The vapour pressure of pure benzene at a certain temperature is 0.850 bar. A non - volatile, non - electrolyte solid weighing 0.5 g when added to 39.0 g of benzene (molar mass 78 g `mol^(-1)`). Vapour pressure of the solution, then, is 0.845 bar. What is the molar mass of the solid substance ?

Explanation

The various quantities known to us are as follows :
`p_(1)^(0)=0.850 " bar, " p_(1)=0.845` bar
`M_(1)=78.0 g mol^(-1), w_(2) =0.5 g, w_(1)=39 g`
Substituting these values in equation :
`(p_(1)^(0)-p_(1))/(p_(1)^(0))=(w_(2)xx M_(1))/(M_(2)xx w_(1))`
`(0.850 " bar " - 0.845 " bar")/("0.850 bar")=(0.5 g xx 78 g mol^(-1))/(M_(2)xx 39 g)`
Therefore, `M_(2)=170 g mol^(-1)`.