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Solutions question

2025 · 4 Apr · Shift 2 · Q7
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Solutions question

2025 · 4 Apr · Shift 2 · Q7

JEE MainChemistrySolutionsMCQ+4 / −1
Given below are two statements: Statement (I) : Molal depression constant Kf\mathrm{K}_fKf​ is given by M1RTfΔ Sfus\frac{\mathrm{M}_1 \mathrm{RT}_f}{\Delta \mathrm{~S}_{\mathrm{fus}}}Δ Sfus​M1​RTf​​, where symbols have their usual meaning. Statement (II) : Kf\mathrm{K}_fKf​ for benzene is less than the Kf\mathrm{K}_fKf​ for water. In the light of the above statements, choose the most appropriate answer from the options given below :
  1. A
    Statement I is correct but Statement II is incorrect
  2. B
    Both Statement I and Statement II are incorrect
  3. C
    Statement I is incorrect but Statement II is correct
  4. D
    Both Statement I and Statement II are correct
View written solutionFree

Correct answer: A

  1. Check Statement (I)

For depression in freezing point,

ΔTf=Kfm\Delta T_f = K_f mΔTf​=Kf​m

and the cryoscopic constant is

Kf=RTf2M11000 ΔHfusK_f = \frac{R T_f^2 M_1}{1000\,\Delta H_{\text{fus}}}Kf​=1000ΔHfus​RTf2​M1​​

If we use

ΔSfus=ΔHfusTf\Delta S_{\text{fus}} = \frac{\Delta H_{\text{fus}}}{T_f}ΔSfus​=Tf​ΔHfus​​

then

ΔHfus=Tf ΔSfus\Delta H_{\text{fus}} = T_f\,\Delta S_{\text{fus}}ΔHfus​=Tf​ΔSfus​

Substituting:

= \frac{R T_f M_1}{1000\,\Delta S_{\text{fus}}}$$ If $M_1$ is taken in $\text{g mol}^{-1}$, the factor $1000$ is absorbed in the usual practical expression depending on unit convention. Thus the given relation $$K_f = \frac{M_1 R T_f}{\Delta S_{\text{fus}}}$$ is the standard form in that convention. So, **Statement (I) is correct**. --- 2. **Check Statement (II)** Known values of cryoscopic constants are approximately: - For water: $$K_f \approx 1.86\ \text{K kg mol}^{-1}$$ - For benzene: $$K_f \approx 5.12\ \text{K kg mol}^{-1}$$ Therefore, $$K_f(\text{benzene}) > K_f(\text{water})$$ So the statement " $K_f$ for benzene is less than the $K_f$ for water" is **incorrect**. --- 3. **Choose the correct option** - Statement I: Correct - Statement II: Incorrect Hence, the correct option is: $$\boxed{\text{A}}$$ --- 4. **Comparison with stored answer** Stored correct answer: **A** My derived answer: **A** They match.
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