A mixture which contains `0.550 g` of camphor and `0.090 g` of an organic solute melts at `161^(@)C`. The solute contains `93.75%C` and `6.25%` H by weight.What is the molecular formula of compound? `K_(f)` for camphor is `37.5^(@)C "mol"^(-1) kg`. The melting point of camphor is `209^(@)C`.

Explanation

Given,
`Delta=209-161=48^(@)C`
`W_(2)=0.09 g` (organic solute)
`W_(1)=0.55 g` (camphor)
`K_(f)=37.5^(@)C mol^(-1) kg`
`DeltaT=(1000 xx K_(f)xxW_(2))/(Mw_(2)xx0.55)`
`:. Mw_(2) = 127.84`

`:. C : H :: 1.25:1` or `5:4`
`:.` Empirical formula is `C_(5)H_(4)` and empirical formula weight =`64`
`:.`Molecular formula is `(C_(5)H_(4))_(n)` and `n=127.84/64 ~~2`
`:.`Molecular formula of solute is `(C_(5)H_(4))_(2) =C_(10)H_(8)`