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JEE Advanced 2016 Paper 2 · Chemistry · Solutions, Solid State and Surface Chemistry · hard

22 g of benzoic acid (M=122 g mol^-1) is dissolved in 50.0 g of benzene (Kf=5.12 K kg mol^-1). Assuming the acid exists only as monomers and dimers…

One or more options correct

1.221.22 g of benzoic acid (M=122 g mol−1M=122\ \mathrm{g\,mol^{-1}}) is dissolved in 50.050.0 g of benzene (Kf=5.12 K kg mol−1K_f=5.12\ \mathrm{K\,kg\,mol^{-1}}). The observed depression in freezing point is 0.640.64 K. Assuming the acid exists only as monomers and dimers (2C6H5COOH⇌(C6H5COOH)22\mathrm{C_6H_5COOH}\rightleftharpoons(\mathrm{C_6H_5COOH})_2) in benzene, select the correct statement(s).
  1. A. The van't Hoff factor ii is 0.6250.625.
  2. B. The degree of association of benzoic acid is 62.5%62.5\%.
  3. C. The apparent molar mass of the solute is 76.3 g mol−176.3\ \mathrm{g\,mol^{-1}}.
  4. D. The mole fraction of the dimer among the dissolved solute species is 0.750.75.
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Answer: A

Molality assuming no association: m=(1.22/122)/0.0500=0.200 mol kg−1m=(1.22/122)/0.0500=0.200\ \mathrm{mol\,kg^{-1}}, so the expected depression is 5.12×0.200=1.0245.12\times0.200=1.024 K. Observed is 0.640.64 K, hence i=0.64/1.024=0.625i=0.64/1.024=0.625 (A is correct). For dimerisation, if a fraction α\alpha of the monomers associates, total particles =1−α/2=1-\alpha/2 per mole of monomer, so α=2(1−i)=0.75\alpha=2(1-i)=0.75, i.e. 75%75\%, not 62.5%62.5\% (B is wrong; it confuses ii with α\alpha). Association reduces the number of particles, so the apparent molar mass is 122/0.625=195.2 g mol−1122/0.625=195.2\ \mathrm{g\,mol^{-1}}, not 76.376.3 (C is wrong). Species per mole of monomer units: monomer 0.250.25, dimer 0.3750.375, total 0.6250.625, so the dimer fraction is 0.375/0.625=0.600.375/0.625=0.60 (D is wrong). Only A is correct.
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