Question:
1.80 g of solute A was dissolved in 62.5 cm3 of ethanol and freezing point of the solution was found to be 155.1 K. The molar mass of solute A is ____ g mol–1.
[Given : Freezing point of ethanol is 156.0 K, Density of ethanol is 0.80 g cm–3, Freezing point depression constant of ethanol is 2.00 K kg mol–1]
1.80 g of solute A was dissolved in 62.5 cm3 of ethanol and freezing point of the solution was found to be 155.1 K. The molar mass of solute A is ____ g mol–1.
[Given : Freezing point of ethanol is 156.0 K, Density of ethanol is 0.80 g cm–3, Freezing point depression constant of ethanol is 2.00 K kg mol–1]
[Given : Freezing point of ethanol is 156.0 K, Density of ethanol is 0.80 g cm–3, Freezing point depression constant of ethanol is 2.00 K kg mol–1]
Updated On: Feb 3, 2026
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Correct Answer: 80
Approach Solution - 1
To find the molar mass of solute A, we will use the formula for freezing point depression: ΔTf = iKfm, where ΔTf is the change in freezing point, Kf is the freezing point depression constant, and m is the molality of the solution. Since solute A is non-electrolyte, i=1.
1. Calculate ΔTf: ΔTf = 156.0 K - 155.1 K = 0.9 K.
2. Determine the mass of ethanol in kg: Volume = 62.5 cm3, Density = 0.80 g/cm3.
Mass = Density × Volume = 0.80 g/cm3 × 62.5 cm3 = 50 g = 0.050 kg.
Mass = Density × Volume = 0.80 g/cm3 × 62.5 cm3 = 50 g = 0.050 kg.
3. Calculate molality (m): m = nsolute/masssolvent (kg). We rearrange ΔTf = Kf m to find m = ΔTf/Kf = 0.9 K / 2.00 K kg mol–1 = 0.45 mol/kg.
4. Express molality as nsolute/0.050 kg = 0.45 mol/kg, yielding nsolute = 0.0225 mol.
5. Calculate molar mass (M) of solute A: M = masssolute/nsolute = 1.80 g / 0.0225 mol = 80 g/mol.
6. Verification: The calculated molar mass (80 g/mol) lies within the given range (80, 80). Thus, the molar mass of solute A is confirmed to be 80 g/mol.
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Approach Solution -2
\(ΔT_f=k_fm\)
\(0.9=\frac {2×1.8×1000}{62.5×0.8×M}\)
Then, the molar mass of solute A,
\(M=\frac {2×1800}{62.5×0.8×0.9}\)
\(M=80\) g/mol
So, the answer is \(80\).
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Concepts Used:
Solutions
A solution is a homogeneous mixture of two or more components in which the particle size is smaller than 1 nm.
For example, salt and sugar is a good illustration of a solution. A solution can be categorized into several components.
Types of Solutions:
The solutions can be classified into three types:
- Solid Solutions - In these solutions, the solvent is in a Solid-state.
- Liquid Solutions- In these solutions, the solvent is in a Liquid state.
- Gaseous Solutions - In these solutions, the solvent is in a Gaseous state.
On the basis of the amount of solute dissolved in a solvent, solutions are divided into the following types:
- Unsaturated Solution- A solution in which more solute can be dissolved without raising the temperature of the solution is known as an unsaturated solution.
- Saturated Solution- A solution in which no solute can be dissolved after reaching a certain amount of temperature is known as an unsaturated saturated solution.
- Supersaturated Solution- A solution that contains more solute than the maximum amount at a certain temperature is known as a supersaturated solution.