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Solutions question

2021 · 27 Jul · Shift 2 · Q19
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Solutions question

2021 · 27 Jul · Shift 2 · Q19

JEE MainChemistrySolutionsNumerical+4 / −1
In a solvent 50% of an acid HA dimerizes and the rest dissociates. The van't Hoff factor of the acid is ‾×\underline{\hspace{2cm}}\times​× 10 −-− 2. (Round off to the nearest integer)
Numerical answer
View written solutionFree

Correct answer: 125

  1. Let initial moles of acid be 1

    Take 111 mole of HAHAHA initially.

  2. Given behavior

    • 50%50\%50% of HAHAHA dimerizes.
    • The remaining 50%50\%50% dissociates.

  3. Dimerization part

    50%50\%50% of 111 mole =0.5=0.5=0.5 mole of HAHAHA dimerizes.

    Dimerization process: 2HA→(HA)22HA \rightarrow (HA)_22HA→(HA)2​

    So, 0.50.50.5 mole of HAHAHA forms: 0.52=0.25 mole of (HA)2\frac{0.5}{2}=0.25 \text{ mole of } (HA)_220.5​=0.25 mole of (HA)2​

  4. Dissociation part

    Remaining 0.50.50.5 mole of HAHAHA dissociates: HA→H++A−HA \rightarrow H^+ + A^-HA→H++A−

    Thus, 0.50.50.5 mole of HAHAHA gives:

    • 0.50.50.5 mole H+H^+H+
    • 0.50.50.5 mole A−A^-A−

    Total particles from this part =0.5+0.5=1.0=0.5+0.5=1.0=0.5+0.5=1.0 mole particles.

  5. Total particles after association/dissociation

    Final particles are:

    • 0.250.250.25 mole of (HA)2(HA)_2(HA)2​
    • 0.50.50.5 mole of H+H^+H+
    • 0.50.50.5 mole of A−A^-A−

    Therefore total number of solute particles: 0.25+0.5+0.5=1.250.25+0.5+0.5=1.250.25+0.5+0.5=1.25

  6. Van't Hoff factor

    i=actual number of particlesinitial number of formula unitsi=\frac{\text{actual number of particles}}{\text{initial number of formula units}}i=initial number of formula unitsactual number of particles​

    Since initially we had 111 mole of HAHAHA, i=1.251=1.25i=\frac{1.25}{1}=1.25i=11.25​=1.25

  7. Match with required form

    The question says van't Hoff factor is ‾×10−2\underline{\hspace{2cm}}\times 10^{-2}​×10−2.

    So write: 1.25=125×10−21.25 = 125 \times 10^{-2}1.25=125×10−2

    Hence the required integer is: 125\boxed{125}125​

  8. Comparison with stored answer

    Stored correct answer = 125125125

    This matches our result.

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