The mole fraction of methanol in its 4.5 molal aqueous solution is

Options

A. `0.250`
B. `0.125`
C. `0.100`
D. `0.075`

Answer

D

Explanation

Let a mole of `CH_(3)OH` and b mole of water be present in the solution.
Mass of water `=b xx 18`
Molality of solution
`=(a)/(b xx 18)xx1000=4.5`
or `a/b=(18xx4.5)/(1000)=0.081`
Mole fraction of `CH_(3)OH`
`=(a)/(a+b)` or `(1)/(1+b//a)`
`=(1)/(1+(1)/(0.081))=(1)/(1+12.34)=0.075`