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Solutions question

2023 · 30 Jan · Shift 2 · Q22
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Solutions question

2023 · 30 Jan · Shift 2 · Q22

JEE MainChemistrySolutionsNumerical+4 / −1
Lead storage battery contains 38%38 \%38% by weight solution of H2SO4\mathrm{H}_{2} \mathrm{SO}_{4}H2​SO4​. The van't Hoff factor is 2.672.672.67 at this concentration. The temperature in Kelvin at which the solution in the battery will freeze is ‾\underline{\hspace{2cm}}​. (Nearest integer). Given Kf=1.8 K kg mol−1\mathrm{K}_{f}=1.8 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}Kf​=1.8 K kg mol−1
Numerical answer
View written solutionFree

Correct answer: 243

  1. Use freezing point depression

For a solution, ΔTf=iKfm\Delta T_f = i K_f mΔTf​=iKf​m where:

  • i=2.67i = 2.67i=2.67
  • Kf=1.8 K kg mol−1K_f = 1.8\ \text{K kg mol}^{-1}Kf​=1.8 K kg mol−1
  • mmm = molality of H2SO4\mathrm{H_2SO_4}H2​SO4​ solution

The freezing point of the solution is: Tf=273−ΔTfT_f = 273 - \Delta T_fTf​=273−ΔTf​

  1. Calculate molality of the acid solution

A 38%38\%38% by weight H2SO4\mathrm{H_2SO_4}H2​SO4​ solution means:

  • Mass of H2SO4\mathrm{H_2SO_4}H2​SO4​ in 100 g100\,\text{g}100g solution = 38 g38\,\text{g}38g
  • Mass of solvent (water) = 62 g=0.062 kg62\,\text{g} = 0.062\,\text{kg}62g=0.062kg

Moles of H2SO4\mathrm{H_2SO_4}H2​SO4​: n=3898=0.3878 moln = \frac{38}{98} = 0.3878\,\text{mol}n=9838​=0.3878mol

Molality: m=0.38780.062=6.255 mol kg−1m = \frac{0.3878}{0.062} = 6.255\,\text{mol kg}^{-1}m=0.0620.3878​=6.255mol kg−1

  1. Calculate depression in freezing point

ΔTf=iKfm=2.67×1.8×6.255\Delta T_f = iK_f m = 2.67 \times 1.8 \times 6.255ΔTf​=iKf​m=2.67×1.8×6.255

First, 1.8×6.255=11.2591.8 \times 6.255 = 11.2591.8×6.255=11.259

Then, ΔTf=2.67×11.259≈30.06 K\Delta T_f = 2.67 \times 11.259 \approx 30.06\,\text{K}ΔTf​=2.67×11.259≈30.06K

  1. Find freezing temperature

Tf=273−30.06≈242.94 KT_f = 273 - 30.06 \approx 242.94\,\text{K}Tf​=273−30.06≈242.94K

Nearest integer: 243\boxed{243}243​

  1. Comparison with stored answer

Derived answer = 243243243

Stored correct answer = 243243243

So they agree.

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