Question:

A solution containing $10\,g$ per $dm^{ 3}$ of urea (molecular mass = $60\,g\, mol^{-1})$ is isotonic with a $5\%$ solution of a non-volatile solute. The molecular mass of this non-volatile solute is :

Updated On: May 2, 2024

  • \(200\, g\, mol^{-1}\)

  • $300 \,g \,mol^{-1}$
  • $400 \,g \,mol^{-1}$
  • $500\, g\, mol^{-1}$
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The Correct Option is B

Solution and Explanation

For isotonic solution \(\pi_{1}=\pi_{2}\) 
or, \(C _{1}= C _{2}\) (conc. in mol/lit.)
(Urea solution) (unknown solution) 
\(\frac{10}{60}=\frac{5 \times 1000}{ m _{ w } \times 100}\)
\(m _{ w }=300 \,gm\, mol ^{-1}\)

So, the correct option is (B): \(300 \,g \,mol^{-1}\)

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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:

  1. Unsaturated Solution- A solution in which more solute can be dissolved without raising the temperature of the solution is known as an unsaturated solution.
  2. 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.
  3. Supersaturated Solution- A solution that contains more solute than the maximum amount at a certain temperature is known as a supersaturated solution.