Molality and Molarity Calculator

Conversion Formulas:

\[ \text{Molality (b)} = \frac{\text{Molarity (M)}}{\text{Density} - \text{Molarity} \times \text{MW} / 1000} \] \[ \text{Molarity (M)} = \frac{\text{Molality (b)} \times \text{Density}}{1 + \text{Molality} \times \text{MW} / 1000} \]

Calculation Type:

Molarity (M):

mol/L

Molality (b):

mol/kg

Solution Density:

kg/L

Molecular Weight (MW):

g/mol

1. What is Molality and Molarity?

Molarity (M) is the number of moles of solute per liter of solution. Molality (b) is the number of moles of solute per kilogram of solvent. While molarity depends on temperature (through volume changes), molality is temperature-independent.

2. Conversion Formulas

The conversion between molality and molarity requires knowing the solution density and solute molecular weight:

\[ \text{Molality} = \frac{\text{Molarity}}{\text{Density} - \text{Molarity} \times \text{MW} / 1000} \] \[ \text{Molarity} = \frac{\text{Molality} \times \text{Density}}{1 + \text{Molality} \times \text{MW} / 1000} \]

Where:

Molarity (M) — moles of solute per liter of solution (mol/L)
Molality (b) — moles of solute per kilogram of solvent (mol/kg)
Density — mass of solution per unit volume (kg/L)
MW — molecular weight of solute (g/mol)

3. When to Use Each Measurement

Molarity is commonly used in laboratory preparations and stoichiometric calculations. Molality is preferred when working with temperature-sensitive experiments or colligative properties (boiling point elevation, freezing point depression).

4. Using the Calculator

Steps: Select calculation type (molality or molarity), enter the known concentration value, solution density, and solute molecular weight. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why does molality not change with temperature?
A: Molality uses mass (kg of solvent) which doesn't change with temperature, unlike volume which expands or contracts.

Q2: When would molarity and molality be nearly equal?
A: In dilute aqueous solutions where the density is approximately 1 kg/L and the solute mass is negligible.

Q3: What's the difference between molality and molarity for a 1M NaCl solution?
A: For 1M NaCl (MW=58.44 g/mol) in water (density≈1.04 kg/L), molality is about 1.02 mol/kg.

Q4: Can I use this calculator for mixed solvents?
A: No, this calculator assumes a single solvent. For mixed solvents, additional information about solvent composition is needed.

Q5: Why does the calculator sometimes show an error?
A: An error occurs if the denominator becomes zero or negative, which happens when the solution density is too low for the given molarity and molecular weight.