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Solutions question

2022 · 26 Jun · Shift 1 · Q13
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Solutions question

2022 · 26 Jun · Shift 1 · Q13

JEE MainChemistrySolutionsNumerical+4 / −1
A 0.5 percent solution of potassium chloride was found to freeze at −-− 0.24 ∘^\circ∘ C. The percentage dissociation of potassium chloride is ‾\underline{\hspace{2cm}}​. (Nearest integer) (Molal depression constant for water is 1.80 K kg mol −-− 1 and molar mass of KCl is 74.6 g mol −-− 1)
Numerical answer
View written solutionFree

Correct answer: 98

  1. Use freezing point depression formula

For an electrolyte,

ΔTf=iKfm\Delta T_f = i K_f mΔTf​=iKf​m

where:

  • ΔTf=0.24 ∘C\Delta T_f = 0.24\,^\circ\text{C}ΔTf​=0.24∘C
  • Kf=1.80 K kg mol−1K_f = 1.80\,\text{K kg mol}^{-1}Kf​=1.80K kg mol−1
  • mmm = molality
  • iii = van’t Hoff factor
  1. Interpret 0.5% solution

A 0.5%0.5\%0.5% solution means 0.50.50.5 g of KCl in 100100100 g of solution.

So, mass of solvent (water) is

100−0.5=99.5 g=0.0995 kg100 - 0.5 = 99.5\text{ g} = 0.0995\text{ kg}100−0.5=99.5 g=0.0995 kg

Moles of KCl:

moles of KCl=0.574.6=0.006702 mol\text{moles of KCl} = \frac{0.5}{74.6} = 0.006702\text{ mol}moles of KCl=74.60.5​=0.006702 mol

Molality:

m=0.0067020.0995≈0.06736 mol kg−1m = \frac{0.006702}{0.0995} \approx 0.06736\,\text{mol kg}^{-1}m=0.09950.006702​≈0.06736mol kg−1
  1. Calculate van’t Hoff factor

From

i=ΔTfKfmi = \frac{\Delta T_f}{K_f m}i=Kf​mΔTf​​

we get

i=0.241.80×0.06736i = \frac{0.24}{1.80 \times 0.06736}i=1.80×0.067360.24​ i≈0.240.12125≈1.979i \approx \frac{0.24}{0.12125} \approx 1.979i≈0.121250.24​≈1.979
  1. Relate iii to degree of dissociation

KCl dissociates as

KCl→K++Cl−\text{KCl} \rightarrow \text{K}^+ + \text{Cl}^-KCl→K++Cl−

If degree of dissociation is α\alphaα, then

i=1+αi = 1 + \alphai=1+α

So,

α=i−1=1.979−1=0.979\alpha = i - 1 = 1.979 - 1 = 0.979α=i−1=1.979−1=0.979

Percentage dissociation:

0.979×100=97.9%0.979 \times 100 = 97.9\%0.979×100=97.9%

Nearest integer:

98\boxed{98}98​
  1. Comparison with stored correct answer

Stored correct answer = 989898

Our derived answer = 989898

So they agree.

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