Solutions and Colligative Properties - Result Question 63

####34. Addition of $0.643 g$ of a compound to $50 mL$ of benzene (density : $0.879 g / mL$ ) lowers the freezing point from $5.51^{\circ} C$ to $5.03^{\circ} C$. If $K _f$ for benzene is 5.12 , calculate the molecular weight of the compound.

$(1992,2 M)$

Passage Based Questions

Passage 1

Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added to get homogeneous solution. These are called colligative properties. Applications of colligative properties are very useful in day-to-day life.

One of its examples is the use of ethylene glycol and water mixture as anti-freezing liquid in the radiator of automobiles.

A solution $M$ is prepared by mixing ethanol and water. The mole fraction of ethanol in the mixture is 0.9 .

Given, freezing point depression constant of water

$$ \left(K _f^{\text {water }}\right)=1.86 K kg mol^{-1} $$

Freezing point depression constant of ethanol

$$ \left(K _f^{\text {ethanol }}\right)=2.0 K kg mol^{-1} $$

Boiling point elevation constant of water

$$ \left(K _b^{\text {water }}\right)=0.52 K kg mol^{-1} $$

Boiling point elevation constant of ethanol

$$ \left(K _b^{\text {ethanol }}\right)=1.2 K kg mol^{-1} $$

Standard freezing point of water $=273 K$

Standard freezing point of ethanol $=155.7 K$

Standard boiling point of water $=373 K$ Standard boiling point of ethanol $=351.5 K$

Vapour pressure of pure water $=32.8 mm Hg$

Vapour pressure of pure ethanol $=40 mm Hg$

Molecular weight of water $=18 g mol^{-1}$

Molecular weight of ethanol $=46 g mol^{-1}$

In answering the following questions, consider the solutions to be ideal dilute solutions and solutes to be non-volatile and non-dissociative.

$(2008,3 \times 4 M=12 M)$

Show Answer

Solution:

  1. $-\Delta T _f=5.51-5.03=0.48$

$\Rightarrow \quad-\Delta T _f=0.48=K _f \cdot m$

$\Rightarrow \quad 0.48=5.12 \times \frac{0.643}{M} \times \frac{1000}{50 \times 0.879}$

$\Rightarrow \quad M=156 g / mol$



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