In the accompanying chart are appropriate vapor pressures for benzene and toluene at various temperatures:
Temp (C) mmHg Temp (C) mmHg
Benzene 30 120 Toluene 30 37
40 180 40 60
50 270 50 95
60 390 60 140
70 550 70 200
80 760 80 290
90 1010 90 405
100 1340 100 560
110 760
d. Calculate the composition of the vapor (mole fraction of each component) that is in equilibrium in the solution at the boiling point of this solution.
Organic CHemistry Please help me out - Aishwarya, Thursday, October 17, 2013 at 4:53pm
Also this is part e) of same question
e. Calculate the composition in weight percentage of the vapor that is in equilibrium with the solution.
To calculate the composition of the vapor in equilibrium with the solution at its boiling point, we need to determine the mole fraction of each component (benzene and toluene) in the vapor.
At the boiling point, the vapor pressure of the solution is equal to the atmospheric pressure. Looking at the chart, we can see that the boiling point of benzene is 80°C, and the boiling point of toluene is 110°C.
At these temperatures, the vapor pressures of benzene and toluene are 760 mmHg and 760 mmHg, respectively.
To calculate the mole fraction of each component, we can use the equation:
mole fraction = vapor pressure of component / total vapor pressure
For benzene:
mole fraction of benzene = 760 mmHg / (760 mmHg + 760 mmHg) = 0.5
For toluene:
mole fraction of toluene = 760 mmHg / (760 mmHg + 760 mmHg) = 0.5
Thus, at the boiling point of the solution, the vapor composition is 50% benzene and 50% toluene in terms of mole fraction.
Moving on to part (e) of the question, to calculate the composition in weight percentage of the vapor in equilibrium with the solution, we need to convert the mole fractions to weight percentages.
To do this, we need to know the molecular weights of benzene and toluene. The molecular weight of benzene is 78.11 g/mol, and the molecular weight of toluene is 92.14 g/mol.
To calculate the weight percentage of each component, we use the equation:
weight percentage = mole fraction * molecular weight / total molecular weight
For benzene:
weight percentage of benzene = 0.5 * 78.11 g/mol / (0.5 * 78.11 g/mol + 0.5 * 92.14 g/mol) = 0.458 = 45.8%
For toluene:
weight percentage of toluene = 0.5 * 92.14 g/mol / (0.5 * 78.11 g/mol + 0.5 * 92.14 g/mol) = 0.542 = 54.2%
Thus, at the boiling point of the solution, the vapor composition is approximately 45.8% benzene and 54.2% toluene in terms of weight percentage.
To calculate the composition of the vapor at the boiling point of the solution, we need to consider the vapor pressures of benzene and toluene at that temperature.
From the given data, we can see that the boiling point of the solution is 110°C.
First, we need to find the vapor pressure of benzene and toluene at 110°C. Looking at the chart, we see that the vapor pressure of benzene at 110°C is 760 mmHg. However, the vapor pressure of toluene at 110°C is not given in the chart.
To estimate the vapor pressure of toluene at 110°C, we can use the concept of Raoult's Law. According to Raoult's Law, the vapor pressure of a component in a solution is proportional to its mole fraction in the solution.
Assuming ideal behavior, we can consider the mole fraction of benzene and toluene in the solution at its boiling point (110°C).
The mole fraction of benzene can be calculated by dividing its vapor pressure at 110°C by the sum of the vapor pressures of benzene and toluene at 110°C.
Mole fraction of benzene = Vapor pressure of benzene at 110°C / (Vapor pressure of benzene at 110°C + Vapor pressure of toluene at 110°C)
Since the vapor pressure of toluene at 110°C is not given, we cannot calculate the exact mole fraction of benzene.
Similarly, we need more information to calculate the composition in weight percentage of the vapor that is in equilibrium with the solution. We would need the molar mass of benzene and toluene and the initial composition of the solution to determine the weight percentage composition of the vapor.
Without additional information, we cannot proceed with the calculations for parts d and e of the question.