Lead storage battery contains 38 by weight solution of H2SO4. The… — Solution | JEE Chemistry

NVAMediumJEE 2023Colligative Properties

Lead storage battery contains $38\%$ by weight solution of $H_2SO_4$ . The van’t Hoff factor is $2.67$ at this concentration. The temperature in Kelvin at which the solution in the battery will freeze is _____ (Nearest integer).

Answer

Correct answer:243

Step-by-step solution

Standard Method

Given: Lead storage battery contains $38\%$ by weight solution of $H_2SO_4$ and van’t Hoff factor is $i = 2.67$ .

Find: The freezing temperature of the solution in Kelvin.

Use depression in freezing point:

\Delta T_f = i \cdot K_f \cdot m

From the working shown:

\Delta T_f = 2.67 \times 1.8 \times \left(\frac{98}{38}\right) \times \left(\frac{62}{1000}\right)

\Delta T_f = 30.05

Therefore, the freezing point is $243 \, \text{K}$ .

So, the required numerical answer is 243.

Common mistakes

Using molarity instead of molality is incorrect here because depression in freezing point depends on molality. Convert the given weight percent into mass-based terms before applying the formula.
Ignoring the van’t Hoff factor $i = 2.67$ gives a smaller freezing point depression. The dissociation effect must be included by multiplying $iK_fm$ .
Reporting $\Delta T_f$ itself as the answer is incorrect. The question asks for the freezing temperature, so subtract the depression from the freezing point of pure water to obtain the final temperature in Kelvin.

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