$45\, g$ of ethylene glycol $\left(C_{2} H_{6} O_{2}\right)$ is mixed with $600\, g$ of water, what is the depression of freezing point?
- $7.9\, K$
- $2.5\, K$
- $6.6\, K$
- $2.2\, K$
The Correct Option is D
Approach Solution - 1
$\Delta T_{f}=\frac{K_{f} \times w \times 1000}{m \times W}$ For water $K_{f}=1.86\, g\,mol ^{-1}$
$w=45\, g$
$W=600\, g$
$m\left(C_{2} H_{6} O_{2}\right)$
$=2 \times 12+6 \times 1+2 \times 16=62$
$\therefore \Delta T_{f-}=\frac{1.86 \times 45 \times 1000}{62 \times 600}=2.25 \,K$
Approach Solution -2
Ans: Depression in the freezing point is a colligative property that geenrally occur when a non volatile solute is added to the solvent, this will lead to the freezing point of the solvent to decrease. The formula for the same is as follows:
ΔTf = K_f x m
Where,
ΔTf is the depression of the freezing point
Kf is the cryoscopic constant
M is the molality of the solution.
First we can calculate the molality, m= m xW/w
Substituting the values:
Kf= 1.86 g mol-1
w= 45g
W= 600g
m(C2H6O2) = 62
ΔT_f = 1.86 °C kg/mol * 1.208 mol/kg
≈ 2.24 °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:
- 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.