Molality Calculator
Calculate molality (moles of solute per kilogram of solvent), and convert between molality and molarity. Enter your values below and hit Calculate.
Step 2: Mass of solvent = 500 g = 0.500000 kg
Step 3: Molality = 3.000000 mol / 0.500000 kg = 6.0000 mol/kg
Molality to Molarity
Molarity to Molality
What Is Molality?
Molality is a measure of the concentration of a solute in a solution. It is defined as the number of moles of solute dissolved per kilogram of solvent (not per kilogram of solution). The SI unit of molality is mol/kg, and it is sometimes represented by the symbol b or m.
Unlike molarity, molality does not depend on the volume of the solution. Because mass does not change with temperature or pressure, molality is considered a temperature-independent concentration unit. This makes it especially useful in thermodynamic calculations and when working with colligative properties.
Molality Formula Explained
The molality of a solution is calculated using the following formula:
Where:
- b = molality (mol/kg)
- n = moles of solute (mol)
- msolvent = mass of the solvent in kilograms (kg)
If you know the mass of the solute rather than the moles, you can first calculate the number of moles using:
Then substitute the calculated moles into the molality formula.
Molality vs Molarity: Key Differences
Molality and molarity are both ways to express solution concentration, but they differ in important ways. Understanding these differences is crucial for choosing the right unit in your calculations.
| Property | Molality (b or m) | Molarity (M) |
|---|---|---|
| Definition | Moles of solute per kg of solvent | Moles of solute per liter of solution |
| Unit | mol/kg | mol/L |
| Denominator based on | Mass of solvent only | Volume of entire solution |
| Temperature dependence | Independent of temperature | Changes with temperature (volume changes) |
| Pressure dependence | Independent of pressure | Changes with pressure |
| Primary use | Colligative properties, thermodynamics | Volumetric analysis, titrations |
| Ease of preparation | Requires weighing solvent | Easier (use volumetric flask) |
When to Use Molality Over Molarity
While molarity is more commonly used in everyday laboratory work because of its convenience, there are situations where molality is the preferred or required concentration unit:
- Temperature-sensitive experiments: Because molality depends on mass rather than volume, it does not change when the temperature changes. This is essential for experiments conducted over a range of temperatures.
- Colligative properties: Boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure calculations all require molality because these properties depend on the ratio of solute particles to solvent molecules.
- Precise thermodynamic calculations: Standard thermodynamic tables and chemical potential expressions often use molality as the concentration scale.
- Highly concentrated solutions: In very concentrated solutions, the volume can change significantly as solute is added, making molarity less reliable. Molality avoids this issue.
- Non-aqueous solvents: When working with solvents whose densities differ substantially from water, molality provides a more consistent measure of concentration.
How to Calculate Molality Step by Step
Follow these steps to calculate the molality of any solution:
- Identify the solute and solvent. The solute is the substance being dissolved; the solvent is the substance doing the dissolving.
- Determine the moles of solute. If you are given the mass of the solute, divide it by the solute's molar mass to find the moles: n = mass / molar mass.
- Determine the mass of the solvent in kilograms. If the mass is given in grams, divide by 1000 to convert to kilograms. Important: use the mass of the solvent alone, not the total solution mass.
- Apply the formula. Divide the moles of solute by the mass of solvent in kg: b = n / msolvent.
Worked Example
Problem: Calculate the molality of a solution prepared by dissolving 11.7 g of NaCl (molar mass = 58.44 g/mol) in 200 g of water.
Step 1: Calculate moles of NaCl: n = 11.7 g / 58.44 g/mol = 0.2002 mol
Step 2: Convert solvent mass to kg: 200 g = 0.200 kg
Step 3: Apply the formula: b = 0.2002 mol / 0.200 kg = 1.001 mol/kg
Converting Between Molality and Molarity
To convert between molality (m) and molarity (M), you need to know the density of the solution (d) and the molar mass of the solute (W). The two conversion formulas are:
Molality to Molarity
Where M is molarity (mol/L), m is molality (mol/kg), d is solution density (g/mL or kg/L), and W is molar mass of the solute (g/mol).
Worked Example: Molality to Molarity
Problem: A 2 mol/kg NaCl solution has a density of 1.07 g/mL. The molar mass of NaCl is 58.44 g/mol. Find the molarity.
Solution:
M = m × d / (1 + m × W / 1000)
M = 2 × 1.07 / (1 + 2 × 58.44 / 1000)
M = 2.14 / (1 + 0.11688)
M = 2.14 / 1.11688 = 1.916 mol/L
Molarity to Molality
Worked Example: Molarity to Molality
Problem: A 1.5 mol/L NaCl solution has a density of 1.06 g/mL. The molar mass of NaCl is 58.44 g/mol. Find the molality.
Solution:
m = M / (d - M × W / 1000)
m = 1.5 / (1.06 - 1.5 × 58.44 / 1000)
m = 1.5 / (1.06 - 0.08766)
m = 1.5 / 0.97234 = 1.543 mol/kg
Colligative Properties and Molality
Colligative properties are solution properties that depend on the number of solute particles rather than their identity. Because molality directly measures the ratio of solute particles to the mass of solvent, it is the concentration unit used in colligative property formulas.
Boiling Point Elevation
Where ΔTb is the boiling point elevation, i is the van 't Hoff factor (number of particles the solute dissociates into), Kb is the ebullioscopic constant of the solvent, and m is the molality. For water, Kb = 0.512 °C/m.
Freezing Point Depression
Where ΔTf is the freezing point depression, Kf is the cryoscopic constant, and m is molality. For water, Kf = 1.86 °C/m.
Example: Freezing Point Depression
If you dissolve 1 mol of NaCl in 1 kg of water, NaCl dissociates into Na+ and Cl- (i = 2), so:
ΔTf = 2 × 1.86 × 1 = 3.72 °C
The freezing point drops from 0 °C to -3.72 °C.
Vapor Pressure Lowering and Osmotic Pressure
Vapor pressure lowering (Raoult's law) and osmotic pressure are also colligative properties. While osmotic pressure is typically calculated using molarity, the underlying particle count ratios that drive these phenomena relate directly to molality. In precise thermodynamic treatments, molality is preferred.
Frequently Asked Questions
What is the difference between molality and molarity?
Molality measures moles of solute per kilogram of solvent, while molarity measures moles of solute per liter of solution. Molality is independent of temperature because it is based on mass, whereas molarity changes with temperature because solution volume expands or contracts.
Why is molality used for colligative properties instead of molarity?
Colligative properties depend on the number of solute particles relative to solvent molecules. Since molality is defined per mass of solvent, it directly reflects this ratio without being affected by temperature-induced volume changes. This makes it the natural choice for calculations like boiling point elevation and freezing point depression.
Can molality and molarity ever be equal?
For very dilute aqueous solutions, molality and molarity are approximately equal. This is because the density of a dilute aqueous solution is close to 1 g/mL, and the mass of solute is negligible compared to the solvent. In such cases, 1 kg of solvent is approximately 1 L of solution.
What is the unit of molality?
The SI unit of molality is mol/kg (moles per kilogram). It is sometimes written as "m" (lowercase italic m) to distinguish it from molarity, which uses "M" (uppercase M). For example, a 2 m solution means 2 mol of solute per 1 kg of solvent.
How do I convert mass of solute to moles?
Divide the mass of the solute (in grams) by its molar mass (in g/mol). For example, 58.44 g of NaCl (molar mass = 58.44 g/mol) equals 1.00 mol. The molar mass can be found by summing the atomic masses of all atoms in the chemical formula from the periodic table.
Does molality change with temperature?
No. Molality is based on mass (kilograms), which does not change with temperature. This is one of the key advantages of molality over molarity. Volume-based units like molarity change when a solution expands or contracts with temperature shifts.
What is the molality of pure water?
Pure water has no solute, so its molality is 0 mol/kg. The concept of molality only applies when there is a solute dissolved in a solvent. However, the "molality" of water as a solvent is sometimes referenced as 55.51 mol/kg (1000 g / 18.015 g/mol) for specialized thermodynamic calculations.