Methanol boils at 65Celcius. The vapor pressure of ethanol at 65Celcius is at 410 torr. for a mixture containing .200 mol of methanol and .100 mol of ethanlol (at 65 Celcius) calculate the:
1. partial pressure of each liquid
2. total vapor pressure of the solution
3. percent composition of the vapor above the solution
4. would the solution boil at 65C (assuming standard atmospheric pressure) why or why not?
To calculate the requested values, we will use Raoult's Law, which states that the vapor pressure of a component in an ideal solution is proportional to its mole fraction in the solution.
Given:
Methanol (CH3OH) boils at 65 degrees Celsius.
Vapor pressure of ethanol (C2H5OH) at 65 degrees Celsius is 410 torr.
Mixture contains:
- 0.200 mol of methanol
- 0.100 mol of ethanol
Let's calculate the values step by step:
1. Partial Pressure of Each Liquid:
According to Raoult's Law, the partial pressure of a component in the vapor phase is given by the product of its mole fraction in the liquid phase and its vapor pressure at that temperature.
Mole fraction of methanol (Xmethanol) = moles of methanol / total moles of the mixture
Xmethanol = 0.200 mol / (0.200 mol + 0.100 mol) = 0.6667
Partial pressure of methanol (Pmethanol) = Xmethanol * vapor pressure of methanol
Pmethanol = 0.6667 * 65 torr = 43.33 torr
Mole fraction of ethanol (Xethanol) = moles of ethanol / total moles of the mixture
Xethanol = 0.100 mol / (0.200 mol + 0.100 mol) = 0.3333
Partial pressure of ethanol (Pethanol) = Xethanol * vapor pressure of ethanol
Pethanol = 0.3333 * 410 torr = 136.66 torr
2. Total Vapor Pressure of the Solution:
The total vapor pressure of the solution is the sum of the partial pressures of the two components.
Total vapor pressure = Pmethanol + Pethanol
Total vapor pressure = 43.33 torr + 136.66 torr = 180 torr
3. Percent Composition of the Vapor Above the Solution:
Percent composition of a component in the vapor phase is given by the ratio of its partial pressure to the total vapor pressure, multiplied by 100.
Percent composition of methanol = (Pmethanol / Total vapor pressure) * 100
Percent composition of methanol = (43.33 torr / 180 torr) * 100 = 24.07%
Percent composition of ethanol = (Pethanol / Total vapor pressure) * 100
Percent composition of ethanol = (136.66 torr / 180 torr) * 100 = 75.93%
4. Would the Solution Boil at 65°C (Assuming Standard Atmospheric Pressure) and Why or Why Not?
No, the solution would not boil at 65°C (assuming standard atmospheric pressure) because the total vapor pressure of the solution (180 torr) is below the standard atmospheric pressure (760 torr). For the solution to boil, its vapor pressure should equal or exceed the external pressure.
To solve this problem, we need to use the concept of Raoult's Law, which states that the vapor pressure of an ideal solution is equal to the mole fraction of each component multiplied by its vapor pressure when it behaves as an ideal gas. We'll go step by step to solve the problem:
1. Partial pressure of each liquid:
The mole fraction of methanol (Xmethanol) can be calculated by dividing the number of moles of methanol by the total number of moles in the solution:
Xmethanol = nmethanol / (nmethanol + nethanol)
= 0.200 mol / (0.200 mol + 0.100 mol)
= 0.667
The partial pressure of methanol (Pmethanol) can be calculated by multiplying its mole fraction by its vapor pressure at 65°C:
Pmethanol = Xmethanol * Pmethanol_65°C
= 0.667 * 410 torr
= 273.37 torr
Similarly, we can calculate the partial pressure of ethanol (Pethanol):
Pethanol = Xethanol * Pethanol_65°C
= (1 - Xmethanol) * Pethanol_65°C
= (1 - 0.667) * 410 torr
= 136.63 torr
2. Total vapor pressure of the solution:
The total vapor pressure of the solution (Ptotal) is the sum of the partial pressures of methanol and ethanol:
Ptotal = Pmethanol + Pethanol
= 273.37 torr + 136.63 torr
= 410 torr
3. Percent composition of the vapor above the solution:
The percent composition of a component in the vapor can be calculated by dividing its partial pressure by the total vapor pressure, then multiplying by 100:
Percent composition of methanol = (Pmethanol / Ptotal) * 100
= (273.37 torr / 410 torr) * 100
= 66.65%
Percent composition of ethanol = (Pethanol / Ptotal) * 100
= (136.63 torr / 410 torr) * 100
= 33.35%
4. Will the solution boil at 65°C (assuming standard atmospheric pressure)?
To determine if the solution will boil at a specific temperature, we need to compare the boiling point of the solution to the temperature at which the solution is being heated (65°C in this case). Since the total vapor pressure of the solution (410 torr) is lower than the standard atmospheric pressure (760 torr), the solution will boil at 65°C. The boiling point is defined as the temperature at which the vapor pressure of a liquid is equal to the external pressure, which in this case, is the standard atmospheric pressure.