The vapour pressure of ethanol `(C_(6)H_(5) OH)` and methanol `(CH_(3) OH)` are 44.5 and 88.7 mm Hg respectively. An ideal solution is formed at the same temperature by mixing 60 g of ethanol and 40 g methanol
(i) Calculate the total vapour pressure of the solution
(ii) Find mole fraction of each component in vapour phase

Explanation

`underset((C_2H_5OH))(P_A^0)=44.5` mm Hg
`M_A=60 g`
`underset((CH_3OH))(P_B^0)=88.7` mm Hg
`M_B=40 g`
Moles of a `= 60/46`
= 1.30
Moles of B `= 40/32 1.25`
Mole fraction of a `= ("Moles of A")/("Moles of A+B")`
`=(1.30)/(1.30+1.25)`
`=0.50`
`x_B = 1-x_A`
`= 1-0.50`
= 0.5
`P_A=P_A^0x_A=44.5xx0.5`
`= 44.35`
`P_("sol"^4)=P_A+P_B`
`= 22.25 +44.35`
= 66.16
`y_A=(22.25)/(66.16)=0.34`
`y_B=(44.35)/(66.16)=0.66`