Question:

An aqueous solution containing 3g3\, g of a solute of molar mass 111.6gmol1111.6 \,g\, mol ^{-1} in a certain mass of water freezes at 0.125C-0.125^{\circ} C. The mass of water in grams present in the solution is (Kf=1.86Kkgmol1)\left(K_{f}=1.86\, Kkg \,mol ^{-1}\right)

Updated On: May 20, 2024
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The Correct Option is D

Solution and Explanation

Water freezes at =0.125C=0.125^{\circ} C.

Freezing point of water =0C=0^{\circ} C

Depression in freezing point,

ΔTf=0(0.125)\Delta T_{f} =0-(-0.125)
=+0.125=+0.125

We know that

ΔTf=Kf×w×1000M×W\Delta T_{f}=\frac{K_{f} \times w \times 1000}{M \times W}

(where, ww and M=M= weight and molar mass of solute and W=W= weight of solvent or water)

On substituting values, we get

125=1.86×3×1000111.6×W125 =\frac{1.86 \times 3 \times 1000}{111.6 \times W}

or W=1.86×3×10000.125×111.6W =\frac{1.86 \times 3 \times 1000}{0.125 \times 111.6}
=400g=400\, g
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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.