The vapour pressure of ethanol and methanol are `44.0 mm Hg` and `88.0 mm Hg`, respectively. An ideal solution is formed at the same temperature by mixing `60 g` of ethanol with `40g` of methanol. Calculate the total vapour pressure of the solution and the mole fraction of methanol in the vapour.

Options

A. 0.467
B. 0.502
C. 0.513
D. 0.556

Answer

C

Explanation

`P_(m) = P_(CH_(3)OH)^(@) X_(CH_(3)OH)^(@) + P_(C_(2)H_(5)OH)^(@) X_(C_2H_5OH)^(@)`
Thus,
`P_(m)=88.5xx[(16/32)/(16/32+46/46)]+42 xx [(46/46)/(16/32+46/46)]=57.5`
`:.P_(m)X_(CH_(3)OH)(g)=P_(CH_(3)OH)^(@) X_(CH_(3)OH)^(@)`
`:. 88.5 xx [(16//32)/(16/32+46/46)]=57.5 X_(CH_(3)OH(g))`
`:. X_(CH_(3)OH(g))=0.513`