Respuesta :
Answer:
[tex]y_{prop}[/tex] = 0.134; [tex]y_{iso}[/tex] = 0.866
The partial pressure of isopropanol = 34.04 Torr; The partial pressure of propanol = 5.26 Torr
Explanation:
For each of the solutions:
mole fraction of isopropanol ([tex]x_{iso}[/tex]) = 1 - mole fraction of propanol ([tex]x_{prop}[/tex]).
Given: mole fraction of propanol = 0.247. Thus, the mole fraction of isopropanol = 1 - 0.247 = 0.753.
Furthermole, the partial pressure of isopropanol = [tex]x_{iso}[/tex]*vapor pressure of isopropanol = 0.753*45.2 Torr = 34.04 Torr
The partial pressure of propanol = [tex]x_{prop}[/tex]*vapor pressure of propanol = 0.247*20.9 Torr = 5.16 Torr
Similarly,
In the vapor phase,
The mole fraction of propanol ([tex]y_{prop}[/tex]) = [tex]\frac{P_{prop} }{P_{prop}+P_{iso}}[/tex]
Where, [tex]P_{prop}[/tex] is the partial pressure of propanol and [tex]P_{iso}[/tex] is the partial pressure of isopropanol.
Therefore,
[tex]y_{prop}[/tex] = 5.26/(34.04+5.16) = 0.134
[tex]y_{iso}[/tex] = 1 - 0.134 = 0.866
The partial pressure of porpanol in vapor phase is 5.16 torr, and isopropanol is 34.04 torr. The mole fraction of propanol in vapor phase is 0.132, and isopropanol is 0.868.
What is partial pressure?
The partial pressure is the pressure exerted by the solute molecule is the solution.
The mixture is the solution of propanol and isopropanol. The total mole fraction of the solution is 1.
The given mole fraction of propanol is 0.247.
The mole fraction of isopropanol is:
[tex]\rm Mole\;fraction\;Isopropanol=1-Mole\;fraction\;Propanol\\Mole\;fraction\;Isopropanol=1-0.247\\Mole\;fraction\;Isopropanol=0.753[/tex]
According to the Roult's law, the partial pressure can be given as:
[tex]\rm Partial\;pressure=Mole\;fraction\;\times\;Vapor \;pressure[/tex]
- The partial pressure of Isopropanol is :
[tex]\rm Partial\;pressure\;Isopropanol=0.753\;\times\;45.2\;torr\\Partial\;pressure\;Isopropanol=34.04\;torr[/tex]
- The partial pressure of Propanol is :
[tex]\rm Partial\;pressure\;Propanol=0.247\;\times\;20.9\;torr\\Partial\;pressure\;Propanol=5.16\;torr[/tex]
The mole fraction in the vapor phase is given as:
[tex]\rm Mole\;fraction=\dfrac{Partial\;pressure}{Total\;pressure}[/tex]
- The mole fraction of isopropanol is;
[tex]\rm Mole\;fraction\;Isopropanol=\dfrac{34.04}{34.04+5.16}\\ Mole\;fraction\;Isopropanol=0.868[/tex]
The mole fraction of isopropanol is 0.868.
- The mole fraction of propanol is:
[tex]\rm Mole\;fraction\;Propanol=\dfrac{5.16}{34.04+5.16}\\ Mole\;fraction\;Propanol=0.132[/tex]
The mole fraction of propanol is 0.132.
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