Fractional Distillation Calculations

[boredbluejay]

Homework Statement

4-bromotoluene was synthesized and purified by distillation. There are 5ml of the crude product. A fractional distillation is being carried out in a 100ml round bottom flask. Assume that the volume of the column is 16ml. Determine the number of moles of 4-bromotoluene that will remain vaporized and cannot be collected. What will the volume of the condensed vapor be?

Homework Equations

PV=nRT
Total Pressure=χaPa+χbPb, where χis the mole fraction of a or b and P is the normal pressure of a or b.
bp of 4-bromotoluene is 184C
density=1.39g/ml
MW=171.13g/mol

The Attempt at a Solution

I know that we are trying to find n using PV=nRT. However, I'm not sure which values we plug in. Do I use V=16ml for the volume inside the column? Do I use the boiling point for T? Also, how do you find the pressure of the system? If P= the total pressure of the mixture, how would you find it if you don't know how much of the compound is made up of 4-bromotoluene and what the pressure of 4-bromotoluene is?

Thank you very much!

 

[nate808]

To determine the number of moles of 4-bromotoluene that will remain vaporized and cannot be collected, we need to use the ideal gas law equation PV=nRT. In this equation, P represents the pressure of the system, V represents the volume of the system, n represents the number of moles, R is the gas constant, and T is the temperature in Kelvin.

First, let's determine the pressure of the system. We know that the total pressure of a mixture is equal to the sum of the partial pressures of each component. In this case, the mixture is composed of 4-bromotoluene and other components. We can assume that the pressure of the other components is negligible compared to the pressure of 4-bromotoluene. Therefore, we can use the total pressure formula: Total Pressure = χaPa + χbPb, where χ is the mole fraction of the component and P is the normal pressure of that component. In this case, we can assume that χa = 1, since we are only dealing with 4-bromotoluene. We can also assume that Pb is negligible. Therefore, the total pressure of the system is equal to the normal pressure of 4-bromotoluene.

Next, we need to determine the volume of the system. The total volume of the system is equal to the volume inside the column (16ml) plus the volume of the round bottom flask (100ml). Therefore, the total volume is 116ml.

Now, we can plug in the values into the ideal gas law equation: PV=nRT. We know that R is a constant, so we can solve for n by rearranging the equation to n=PV/RT. We can use the boiling point of 4-bromotoluene (184C or 457K) for T. We also know that the density of 4-bromotoluene is 1.39g/ml and the molecular weight is 171.13g/mol. Therefore, we can calculate the number of moles of 4-bromotoluene that will remain vaporized and cannot be collected.

To determine the volume of the condensed vapor, we need to use the ideal gas law again. This time, we can use the number of moles we calculated earlier (n) and the temperature of the vapor (457K). We can rearr