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12.2 g of benzoic acid is dissolved in (...

`12.2 g` of benzoic acid is dissolved in (i) `1 kg` acetone `(K_(b) = 1.9 K kg mol^(-1))` and (ii) 1 kg benzene `(K_(b) = 2.6 K kg mol^(-1)`.
The elevation of boiling points are `0.19^(@)C` and `0.13^(@) C`, respectively.
a. What are the molar masses of benzoic acid in the two solutions ?
, b. What are the structures of benzoic acid in the two solutions ?

Text Solution

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Let `Mw_(B)` be the molar mass of benzoic acid in the two solutions .
The molality of the solution is :
`m = n_(B)/W_(A) = ((12.2 g )//Mw_(B)) /(1 kg)`
Since `DeltaT_(b) = K_(b) m`, we get: a.(i) Acetone solution
`0.19 K = (1.9 K kg mol^(-1))[(12.2 g//Mw_("benzoic acid"))/(1 kg)]`
`Mw_("benzoic acid") = (1.9 xx 12.2)/0.19 g mol^(-1) = 122 g mol^(-1)`
(ii) Benzene solution
`0.13 K = (2.6 K kg mol^(-1))[(12.2 g//(Mw_("benzoic acid"))/(1 kg))]`
`Mw_("benzoic acid") = (2.6 xx 12.2)/(0.13) g mol^(-1) = 244 g mol^(-1)`
b. The actual molar mass of benzoic acid `(C_(6)H_(5)COOH)` is `122 g mol^(-1)`. This means benzoic acid is present as a monomer in acetone solution while it dimerzes in benzene solution. The structure of dimerized benzoic acid is
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