Respuesta :
Answer:
The composition of vapor is 0.86 and the composition of toluene is 0.14
Explanation:
Given:
Vapor composition [tex]y_{s} = 0.65[/tex]
Toluene composition [tex]y_{t} = 0.35[/tex]
Pressure of the system [tex]P = 150[/tex] mm Hg
From Raoult's law,
For toluene,
[tex]Py_{t} = x_{t} P _{t}[/tex]
[tex]150 \times 0.35 = x_{t} P_{t}[/tex]
[tex]x_{t} = \frac{52.5}{P_{t} }[/tex]
For vapor,
[tex]Py_{s} = x_{s} P _{s}[/tex]
[tex]150 \times 0.65 = x_{s} P _{s}[/tex]
[tex]x_{s} = \frac{97.5}{P_{s} }[/tex]
Since, [tex]x_{t} + x_{s} = 1[/tex]
[tex]\frac{52.5}{P_{t} } + \frac{97.5}{P_{s} } = 1[/tex]
Since [tex]P_{s}, P_{t}[/tex] are dependent on temperature.
At [tex]T = 358.6[/tex] K, value of [tex]P_{s} = 112.876[/tex] mm Hg and [tex]P_{t} = 359.03[/tex] mm Hg
So calculate [tex]x_{t}[/tex]
[tex]x_{t} = \frac{52.5}{359.03} = 0.14[/tex]
For [tex]x_{s}[/tex]
[tex]x_{s} = 1-x_{t}[/tex]
[tex]x_{s} = 1-0.14[/tex]
[tex]x_{s} = 0.86[/tex]
Therefore, the composition of vapor is 0.86 and the composition of toluene is 0.14
