Molarity to Molality Formula & Conversion

This calculator converts molarity (moles of solute per liter of solution) to molality (moles of solute per kilogram of solvent). You enter the molarity, the molar mass of the solute, and the density of the solution, and it returns the molality in mol/kg. The conversion requires the solution density because molarity uses solution volume while molality uses solvent mass.

Formula

The conversion from molarity (M) to molality (m) uses the solution density (ρ) and the solute’s molar mass (M_w):

m = (M × 1000) / (ρ × 1000 − M × M_w)

Where:

• m = molality (mol solute / kg solvent)
• M = molarity (mol solute / L solution)
• ρ = density of the solution (g/mL, which equals kg/L)
• M_w = molar mass of the solute (g/mol)

The numerator (M × 1000) converts moles per liter to moles per 1000 mL (1 L). The denominator (ρ × 1000) gives the mass of 1 L of solution in grams; subtracting the solute mass (M × M_w) leaves the solvent mass in grams. Dividing by 1000 converts grams to kilograms.

Worked Example

Using the default values: M = 1.0 mol/L, M_w = 58.44 g/mol (NaCl), ρ = 1.05 g/mL.

1. Mass of 1 L solution = 1.05 g/mL × 1000 mL = 1050 g
2. Mass of solute in 1 L = 1.0 mol × 58.44 g/mol = 58.44 g
3. Mass of solvent = 1050 g − 58.44 g = 991.56 g = 0.99156 kg
4. Molality = 1.0 mol / 0.99156 kg = 1.0085 mol/kg

The calculator rounds to 4 decimals, giving 1.0085 mol/kg.

Why Density Matters

Molarity is defined per volume of solution, while molality is per mass of solvent. A solution’s density links volume to mass. Without density, you cannot know how much solvent is present because the solute itself contributes to the solution’s volume and mass. For dilute aqueous solutions (below ~0.1 M), the density is close to 1 g/mL and the solute mass is small, so molarity and molality are numerically similar. But for concentrated solutions, the difference can be significant—a 10 M NaOH solution has a molality around 14 mol/kg because the solute adds substantial mass.

When to Use Each Unit

Molarity is convenient for laboratory work because you measure volumes with pipettes and volumetric flasks. Molality is preferred when temperature changes matter, because molality depends only on masses, which do not expand or contract with temperature. Solution volume changes with temperature, so molarity changes too. Colligative properties—boiling point elevation, freezing point depression, osmotic pressure—are formally based on molality, not molarity, because they depend on the ratio of solute to solvent particles, not on the solution’s volume.

Choose molality when:

• You are measuring a colligative property (freezing point, boiling point, vapor pressure).
• You work at a temperature different from the one at which the solution was prepared.
• You need a concentration that stays constant with temperature changes.

Common Mistakes and How to Avoid Them

• Using solution volume instead of solvent mass: The denominator must be the mass of the solvent only, not the total solution mass. Subtract the solute mass from the solution mass.
• Unit mismatches: Density in g/mL must be converted to kg/L (1 g/mL = 1 kg/L). Molar mass must be in g/mol, not kg/mol.
• Forgetting to convert grams to kilograms: The solvent mass must be in kilograms. Divide the gram result by 1000.
• Assuming density equals 1 for all solutions: Only pure water at 4°C has a density of exactly 1.000 g/mL. Many solutions have densities above or below that.

Limits of the Formula

The formula assumes the solute dissolves completely and does not react with the solvent. It also assumes you know the true density of the final solution at the working temperature. For electrolytes like NaCl, the van’t Hoff factor (i) is not included in the conversion—molality is simply moles of solute per kg of solvent, regardless of how many particles the solute produces. If you need the effective concentration of particles (for colligative properties), multiply molality by the van’t Hoff factor separately.

For very high concentrations, the density must be measured accurately; small errors in density lead to larger errors in molality. Also, the formula assumes the solute’s molar mass is known exactly—for hydrates or impure reagents, use the effective molar mass of the actual solute species.

Frequently Asked Questions

Can I convert molality back to molarity with the same formula?

Yes, rearrange the formula: M = (m × ρ × 1000) / (1000 + m × M_w). You still need the solution density and solute molar mass. The relationship is symmetric; knowing any two of molarity, molality, and density lets you find the third.

Why is molality used in freezing point depression instead of molarity?

Freezing point depression depends on the number of solute particles relative to solvent particles. Molality directly gives moles of solute per kg of solvent, which is temperature-independent. Molarity changes with temperature because volume changes, so using molality avoids errors when the solution is cooled or heated.

Does this formula work for non-aqueous solutions?

Yes, as long as you use the density of that specific solution and the solute’s molar mass. The solvent can be ethanol, benzene, or any other liquid. The formula is general; it does not assume water.

What if the density is given in kg/L?

Then you can skip the ×1000 conversions: m = M / (ρ − M × M_w/1000). Just be consistent with units. Many handbooks give density in g/mL, so the original formula is more common.

Is molality ever larger than molarity?

Yes, whenever the solute is dense and the solution is concentrated. For example, a 5 M NaCl solution has a density around 1.19 g/mL, giving a molality of about 5.4 mol/kg. The molality is higher because the solvent mass is less than the solution mass.

How do I find the density if I don’t have it?

You can measure it with a hydrometer or pycnometer, or look it up in a reference table for the specific solute concentration and temperature. For dilute solutions, you can approximate with the density of the pure solvent, but the approximation becomes poor above ~0.5 M.

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in m | Molarity (M) | mol/L | 1.0 | 0
in mm | Solute molar mass | g/mol | 58.44 | 0
in d | Solution density | g/mL | 1.05 | 0
out molality | Molality | mol/kg | (m * 1000) / ((d * 1000) - (m * mm)) | 4