An aqueous solution containing 288gm of a non-volatile compound having the stochiometric composition `"C"_("X")"H"_("2X")"O"_("X")` in 90gm water boils at `101.24^(@)"C"` at 1.00 atmospheric pressure. What is the molecular formula?
`"K"_("b")("H"_(2)"O")=0.512" K mol"^(-1) "kg"" T"_("b")("H"_(2)"O")=100^(@)"C"`

Answer

`C_(44)H_(88)O_(44)`

Explanation

`DeltaT_(b)=101.24-100=1.24^(@),i=1` solute being non-electrolyte
`DeltaT_(b)=(1000k_(b)w_(1))/(m_(1)w_(2))(i) =(1000xx0.512xx288xx1)/(m_(1)xx90)`
`m_(1)=1321.3g "mol"^(-1)`
molecular mass of `C_(n)H_(2n)O_(n)=30n`
`30n=1321.3,n=44`
Hence, molecular formula is `C_(44)H_(88)O_(44)`.