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Association (dimerisation) of a solute from colligative data

This type of question, asked 4 times: 2021 Paper 17, 2021 Paper 23, 2021 Paper 26, 25 Jun 2022. All 4 questions below, oldest first.

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  1. Question 1

    2021 Paper 17

    57
    In a solvent 50%50\% of an acid HA dimerizes and the rest dissociates. The van't Hoff factor of the acid is ____ ×10−2\times10^{- 2}. (Round off to the nearest integer)

  2. Question 2

    2021 Paper 23

    52
     1.22 g\ 1.22\text{ }g of an organic acid is separately dissolved in 100 g100\text{ }g of benzene (Kb=2.6 K kg mol−1)\left( K_{b}= 2.6\text{ }K\text{ }kg{\text{ }mol}^{- 1} \right) and 100 g100\text{ }g of acetone (Kb=1.7 K kg mol−1)\left( K_{b}= 1.7\text{ }K\text{ }kg{\text{ }mol}^{- 1} \right). The acid is known to dimerize in benzene but remain as a monomer in acetone. The boiling point of the solution in acetone increases by 0.17∘C0.17^{\circ}C. The increase in boiling point of solution in benzene in  ∘C\ ^{\circ}C is x×10−2x \times10^{- 2}. The value of xx is (Nearest integer) [Atomic mass: =12.0,H=1.0,O=16.0= 12.0,H = 1.0,O = 16.0 ]

  3. Question 3

    2021 Paper 26

    57
    When 12.2 g12.2\text{ }g of benzoic acid is dissolved in 100 g100\text{ }g of water, the freezing point of solution was found to be −0.93∘C(Kf(H2O)=1.86 K kg mol−1)-0.93^{\circ}C\left( K_{f}\left( H_{2}O \right)= 1.86\text{ }K\text{ }kg{\text{ }mol}^{- 1} \right). The number (n)(n) of benzoic acid molecules associated (assuming 100%100\% association) is

  4. Question 4

    25 Jun 2022

    123
    Solute AA associates in water. When 0.7 g0.7\text{ }g of solute AA is dissolved in 42.0 g42.0\text{ }g of water, it depresses the freezing point by 0.2∘C0.2^{\circ}C. The percentage association of solute AA in water, is [Given: Molar mass of A=93 g mol−1A = 93\text{ }g{\text{ }mol}^{- 1}. Molal depression constant of water is 1.86 K kg mol−11.86\text{ }K\text{ }kg{\text{ }mol}^{- 1} ]

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