass of the solution, or by its volume, instead of the solvent. In the example that would give 8.5 m rather than 17.9 m. Second, the solvent mass must be in kilograms: 500 g of water is 0.500 kg, or pick grams in the solvent unit box and let the calculator convert. Third, the letter m means molal, not meter, and it is not the same as capital M for molarity. Finally, an ionic solute gives molality of the formula units; for colligative properties each dissolved particle counts, so multiply by the van ’t Hoff factor, as the freezing point depression calculator does.
Sources: OpenStax Chemistry 2e, section 11.4 “Colligative Properties” (molality, molarity versus molality, Kb and Kf of water, Examples 11.3, 11.5 and 11.7). Related: freezing point depression calculator, molarity calculator, osmotic pressure calculator and grams to moles calculator.