When a liquid is completely miscible with another liquid, a homogeneous solution consisting of a single phase is formed. If such a solution is placed in a closed evacuated vessel, the total pressure exerted by the vapour, after the system attained equilibrium will be equal to the sum of partial pressures of the constituents. A solution is said to be ideal if its constituents follow Raoult's law under all conditions of concentrations, i.e., where `p_(i)` is the partial pressures of the constituent i, whose mole fraction in the solution is `x_(i)` and `p_(i)^(@)` is the corresponding vapour pressure of the pure constituent. The change in the thermodynamic functions when an ideal solution is formed by mixing pure components is given by the following expression.
`Delta_(mix) = G = n_("total") RT sum_(i) x_(i) In x_(i)` ...(i)
where, `n_("total")` is the total amount of all the constituents present in the solution.
`Delta_(mix)F =- n_("total") R sum_(i) x_(i) In x_(i)` ......(ii)
`Delta_(mix)H =- n_("total") RT sum_(i) x_(i) In x_(i) - n_("total") R sum_(i) x_(i) In x_(i) = 0` ........(iii)
`Delta_(mix) U = 0` .........(iv)
Since botli the components of an ideal binary system follow Raoult's law of the entire range of the compositions, the partial pressure exerted by the vapours of these constituents over the solution will be given by
`p_(A) = x_(A) p_(A)^(@)` ..........(v)
`p_(B) = x_(B) p_(B)^(@)` .........(vi)
where, `x_(A)` and `x_(B)` are the mole fractions of the two constituents in the liquid phase and `p_(A)^(@)` and `p_(B)^(@)` are the respective vapour pressure of the pure constituents. The total pressure (p) over the solution will be the sum of the partial pressure. The composition of the vapour phase `(y_(A))` can be determined with the help of Dalton's law of partial pressures.
A plot of reciprocal of total pressure `((1)/(p))` (y-axis) us `y_(A)` (x-axis) gives :

Options

A. a linear plot with slope `= ((1)/(p_(B)^(@))-(1)/(p_(A)^(@)))`
B. a linear plot with slop `= ((1)/(p_(A)^(@))-(1)/(p_(B)^(@)))`
C. a linear plot with slope `= (1)/(p_(B)^(@))`
D. a linear plot with slope `= p_(A)^(@) p_(B)^(@)`

Answer

B