A solution containing 0.730 g of camphor (molar mass = 152 ) in 36.8g of acetone (b.p. `56.30^(@)C`) boils at `56.55^(@)C`. A solution of 0.564 g of an unknown compound in the same weight of solvent boils at `56.46^(@)C` . Calculate the molar mass of the unknown compound.

Explanation

In this problem , the value of `k_(b)` is not given. The first data is used to calculate `k_(b)` which is used to calculate the molar mass from the second data.
(i) Calculation of `k_(b)` for acetone .
`k_(b) = (Delta_(b) xx M_(B) xx w_(A))/(w_(B) xx 1000)`
`Delta T_(b) = 56.55 - 56.30 = 0.25^(@)C, M_(B) = 152`
`w_(B) = 0.730 g, w_(B) = 36.8 g`
`therefore " "k_(b) = (0.25 xx 152 xx 36.8)/(0.736 xx 1000) = 1.92 K m^(-1)`
(ii) Calculation of molar mass of unknown compound.
`M_(B) = (k_(b) xx 1000 xx w_(B))/(Delta T_(b) xx w_(A))`
`k_(b) = 1.92 km^(-1) , Delta T_(b) = 56.46 = 56.30`
` = 0.16^(@)C`
`w_(B) = 0.564 g, w_(A) = 36.8 g `
`M_(B) = (1.92 xx 1000 xx 0.564)/(0.16 xx 36.8) = 183.9 g mol^(-1)`