For an ideal binary liquid solutions with `P_(A)^(@)gtP_(B)^(@)`, which relation between `X_(A)` (mole fraction of `A` in liquid phase) and `Y_(A)` (mole fraction of `A` in vapour phase) is correct:

Options

A. `y_A lt y_B`
B. `x_A gt x_B`
C. `(y_A)/(y_B) gt (x_A)/(x_B)`
D. `y_A/y_B lt x_A/x_B`

Answer

C

Explanation

`y_A = (P_A^@xx x_A)/(P_A^@x_A + P_B^@ x_B) = (x_A)/(x_A + x_B (P_B^@/P_A^@))[:.P_A^@ gt P_B^@]`
`:.y_A/x_A = (1)/(x_A + x_B (P_B^@/P_A^@)) gt 1 rArr y_A gt x_A R ...(1)`
Similarly,`y_B = (p_B^@ xx x_B)/(P_A^@x_A + P_B^@x_B) = (x_B)/(x_B + x_A(P_A^@/P_B^@))...(2)`
`:.y_B gtx_B`
`:.y_A/y_B gt x_A/x_B`