Question

A solution containing 62 g Ethyl glycol in 250 g water is cooled to $-10°\mathrm{C}$. If K_f for water is 1.86 K Kg/mol, the amount of water separated as ice is

• A. 32
• B. 48
• C. 16
• D. 64

Answer 1

The correct option is D

64

Explanation for the correct answer:-

Option (D) 64

Step 1: Given data

Temperature= $-10°\mathrm{C}$

Given weight of Ethyl glycol$=62\mathrm{g}$

Given weight of water$=250g$

${\mathrm{K}}_{\mathrm{f}}=1.86\mathrm{K}\mathrm{kg}{\mathrm{mol}}^{-1}$

Step 2: Calculating $∆{\mathrm{T}}_{\mathrm{f}}$

We know that the freezing point of water is $0°\mathrm{C}$

$$\begin{gathered} \therefore ∆{\mathrm{T}}_{\mathrm{f}}={\mathrm{T}}_f^0-{\mathrm{T}}_f \\ \Rightarrow ∆{\mathrm{T}}_{\mathrm{f}}=273-263 \\ \Rightarrow ∆{\mathrm{T}}_{\mathrm{f}}=10 \end{gathered}$$

Here, ${\mathrm{T}}_f^0$ is the melting point of the pure solvent and ${\mathrm{T}}_f$ is the melting point of the solution, $∆{\mathrm{T}}_{\mathrm{f}}$= elevation of boiling point

Step 3: Calculating the amount of water

We know that,

$∆{\mathrm{T}}_{\mathrm{f}}={\mathrm{K}}_{\mathrm{f}}\times \mathrm{m}$

And here m= molality=$\frac{\mathrm{no}.\mathrm{of}\mathrm{moles}\mathrm{of}\mathrm{solute}}{\mathrm{volume}\mathrm{of}\mathrm{solvent}\left(\mathrm{Kg}\right)}$

Also, we know that $\mathrm{number}\mathrm{of}\mathrm{moles}=\frac{\mathrm{given}\mathrm{weight}}{\mathrm{molecular}\mathrm{weight}}$

$$\begin{gathered} \therefore ∆{\mathrm{T}}_{\mathrm{f}}={\mathrm{K}}_{\mathrm{f}}\times \mathrm{m} \\ \Rightarrow ∆{\mathrm{T}}_{\mathrm{f}}={\mathrm{K}}_{\mathrm{f}}\times \frac{{\mathrm{weight}}_{\mathrm{solute}}\times 1000}{{\mathrm{weight}}_{\mathrm{solvent}}\times \mathrm{Molecular}{\mathrm{weight}}_{\mathrm{solute}}} \\ \Rightarrow 10=1.86\times \frac{62\times 1000}{{\mathrm{weight}}_{\mathrm{solvent}}\times 62} \\ \Rightarrow {\mathrm{weight}}_{\mathrm{solvent}}=186\mathrm{g} \end{gathered}$$

Now the amount of water separated is

$250\mathrm{g}-186\mathrm{g}=64\mathrm{g}$

Hence it is the correct option

Therefore, option (D) is the correct answer