Question:
45 g of ethylene glycol $(C_2H_6O_2)$ is mixed with 600 g of water. The freezing point of the solution is ($K_f$ for water is $1.86\, K\, kg\, mol^{-1}$)
45 g of ethylene glycol $(C_2H_6O_2)$ is mixed with 600 g of water. The freezing point of the solution is ($K_f$ for water is $1.86\, K\, kg\, mol^{-1}$)
Updated On: Jun 23, 2023
- 273.95 K
- 270.95 K
- 370.95 K
- 373.95 K
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The Correct Option is B
Solution and Explanation
Depression in freezing point is related to the molality, therefore, the molality of the solution with respect to ethylene glycol $= \frac{moles \,of\, ethylene \,glycol}{mass \,of \,water \,in \,kilogram}$
Moles of ethylene glycol $= \frac{45 g }{62\, g \,mol^{-1}} = 0.73 \,mol$
Mass of water in $kg =\frac{600\, kg}{1000 \,kg} = 0.6\, kg$
Hence, molality of ethylene glycol
$= \frac{0.73\, mol}{0.60\, kg} = 1.2\, mol\, kg^{-1}$
Therefore, freezing point depression,
$?T_{f} = 1.86\, K\, kg\,mol^{-1} ? 1.2 \,mol \,kg^{-1} = 2.2\, K$
Freezing point of the aqueous solution
$= 273.15\, K - 2.2\, K = 270.95 \,K$
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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.