Question:

A solution of urea (mol mass $56\, g\, mol^{-1})$ boils at $100.18 ^\circ\,C$ at the atmospheric pressure. If $K_f$ and $K_b$ for water are $1.86$ and $0.512\, K\, kg$ $mol^{-1}$ the above solution will freeze at

Updated On: May 17, 2024
  • -6.54$^\circ$C
  • 6.54$^\circ$C
  • 0.654$^\circ$C
  • -0.654$^\circ$C
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The Correct Option is D

Solution and Explanation

$\Delta T_b = 100.18 - 100 = 0.18 $
$\frac{\Delta T_b}{\Delta T_f} = \frac{K_bm}{K_fm} = \frac{K_b}{K_f}$
$\frac{0.18}{\Delta T_f} = \frac{0.512}{1.86}$
$\Delta T_f = \frac{0.18 \times 1.86}{0.512} = 0.654$
$T_f = (0 - 0.654) ^\circ C = - 0.654^\circ C$
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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.