Molality is defined as the number of moles of solute dissolved in one kilogram of solvent. It is commonly used in chemistry because it depends only on the mass of the solvent and does not change with temperature. This makes molality very useful when studying different properties of solutions. The unit of molality is mol/kg.
Example: if one mole of a substance such as Sodium chloride is dissolved in one kilogram of water, the molality of the solution is 1 molal (1 m)
Molality Formula
It helps in determining the concentration of a solution based on the mass of the solvent. The formula to calculate the Molality of any solution is:
m = \frac{n_{\text{solute}}}{\text{Mass of solvent (kg)}}
Where:
- m = Molality of the solution
- nsolute = Number of moles of the solute dissolved
- Mass of solvent = Mass of the solvent taken in kilograms (kg)
Properties of Molality
The Molality of a solution has several important properties that make it useful for expressing concentration:
- Molality depends on the mass of the solvent in kilograms, which makes it a reliable way to measure concentration.
- Since it is based on mass and not volume, molality does not change with temperature, unlike some other concentration units.
- The unit of molality is mol kg⁻¹, which means the number of moles of solute present in one kilogram of solvent.
- Molality is also very useful in studying colligative properties of solutions, such as boiling point elevation and freezing point depression.
- Because it is based on mass, molality provides accurate and consistent results in chemical calculations and experiments
Method for Calculating Molality
Molality of a solution can be calculated by using the molality formula and the given data about the mass of solute and solvent. To calculate molality, first the number of moles of solute is determined, and then it is divided by the mass of solvent in kilograms.
The steps for calculating molality are as follows:
Step 1: Find the Mass of Solute
First, note the mass of the solute given in the problem. The solute is the substance that is dissolved in the solvent.
Step 2: Calculate the Number of Moles of Solute
The number of moles of solute is calculated using the formula:
n = \frac{\text{Mass of solute}}{\text{Molar mass of solute}}
Step 3: Convert the Mass of Solvent into Kilograms
Molality is defined in terms of kilograms of solvent, so the mass of the solvent must be converted into kilograms if it is given in grams.
1 kg=1000g
Step 4: Apply the Molality Formula
m = \frac{\text{Number of moles of solute}}{\text{Mass of solvent (kg)}}
Relation between Molarity and Molality
- Molality and molarity are two important ways to express the concentration of a solution.
- Although both represent the amount of solute present in a solution, they differ in the way the concentration is measured.
- Molality is defined as the number of moles of solute present in one kilogram of solvent, while molarity is defined as the number of moles of solute present in one litre of solution.
- Because molality depends on the mass of the solvent and molarity depends on the volume of the solution, their values are related through the density of the solution.
The relation between molality and molarity is given by:
m = \frac{1000\,M}{1000d - M \times M_s}
Where:
- m = molality of the solution
- M = molarity of the solution
- d = density of the solution in g cm-3
- Ms = molar mass of the solute
Solved Examples
Example 1: Calculate the molality of 200 g of NaOH dissolved in 150 g of pure water.
Solution:
Given,
Weight of NaOH= 200 g
Weight of pure water = 150 g (0.150kg)We, know that molar mass of NaOH is 40 g/mol.
No of moles of NaOH = 200/40
= 5 moles
Formula of molality
m= (Number of moles of solute) / (Mass of solvent in kgs)
= 5 / 0.150
= 33.3 mol/kg
Therefore, the molality of solution is 33.3 mol/ kg.
Example 2: Calculate the molality of 1000 g of H2SO4 dissolved in 5 kg of water.
Solution:
Given
Weight of H2SO4 = 1000 g
Weight of water = 5 kgWe know that molar mass of H2SO4 is 98.08 g/mol.
No of moles of H2SO4 = 1000/98.08
= 10.2 moles
Formula of molality
m = (Number of moles of solute) / (Mass of solvent in kgs)
= 10.2/5
= 2.04 mol/kg.
Therefore, the molality of solution is 2.04 mol/ kg.
Example 3: Calculate the molality of 136 g of HCl dissolved in 25 g of water.
Solution:
Given
Weight of HCl = 136 g.
Weight of Water = 25 g (0.025kg)We know that molar mass of HCl is 36.46 g/mol.
No of moles of HCl = 136/36.46
= 3.73 moles
Formula of molality
m = (Number of moles of solute)/ (Mass of solvent in kgs)
= 3.73/0.025
= 149.2 mol/kg.
Therefore, the molality of solution is 149.2 mol/ kg.