Here are the calculations for the mole fractions of methylbenzene and the vapor pressure contribution of benzene.
Assumption: The vapor pressure of pure benzene (Pbenzene∘) is not provided. Therefore, the vapor pressure contributions of benzene will be expressed in terms of Pbenzene∘.
Step 1: Calculate the mole fraction of methylbenzene (Xmethylbenzene).
For a binary solution, the sum of mole fractions is 1:
Xbenzene+Xmethylbenzene=1
Therefore, Xmethylbenzene=1−Xbenzene.
Step 2: Calculate the vapor pressure contribution of benzene (Pbenzene).
According to Raoult's Law for an ideal solution:
Pbenzene=XbenzenePbenzene∘
where Pbenzene∘ is the vapor pressure of pure benzene.
Here are the results for the given concentrations:
| Xbenzene | Xmethylbenzene | Pbenzene (Vapor Pressure Contribution) |
| :------------------- | :------------------------- | :------------------------------------------------- |
| 0 | 1−0=1 | 0⋅Pbenzene∘=0 |
| 0.25 | 1−0.25=0.75 | 0.25⋅Pbenzene∘ |
| 0.5 | 1−0.5=0.5 | 0.5⋅Pbenzene∘ |
| 0.75 | 1−0.75=0.25 | 0.75⋅Pbenzene∘ |
| 1 | 1−1=0 | 1⋅Pbenzene∘=Pbenzene∘ |
The respective mole fractions of methylbenzene are 1, 0.75, 0.5, 0.25, 0.
The respective vapor pressure contributions of benzene are 0, 0.25Pbenzene∘, 0.5Pbenzene∘, 0.75Pbenzene∘, Pbenzene∘.
