The boiling point of benzene is `353.23 K`. When `1.80 g` of a non-volatile solute was dissolved in `90 g` benzene, the boiling point is raised to`354.11 K`. Calculate the molar mass of the solute. (`K_(b)` for benzene is `2.53 K kg mol^(-1)`)

Explanation

Given values are:
`T_(("benzene"))^(@) = 353.00 K , K_(b) = 2.53.00 K kg mol_(-1)`
`T_(b("solution")) = 354.00 K`
`W_("solute") = 1.80 g`
`W_("solvent") = 90 g`
The elevation in boiling point ,`DeltaT_(b) = T_(b("solution")) - T_(b("solvent"))^(@)`
`= 354.11 - 353.23`
`=0.88 K`
Molar mass of solute is given as
`Mw_("solute") = (K_(b) xx 1000 xx W_("solute"))/(DeltaT_(b) xx W_("solvent")`
`Mw_("solute") = (2.53 xx 1000 xx 1.80)/(0.88 xx 90) = 58.0 g mol^(-1)`
Hence, the molar mass of solute is `58.0 g mol^(-1)`.