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Phenol associates in benzene to a certai...

Phenol associates in benzene to a certain extent to form a dimmer. A solution containing 20 g of phenol in 1.0 kg of benzene has its freezing point lowered by 0.69 K. Calculate the fraction of phenol that has dimerised. [Given `K_f` for benzene = 5.1 K `m^(-1)`

Text Solution

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`M_2` (observed) ` = (1000 K_f w_2)/(w_1 Delta T_f)`
Substituting the values , we have
`M_2 = (1000 xx 5.12 xx 2 xx 10^(-2) )/(1.0 xx 0.69) = 148.g "mol"^(-1)`
`M_2` (calculated ) = 94 g/mol `i=(M_2("calculated"))/(M_2("observed") = (94)/(148.4) = 0.633`
The association can be expressed as under

where `alpha ` is the degree of association
`i = (1 - alpha//2)/(1) " or " alpha = 2(1 - i) = 2(1-0.633)= 0.734`
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