Calculate The Molality of Each of The Following Aqueous Solutions.
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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 because it's independent of temperature changes, unlike molarity. This guide explains how to calculate molality, provides examples, and compares it to molarity.
What is molality?
Molality (m) is defined as the number of moles of solute dissolved in one kilogram of solvent. The key characteristic of molality is that it's independent of temperature changes because the mass of the solvent remains constant.
Molality is commonly used in:
- Cryoscopy (freezing point depression)
- Ebullioscopy (boiling point elevation)
- Osmotic pressure measurements
- Biochemical applications where temperature variations are significant
How to calculate molality
To calculate molality, you need to know:
- The number of moles of solute
- The mass of the solvent in kilograms
The calculation process involves:
- Determine the mass of the solute in grams and convert it to moles using the molar mass
- Measure or know the mass of the solvent in kilograms
- Divide the moles of solute by the kilograms of solvent
Molality formula
Molality Formula
m = n / msolvent
Where:
- m = molality (mol/kg)
- n = number of moles of solute (mol)
- msolvent = mass of solvent in kilograms (kg)
The formula shows that molality is calculated by dividing the number of moles of solute by the mass of the solvent in kilograms. This makes molality independent of temperature changes, as the mass of the solvent remains constant.
Molality examples
Let's look at some examples to understand how molality is calculated:
Example 1: Sodium chloride solution
Calculate the molality of a solution made by dissolving 25.0 grams of NaCl in 500 grams of water.
- Calculate moles of NaCl: 25.0 g / 58.44 g/mol = 0.428 mol
- Convert solvent mass to kg: 500 g = 0.500 kg
- Calculate molality: 0.428 mol / 0.500 kg = 0.856 mol/kg
Example 2: Sugar solution
Calculate the molality of a solution made by dissolving 10.0 grams of sucrose in 200 grams of water.
- Calculate moles of sucrose: 10.0 g / 342.3 g/mol = 0.0292 mol
- Convert solvent mass to kg: 200 g = 0.200 kg
- Calculate molality: 0.0292 mol / 0.200 kg = 0.146 mol/kg
| Solute | Mass of Solute (g) | Mass of Solvent (g) | Molality (mol/kg) |
|---|---|---|---|
| NaCl | 25.0 | 500 | 0.856 |
| Sucrose | 10.0 | 200 | 0.146 |
Molality vs. molarity
Molality and molarity are both measures of solution concentration, but they differ in their calculation and applications:
| Property | Molality | Molarity |
|---|---|---|
| Definition | Moles of solute per kg of solvent | Moles of solute per liter of solution |
| Formula | m = n / msolvent | M = n / Vsolution |
| Temperature dependence | Independent (mass is constant) | Dependent (volume changes with temperature) |
| Common uses | Cryoscopy, ebullioscopy, biochemical applications | Dilution calculations, titrations, general chemistry problems |
The choice between molality and molarity depends on the specific application. Molality is preferred when temperature variations are significant, while molarity is more commonly used in general chemistry problems.
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 independent of temperature changes, while molarity is affected by temperature because volume changes with temperature.
Why is molality used in cryoscopy and ebullioscopy?
Molality is used in these applications because it's independent of temperature changes. The freezing point depression and boiling point elevation are directly proportional to the molality of the solution, making it a reliable measure for these experiments.
How do I convert between molality and molarity?
Converting between molality and molarity requires knowing the density of the solution. You can use the formula: M = m × (density of solution / density of pure solvent). This conversion is necessary when you need to compare concentration measurements made under different conditions.
What are the units for molality?
The units for molality are moles per kilogram (mol/kg). This indicates the number of moles of solute dissolved in one kilogram of solvent.