What is Molality? Definition and Formula

Core Concepts

In this tutorial on molality, you will learn the definition, importance, and how to calculate molality in understanding the concentration of a solution. Example calculations are provided.

Topics Covered in Other Articles

Vocabulary

Molality ( $m$ ): A measurement of concentration using the number of moles of solute per mass of solvent
Solutions: homogeneous mixtures comprising of a solute and solvent
Colligative properties: characteristics of a solution that are dependent on the concentration of solute ions
Molarity ( $M$ ): A measurement of concentration using the number of moles of solute per liters of solution

Solution Basics

Solutions are mixtures with evenly mixed, or homogeneous, components. Furthermore, these mixtures can be made of any state of matter. Solutions consists of two components: the solute and solvent. The solute is the minor or dissolved part of the solution. In comparison, the solvent dissolves the solute. For example, in the solution of table in water, the salt is the solute and the water is the solvent.

Components of a solution
https://chem.libretexts.org/Courses/Palomar_College/PC%3A_CHEM100_-_Fundamentals_of_Chemistry/13%3A_Solutions/13.02%3A_Solutions%3A_Homogeneous_Mixtures

What is Molality?

Molality, or molal concentration, refers to the number of moles of solute divided by the mass of solvent, in kilograms, mol∕kg. This term is useful in understanding the concentration of a solution because its formula is independent of temperature and pressure. Thus, the colligative properties are dependent on molality. The colligative properties include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure.

Calculating Molality

Formula:

$\begin{align*} \text{Molality} = \frac{\text{mol of solute}}{\text{kg of solvent}} \end{align*}$

Example: What is the molality of a $52 \text{g}$ sample of table salt (NaCl) in a $75 \text{kg}$ sample of water?

In this example problem, the mass of the solute (table salt) and mass of the solvent (water) are provided. Using the units of the molality formula ( $\text{mol/kg}$ ), determine if the components of the example problem have the correct units. In this example, the number of moles of solute are not provided, but with the known mass of the solute, the number of moles of solute can be determined. To calculate the number of moles of NaCl, use the molar mass of NaCl. In $1 \text{mole}$ of NaCl, there are $58.44 \text{g}$ of NaCl. With this molar mass of NaCl known, the conversion from grams to moles can be calculated via dimensional analysis.

$\begin{align*} 52\text{g}NaCl\left(\frac{1\text{mol}NaCl}{55.48\text{g}NaCl}\right) = 0.89\text{mol}NaCl \end{align*}$

Looking back at the molality formula, the correct units are $\text{mol/kg}$ . The mass of the solvent with correct units is provided in the problem, so dimensional analysis is not needed. Thus, divide the number of moles of solute by the mass of the solvent to calculate the molality of the solution.

$\begin{align*} \frac{0.89\text{mol}NaCl}{75\text{kg}H_{2}O} = 0.012\text{mol/kg}NaCl \end{align*}$

Molality and Molarity

Similarly, molarity is useful in calculating the concentration of a solution. Molarity measures the number of moles of solute per volume of solution, mol∕L, or the number of moles per one liter of solution. Additionally, molarity is dependent on temperature and is impacted by the colligative properties.

Molarity	Molality
The ratio of moles of solute to the volume of solution in liters	The ratio of moles of solute to the mass of solvent in kilograms
Represented by ‘ $M$ ‘	Represented by ‘ $m$ ‘
$M = \frac{\text{mol of solute}}{\text{liters of solution}}$	$m = \frac{\text{mol of solute}}{\text{kg of solvent}}$
Depends on the volume of whole solution	Depends only on the mass of solvent
Dependent on pressure and temperature	Independent of changes in pressure and temperature
Units: $mol/L$	Units: $mol/kg$

Table comparing molality and molarity

Molality Practice Problems

Formula:

$\begin{align*} \text{Molality} = \frac{\text{mol of solute}}{\text{kg of solvent}} \end{align*}$

Remember to acknowledge units ( $\text{mol/kg}$ )

Calculate the molality of a solution consisting of $35\text{g}$ MgCl₂dissolved in $100\text{mL}$ of water. The molar mass of MgCl₂ is $95.21\text{g/mol}$ and the density of water is $1\text{g/mL}$ .
Calculate the molality of a solution consisting of $20\text{g}$ ethanol dissolved in $300\text{mL}$ of acetone. The molar mass of ethanol is $46.07\text{g/mol}$ and the density of acetone is $0.790\text{g/mol}$ .
Calculate the number of grams of NaCl dissolved in $10\text{kg}$ of water. The molality of the solution is $0.64\text{mol/kg}$ and the molar mass of NaCl is $55.48\text{g/mol}$ .