Question

When '$x \times 10^{-2} \, \text{mL}$' methanol (molar mass $= 32 \, \text{g}$; density $= 0.792 \, \text{g/cm}^3$) is added to $100 \, \text{mL}$ water (density $= 1 \, \text{g/cm}^3$), the following diagram is obtained.

x = __________ (nearest integer)  
[Given: Molal freezing point depression constant of water at $273.15 \, \text{K}$ is $1.86 \, \text{K kg mol}^{-1}$]

Answer 1

Correct Answer: 543

• Calculate the freezing point depression (\( \Delta T_f \)):

\( \Delta T_f = 273.15 - 270.65 = 2.5 \, \text{K} \)

• Using the formula for freezing point depression:

\( \Delta T_f = K_f \cdot m = 2.5 = 1.86 \times \frac{n}{0.1} \)

• Solve for moles of methanol (\( n \)):

\( n = 0.1344 \, \text{moles} \)

• Calculate the mass of methanol (\( w \)):

\( w = 0.1344 \times 32 = 4.3 \, \text{g} \)

• Calculate the volume of methanol:

\( \text{Volume} = \frac{4.3}{0.792} = 5.43 \, \text{mL} = 543 \times 10^{-2} \, \text{mL} \)

Answer: \( x = 543 \)