Calculate The Molality of Each of The Following Solutions 14.3

Molality is a measure of solution concentration that expresses the number of moles of solute per kilogram of solvent. It's particularly useful in chemistry and biochemistry where the solvent's mass is more important than its volume, especially in freezing point depression and boiling point elevation calculations.

What is molality?

Molality (m) is defined as the number of moles of solute divided by the mass of the solvent in kilograms. The formula is:

Molality Formula

m = moles of solute / mass of solvent (kg)

Molality is an intensive property, meaning it doesn't depend on the amount of solution. It's particularly useful when dealing with solutions where the volume changes significantly with temperature, as mass remains relatively constant.

Key characteristics of molality

Independent of temperature changes (unlike molarity)
Useful for cryoscopic and ebulloscopic measurements
Commonly used in biochemical and pharmaceutical applications
Expressed in units of moles per kilogram (mol/kg)

How to calculate molality

To calculate molality, you need to know:

The number of moles of solute
The mass of the solvent in kilograms

Here's a step-by-step calculation process:

Determine the molar mass of the solute
Calculate the number of moles of solute using the formula: moles = mass of solute / molar mass
Identify the mass of the solvent in kilograms
Divide the moles of solute by the mass of the solvent to get molality

Important Note

Molality calculations are temperature-independent because they use mass rather than volume. This makes them particularly useful for solutions where volume changes with temperature.

Example calculations

Let's look at a practical example to calculate molality:

Example 1: Sodium chloride solution

You have 58.44 grams of NaCl dissolved in 1.00 kg of water. Calculate the molality.

Molar mass of NaCl = 58.44 g/mol
Moles of NaCl = 58.44 g / 58.44 g/mol = 1.00 mol
Mass of solvent (water) = 1.00 kg
Molality = 1.00 mol / 1.00 kg = 1.00 mol/kg

Example 2: Sugar solution

You have 200 grams of sucrose dissolved in 500 grams of water. Calculate the molality.

Molar mass of sucrose (C₁₂H₂₂O₁₁) = 342.3 g/mol
Moles of sucrose = 200 g / 342.3 g/mol ≈ 0.584 mol
Mass of solvent (water) = 500 g = 0.500 kg
Molality = 0.584 mol / 0.500 kg ≈ 1.17 mol/kg

Practical applications

Molality is particularly useful in several scientific and industrial applications:

1. Freezing point depression

Molality is used to calculate how much a solution's freezing point is lowered compared to the pure solvent. This is crucial in cryobiology and food preservation.

2. Boiling point elevation

Similar to freezing point depression, molality helps calculate boiling point changes, important in industrial processes and laboratory work.

3. Biochemical research

In biochemistry, molality is used to prepare solutions for experiments where precise solute concentration is critical.

4. Pharmaceutical formulations

Molality is used to ensure consistent drug concentrations in medications where volume changes might occur.

Comparison with molarity

While molarity (moles per liter) is more common in general chemistry, molality is preferred when temperature changes might affect solution volume, as mass remains constant.

FAQ

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 temperature-independent, while molarity changes with temperature because volume changes.

When should I use molality instead of molarity?

Use molality when you need a concentration measure that doesn't change with temperature, especially in freezing point depression and boiling point elevation calculations.

How does molality affect freezing point depression?

The freezing point depression (ΔTf) is directly proportional to the molality of the solution. The formula is ΔTf = Kf × m, where Kf is the cryoscopic constant for the solvent.

Can molality be used for gas solutions?

Molality is typically used for liquid solutions. For gases, other concentration measures like partial pressure or mole fraction are more appropriate.