Molality Calculator
Calculate molal concentration from moles of solute and kilograms of solvent, or let the calculator convert a known mass and molar mass into moles automatically. Switch to molarity-to-molality conversion mode, pick a solvent, and get freezing-point depression and boiling-point elevation as a bonus.
Formula
Worked example
Dissolving 180 g of glucose (M = 180.16 g/mol) in 500 g of water: n = 180/180.16 = 0.9991 mol; kg = 0.500 kg; b = 0.9991/0.500 = 1.998 mol/kg. Freezing-point depression for water (Kf = 1.853, i = 1): 1 x 1.853 x 1.998 = 3.702 K.
What molality measures and why it matters
Molality, symbolised b (occasionally m), expresses concentration as moles of solute per kilogram of solvent. Its defining equation is b = n / m, where n is the amount of solute in moles and m is the mass of the solvent in kilograms. The crucial detail is the denominator: molality uses the mass of the solvent alone, never the mass or volume of the whole solution. A solution containing one mole of solute per kilogram of solvent has a molality of one mole per kilogram, written 1 mol/kg and historically read "one molal." Because mass does not expand or contract with temperature, a molal concentration stays constant across a temperature range, making it the concentration unit of choice for any experiment where the sample will be heated or cooled.
Molality versus molarity: which to use
Molarity (M) is moles of solute per litre of solution, so it depends on volume, and volume changes with temperature. Molality (b) is moles of solute per kilogram of solvent, and mass is temperature-independent. For dilute aqueous solutions near room temperature the two values are numerically very close because one litre of water weighs approximately one kilogram, but they diverge significantly for concentrated or non-aqueous solutions. Choose molality whenever temperature changes are involved, whenever precision is critical, or for calculating colligative properties. The molarity-to-molality conversion used here is b = C / (rho - C x M / 1000), where C is molarity in mol/L, rho is solution density in g/mL, and M is the solute molar mass in g/mol.
Colligative properties: freezing-point depression and boiling-point elevation
Colligative properties depend only on the number of dissolved particles, not their identity. Freezing-point depression is deltaT_f = i x Kf x b and boiling-point elevation is deltaT_b = i x Kb x b, where i is the van t Hoff factor (1 for non-electrolytes, 2 for salts like NaCl that split into two ions, 3 for CaCl2, and so on). Kf and Kb are solvent-specific constants: for water, Kf = 1.853 K/mol/kg and Kb = 0.512 K/mol/kg. This calculator computes both automatically once you choose a solvent and enter i. These formulas underlie applications from antifreeze to determining the molar mass of an unknown solute.
How to use this calculator
Three modes cover the most common scenarios. In the default mode, enter moles of solute and the mass of solvent directly. If you know the mass of the solute but not the moles, switch to the mass-plus-molar-mass mode and the calculator converts for you. If you have a molarity reading from a lab instrument plus the solution density, switch to molarity-to-molality conversion. In all modes, select your solvent and optionally set the van t Hoff factor to get instant freezing-point and boiling-point shifts. Solvent mass can be entered in kilograms, grams, or pounds and the calculator converts automatically.
Cryoscopic and ebullioscopic constants for common solvents
| Solvent | Kf (K/mol/kg) | Kb (K/mol/kg) | Normal bp (C) | Normal fp (C) |
|---|---|---|---|---|
| Water | 1.853 | 0.512 | 100 | 0 |
| Benzene | 5.12 | 2.53 | 80.1 | 5.5 |
| Ethanol | 1.99 | 1.22 | 78.4 | -114.1 |
| Acetic acid | 3.9 | 3.07 | 118.1 | 16.7 |
| Cyclohexane | 20 | 2.79 | 80.7 | 6.5 |
| Camphor | 37.7 | 5.95 | 204 | 178.8 |
Constants for computing freezing-point depression (Kf) and boiling-point elevation (Kb) via DeltaT = i x K x b.
Frequently asked questions
What is the difference between molality and molarity?
Molality (b) is moles of solute per kilogram of solvent, while molarity (M) is moles of solute per litre of solution. Molality depends on mass, which is constant with temperature; molarity depends on volume, which expands or contracts as temperature changes. For dilute aqueous solutions near room temperature the two are numerically close because one litre of water weighs about one kilogram, but they diverge for concentrated or non-aqueous solutions.
Do I use the mass of the solvent or the whole solution?
You use the mass of the solvent alone. This is the defining feature of molality and the most common mistake. If a problem gives the total mass of the solution, subtract the mass of the dissolved solute to find the solvent mass before calculating. Only when the solution is very dilute can the solute mass be neglected safely.
How do I find moles of solute from a mass?
Divide the mass of the solute by its molar mass: n = mass / molar mass. For example, 9.0 g of glucose (molar mass 180.16 g/mol) is 9.0 / 180.16 = 0.0500 mol. Use the mass-plus-molar-mass mode in this calculator and it does that step for you automatically.
How do I convert molarity to molality?
Use the formula b = C / (rho - C x M / 1000), where C is the molarity in mol/L, rho is the solution density in g/mL, and M is the molar mass of the solute in g/mol. Switch this calculator to molarity-to-molality conversion mode and enter those three values. For a dilute aqueous solution where rho is close to 1.0 g/mL and M is moderate, molarity and molality will be nearly equal.
What is the van t Hoff factor and why does it matter?
The van 't Hoff factor (i) accounts for how many particles a dissolved formula unit produces. Non-electrolytes like glucose or sucrose give i = 1 because they do not dissociate. Strong electrolytes give i equal to the number of ions: NaCl gives 2 (Na+ and Cl-), MgCl2 gives 3, K2SO4 gives 3. A higher i multiplies both the freezing-point depression and the boiling-point elevation by the same factor. In practice, ion pairing at higher concentrations means the effective i can be slightly less than the theoretical value.
What are the units of molality and how is it abbreviated?
The SI unit of molality is mol/kg. Older texts abbreviate it as 'm' (lowercase), so a '2 m solution' means 2 mol/kg; the IUPAC now prefers 'b' for the symbol to avoid confusion with metres. The unit mol/kg is sometimes called 'molal' informally, but IUPAC considers that term obsolete.