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Generated on: July 20, 2026 at 09:33 PM

Molarity to Molality Converter

Inputs

ConvertMolarity → molality
Molarity3 M
Molality3 mol/kg
Solution Density1.1 g/mL
Solute Molar Mass58.44 g/mol

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Chemistry

Molarity to Molality Converter

Convert between molarity (mol/L) and molality (mol/kg) using the solution density and the solute molar mass. Switch direction to go either way.

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g/mol

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\begin{aligned} b &= \dfrac{M}{\left(1000\rho - M\,M_w\right)/1000} \\ &= \dfrac{3\,\text{M}}{?\,\text{kg}} \\ &= ?\,\text{mol/kg} \end{aligned}

Details

\begin{aligned} w &= \dfrac{1000\rho - M\,M_w}{1000} \\ &= \dfrac{1000\left(1.1\right) - M\left(58.44\right)}{1000} \\ &= ?\,\text{kg} \end{aligned}

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Two ways to measure concentration

Molarity and molality both describe how much solute sits in a solution, but they divide by different things. Molarity (MM) counts moles of solute per litre of solution — a volume. Molality (mm, sometimes written bb) counts moles of solute per kilogram of solvent — a mass. Because one is anchored to volume and the other to mass, there is no fixed number that converts between them. The bridge is the solution density, which says how many grams a litre of the solution actually weighs.

Imagine one litre of solution. Its total mass is the density times the volume:

msolution=1000 ρm_{\text{solution}} = 1000\,\rho

with ρ\rho in g/mL, so a litre (1000 mL) weighs 1000 ρ1000\,\rho grams. Part of that mass is the dissolved solute. A molarity of MM means MM moles are present, and each mole weighs MwM_w grams, so the solute mass is M⋅MwM \cdot M_w grams. Everything left over is solvent:

msolvent=1000 ρ−M Mw1000 kgm_{\text{solvent}} = \frac{1000\,\rho - M\,M_w}{1000}\ \text{kg}

Molality divides the moles of solute by that solvent mass:

m=Mmsolvent=M(1000 ρ−M Mw)/1000m = \frac{M}{m_{\text{solvent}}} = \frac{M}{\left(1000\,\rho - M\,M_w\right)/1000}
SymbolQuantityUnit
MMolaritymol/L (M)
mMolalitymol/kg (m)
ρSolution densityg/mL
M_wSolute molar massg/mol

Worked example: 3 M sodium chloride

Take a 3 M NaCl solution with a density of 1.10 g/mL. Sodium chloride has a molar mass of 58.44 g/mol. First find the solvent mass in one litre:

msolvent=1000(1.10)−3(58.44)1000=1100−175.321000=0.92468 kgm_{\text{solvent}} = \frac{1000(1.10) - 3(58.44)}{1000} = \frac{1100 - 175.32}{1000} = 0.92468\ \text{kg}

Then divide the molarity by that solvent mass:

m=30.92468≈3.244 mol/kgm = \frac{3}{0.92468} \approx 3.244\ \text{mol/kg}

The molality is higher than the molarity because a litre of this solution holds less than a kilogram of water — the salt has taken up part of both the volume and the mass.

Going the other way: molality to molarity

Rearranging the same relationship to solve for molarity gives a clean closed form:

M=1000 m ρ1000+m MwM = \frac{1000\,m\,\rho}{1000 + m\,M_w}

Feeding the numbers back in confirms the round trip:

M=1000(3.244)(1.10)1000+3.244(58.44)=3568.41189.6≈3.00 mol/LM = \frac{1000(3.244)(1.10)}{1000 + 3.244(58.44)} = \frac{3568.4}{1189.6} \approx 3.00\ \text{mol/L}

When are the two nearly the same?

For a dilute solution in water near room temperature, the density is close to 1.00 g/mL and the solute contributes almost no mass, so one litre of solution holds close to one kilogram of solvent. In that limit molarity and molality nearly coincide. They pull apart as the solution gets more concentrated or the solute gets heavier:

SolutionDensity (g/mL)MolarityMolality
0.1 M glucose in water1.000.10 M0.102 m
1 M NaCl1.041.00 M1.02 m
3 M NaCl1.103.00 M3.24 m
6 M HCl1.106.00 M7.13 m

Why the distinction matters

Molarity is convenient at the bench because solutions are prepared and dispensed by volume. Molality wins whenever temperature enters the picture: volumes expand as a solution warms, so molarity drifts, while mass — and therefore molality — stays put. That is why colligative-property work such as boiling-point elevation and freezing-point depression is written in molality. Converting between the two lets you take a concentration measured by volume and use it in a temperature-independent calculation, or vice versa.

A note on limits

The conversion assumes the density you enter belongs to the solution at the same concentration as the molarity or molality you are converting. A litre of solution can only hold as much solute as its mass allows, so if the dissolved solute would weigh more than the whole litre, the inputs are physically inconsistent — usually a sign the density or molar mass was mistyped.

Frequently Asked Questions (FAQ)

Why do I need the density to convert molarity and molality?

Molarity is per litre of solution (a volume) while molality is per kilogram of solvent (a mass). To move between a volume and a mass you need the solution density, which tells you how many grams one litre of the solution weighs. Subtracting the mass of dissolved solute from that leaves the mass of solvent, which is what molality is measured against. Without the density there is no way to connect the two.

What is the formula from molarity to molality?

One litre of solution weighs 1000·ρ grams, where ρ is the density in g/mL. The dissolved solute contributes M·Mw grams, where M is the molarity and Mw the molar mass. The rest is solvent, so the solvent mass per litre is (1000·ρ − M·Mw)/1000 kilograms. Molality is then the molarity divided by that solvent mass: m = M ÷ [(1000·ρ − M·Mw)/1000].

What is the difference between molarity and molality?

Molarity (M) is moles of solute per litre of solution and depends on volume, which expands slightly as temperature rises. Molality (m) is moles of solute per kilogram of solvent and does not change with temperature because mass is fixed. Molarity is convenient for everyday lab measuring by volume; molality is used for colligative properties such as boiling-point elevation and freezing-point depression, where a temperature-independent measure is required.

When are molarity and molality nearly equal?

They converge for dilute aqueous solutions near room temperature, because the density approaches 1.00 g/mL and the solute takes up almost no mass, so one litre of solution holds close to one kilogram of water. As concentration rises or the solute is heavy, the two diverge: a 3 M NaCl solution at 1.10 g/mL works out to about 3.24 m, noticeably higher than its molarity.

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