If the total vapour presure of the liquid mixture`A`and`B`is given by the equation:`P=180X_(A)+90`then the ratio of the vapour pressure of the pure liquids A and B is given by :

Options

A. `3:2`
B. `4:1`
C. `3:1`
D. `6:2`

Answer

C

Explanation

As we know
`PT=P_(A)^(@)X_(S)+P_(B)^(@)X_(A)`
`=P_(A)^(@)X_(A)+P_(B)^(@)(1-X_(A))=(P_(A)^(@)-P_(B)^(@))X_(A)+P_(B)^(@)…(1)`
But from question,`P_(T)=180X_(A)+90...(2)`
Equating equation(1)and(2)
`:.P_(A)^(@)-P_(B)^(@)=180`
`P_(B)^(@)=90,P_(A)^(@)=180+90=270`
`(P_(A)^(@))/(P_(B)^(@))=(270)/(90)=3:1`