Question:
An aqueous solution containing $3\, g$ of a solute of molar mass $111.6 \,g\, mol ^{-1}$ in a certain mass of water freezes at $-0.125^{\circ} C$. The mass of water in grams present in the solution is $\left(K_{f}=1.86\, Kkg \,mol ^{-1}\right)$
An aqueous solution containing $3\, g$ of a solute of molar mass $111.6 \,g\, mol ^{-1}$ in a certain mass of water freezes at $-0.125^{\circ} C$. The mass of water in grams present in the solution is $\left(K_{f}=1.86\, Kkg \,mol ^{-1}\right)$
Updated On: May 20, 2024
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The Correct Option is D
Solution and Explanation
Water freezes at $=0.125^{\circ} C$.
Freezing point of water $=0^{\circ} C$
Depression in freezing point,
$\Delta T_{f} =0-(-0.125)$
$=+0.125$
We know that
$\Delta T_{f}=\frac{K_{f} \times w \times 1000}{M \times W}$
(where, $w$ and $M=$ weight and molar mass of solute and $W=$ weight of solvent or water)
On substituting values, we get
$125 =\frac{1.86 \times 3 \times 1000}{111.6 \times W} $
or $W =\frac{1.86 \times 3 \times 1000}{0.125 \times 111.6} $
$=400\, g$
Freezing point of water $=0^{\circ} C$
Depression in freezing point,
$\Delta T_{f} =0-(-0.125)$
$=+0.125$
We know that
$\Delta T_{f}=\frac{K_{f} \times w \times 1000}{M \times W}$
(where, $w$ and $M=$ weight and molar mass of solute and $W=$ weight of solvent or water)
On substituting values, we get
$125 =\frac{1.86 \times 3 \times 1000}{111.6 \times W} $
or $W =\frac{1.86 \times 3 \times 1000}{0.125 \times 111.6} $
$=400\, g$
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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:
- 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.