A solution containing 2 g of a non-volatile solute in 20 g of water boils at 373.52 K. The molecular mass of the solute is ------- g mol\(^{-1}\) (Nearest integer).
Given: Water boils at 373 K, \(K_b\) for water = 0.52 K kg mol\(^{-1}\).
A solution containing 2 g of a non-volatile solute in 20 g of water boils at 373.52 K. The molecular mass of the solute is ------- g mol\(^{-1}\) (Nearest integer).
Given: Water boils at 373 K, \(K_b\) for water = 0.52 K kg mol\(^{-1}\).
Show Hint
When solving boiling point elevation problems, always ensure the masses are converted into proper units (grams to kilograms) and the molality formula is applied correctly. Use the given values of Kb and ∆Tb to calculate the molar mass of the solute accurately.
Correct Answer: 100
Solution and Explanation
Step 1: Boiling Point Elevation
The elevation in boiling point (\(\Delta T_b\)) is given as:
\[\Delta T_b = T_b - T_b^\circ = 373.52 - 373 = 0.52\,\text{K}.\]
Step 2: Use the Boiling Point Elevation Formula
The boiling point elevation is related to molality (\(m\)) by:
\[\Delta T_b = K_b \cdot m.\]
Substitute \(m = \frac{\text{mass of solute (g)}}{\text{Molar Mass (g mol}^{-1}) \times \text{mass of solvent (kg)}}\):
\[0.52 = 0.52 \cdot \frac{2}{\text{Molar Mass} \times 20 \times 10^{-3}}.\]
Step 3: Solve for Molar Mass
Simplify:
\[1 = \frac{2}{\text{Molar Mass} \times 0.02}.\]
\[\text{Molar Mass} = \frac{2}{0.02} = 100 \, \text{g mol}^{-1}.\]
Conclusion: The molecular mass of the solute is \(100 \, \text{g mol}^{-1}\).
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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.