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KVPY Sample Paper KVPY Stream-SX Model Paper-21

  • question_answer
    Molecules of benzoic acid \[({{C}_{6}}{{H}_{5}}COOH)\]dimerise in benzene, 'w' g of the acid dissolved in 30 g of benzene shows a depression in freezing point equal to 2 K. If the percentage association of the acid to form dimer in the solution is 80, then w is: (Given that \[{{k}_{f}}=5K\,kg\,mo{{l}^{-1}},\]Molar mass of benzoic acid \[=122\,g\,mo{{l}^{-1}}\])

    A) 2.4 g

    B) 1.0 g

    C) 1.5 g    

    D) 1.8 g

    Correct Answer: A

    Solution :

    \[24\xrightarrow[{}]{{}}{{A}_{2}}\]
    \[1-\alpha \]                    \[\frac{\alpha }{2}\]
    \[1-0.8\]             \[\frac{0.8}{2}\]
    \[i=1-0.8+\frac{0.8}{2}=0.6\]
    \[\Delta {{\Tau }_{f}}={{K}_{f}}\times i\times m\]\[=5\times 0.6\times \frac{x}{122}\times \frac{1000}{30}=2\]             \[(since\Delta {{T}_{f}}=2)\]
    \[\therefore \]      \[x=2.44\text{ }g.\]


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