`P_(A)and P_(B)` are the vapour pressure of pure liquid components , A and B respectively of an ideal binary solution, If `x_(A)` represents the mole fraction of component A, the total pressure of the solution will be

Options

A. `p_(A)+chi_(A)(p_(B)-p_(A))`
B. `p_(A)+chi_(A)(chi_(A)-p_(B))`
C. `p_(B)+chi_(A)(p_(B)-p_(A))`
D. `p_(B)+chi_(A)(p_(A)-p_(B))`

Answer

D

Explanation

According to Raoult's law, if volatile liquid added in pure solvent, then total pressure equal to sum of the partial pressure of volatile liquid and solvent.
Total pressure, `p_(T)=p'_(A)+p'_(B)` …..(i)
We know that, `p_(A)=p_(A)chi_(A)`
`p_(B)=p_(B)chi_(B)`
Substituting the values of `p'_(A)` and `p'_(B)` in Eq. (i)
`p_(T)=p_(A)chi_(A)+p_(B)chi_(B)`
Mole fracion, `chi_(A)+chi_(B)=1rArr chi_(B)=1-chi_(A)`
On substituting above equation,
`p_(T)=p_(A)chi_(A)+p_(B)(1-chi_(A))`
`=p_(A)chi_(A)+p_(B)-p_(B)chi_(A)`
`therefore p_(T)=p_(B)+chi_(A)(p_(A)-p_(B))`