Question:
An aqueous solution of $2\%$ non-volatile solute exerts a pressure of $1.004$ bar at the normal boiling point of the solvent. What is the molecular mass of the solute?
An aqueous solution of $2\%$ non-volatile solute exerts a pressure of $1.004$ bar at the normal boiling point of the solvent. What is the molecular mass of the solute?
Updated On: Jun 23, 2023
- $23.4\, g\, mol^{-1}$
- $41.35\, g\, mol^{-1}$
- $10\, g\, mol^{-1}$
- $20.8\, g\, mol^{-1}$
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The Correct Option is B
Solution and Explanation
Vapour pressure of pure water at boiling point
$=1\, atm = 1.013 \,bar$
Vapour pressure of solution $(ps) = 1.004\, bar$
Let mass of solution $= 100\, g$
Mass of solute $= 2 \,g$
Mass of solvent $= 100 - 2 = 98\, g$
$\frac{p^{\circ}-p_{s}}{p^{\circ}} = \frac{n_{2}}{n_{1}+n_{2}}$
$=\frac{n_{2}}{n_{1}}=\frac{W_{2}/M_{2}}{W_{1}/M_{1}} \left(\because\,n_2 <<< n_{1}\right)$
$\frac{1.013-1.004}{1.013} = \frac{2}{M_{2}} \times \frac{18}{98}$
or $M_{2 } = \frac{2 \times 18}{98} \times \frac{1.013}{0.009}$
$= 41.35\,g\,mol^{-1}$
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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.