Molarity to Molality Converter
Instantly convert molarity molality with our free converter. See conversion tables, formulas, and step-by-step explanations.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Molarity to Molality Converter
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Formula: m = M / (d - M * MM / 1000)
Worked example โ 1 M NaCl = 1.0188 molal
Formula
m = M / (d - M * MM / 1000)
Molality equals molarity divided by the quantity (solution density minus molarity times molar mass divided by 1000). The denominator represents the mass of solvent in kilograms per liter of solution: total solution mass (density times 1000 g) minus solute mass (molarity times molar mass in grams), all divided by 1000 to convert to kg.
Worked Examples
Example 1: NaCl Solution Conversion
Problem:Convert 1 M NaCl solution (molar mass 58.44 g/mol, density 1.04 g/mL) to molality.
Solution:Solution mass per L = 1.04 x 1000 = 1040 g Solute mass = 1 x 58.44 = 58.44 g Solvent mass = 1040 - 58.44 = 981.56 g = 0.98156 kg Molality = 1 / 0.98156 = 1.0188 mol/kg
Result:1 M NaCl = 1.0188 molal
Example 2: Concentrated H2SO4 Conversion
Problem:Convert 5 M H2SO4 (molar mass 98.079, density 1.29 g/mL) to molality.
Solution:Solution mass = 1.29 x 1000 = 1290 g Solute mass = 5 x 98.079 = 490.395 g Solvent mass = 1290 - 490.395 = 799.605 g = 0.7996 kg Molality = 5 / 0.7996 = 6.253 mol/kg
Result:5 M H2SO4 = 6.253 molal
Frequently Asked Questions
What is the difference between molarity and molality?
Molarity (M) is defined as moles of solute per liter of solution, while molality (m) is defined as moles of solute per kilogram of solvent. The key distinction is that molarity uses total solution volume while molality uses only solvent mass. Molality is independent of temperature because mass does not change with temperature, whereas molarity varies because solution volume expands or contracts. This makes molality preferred for precise thermodynamic calculations and colligative property measurements.
Why do you need solution density to convert molarity to molality?
Solution density is required because molarity is volume-based (moles per liter of solution) while molality is mass-based (moles per kilogram of solvent). To bridge this gap, you need to know the mass of one liter of solution, which is the density times 1000 (converting kg/L to g/L). From the total mass, subtract the solute mass (molarity times molar mass) to find the solvent mass. Without density, there is no way to determine the solvent mass from a volume measurement alone.
When is molality preferred over molarity in practical applications?
Molality is preferred in situations involving temperature changes, precise thermodynamic measurements, and colligative property calculations. Since molality depends on mass (which is invariant with temperature), it remains constant whether the experiment is conducted at 20 degrees or 80 degrees Celsius. It is used for boiling point elevation, freezing point depression, and osmotic pressure calculations. In contrast, molarity is more practical for volumetric lab work since measuring volumes with graduated cylinders or pipettes is straightforward.
For dilute aqueous solutions, are molarity and molality approximately equal?
Yes, for very dilute aqueous solutions at room temperature, molarity and molality are nearly identical. This is because the density of a dilute aqueous solution is close to 1.0 g/mL (similar to pure water), and the solute mass is negligible compared to the solvent mass. In such cases, one liter of solution weighs approximately 1000 grams and contains nearly 1 kilogram of water. However, for concentrated solutions, the difference becomes significant because the solute contributes substantial mass to the solution.
References
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