Assume that a round bottom flask holds 100 mL and the distilling head has an internal volume of 12 mL in the vertical section. At the end of a distillation, vapor would fill this volume, but it could not be forced through the system. No liquid would remain in the distillation flask. Assuming this holdup volume of 112 mL, use the ideal gas law and assume a boiling point of 100°C (760 mm Hg) to calculate the number of milliliters of liquid (0.9 g/mL, MW=200) that would recondense into the distillation flask upon cooling.

What's the volume? Is it 12 mL or 112 mL.

If 12 mL, then
PV = nRT
You know P, V, R, and T, solve for n
Then n = grams/molar mass and solve for grams. Convert mass to volume using density.

Ok so volume would be 112 mL. Since it says that at the end of the distillation no liquid remains in the flask and vapor would fill this volume. So I assume that by 'this volume' they mean 112 mL and not just 12 mL. Am I on the right track ?

Why did the round bottom flask go to therapy?

Because it had a distillation crisis!

But hey, let's calculate the recondensation volume. First, we need to calculate the number of moles of the vapor using the ideal gas law.

PV = nRT

Where P is the pressure in atm (760 mm Hg = 1 atm), V is the volume in liters (112 mL = 0.112 L), n is the number of moles, R is the ideal gas constant (0.0821 atm L/mol K), and T is the temperature in Kelvin (100°C = 373 K).

Let's rearrange the equation to solve for n:

n = PV / RT

n = (1 atm)(0.112 L) / (0.0821 atm L/mol K)(373 K)

Now, let's calculate the number of moles:

n ≈ 0.0031 mol

Now, we can calculate the mass of the vapor using the molecular weight (MW) and the number of moles:

mass = n x MW

mass = 0.0031 mol x 200 g/mol

mass ≈ 0.62 g

Finally, we can calculate the volume of the liquid by dividing the mass by the density:

volume = mass / density

volume ≈ 0.62 g / 0.9 g/mL

volume ≈ 0.69 mL

So, approximately 0.69 mL of liquid would recondense into the distillation flask upon cooling. So much for the distillation flask trying to keep a low profile!

To calculate the number of milliliters of liquid that would recondense into the distillation flask upon cooling, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.

First, let's convert the temperature of 100°C to Kelvin:
T = 100°C + 273.15 = 373.15 K

Next, we need to calculate the moles of vapor in the system. We can use the ideal gas law equation to solve for n:
n = PV / RT

Since the system is at atmospheric pressure (760 mm Hg), we need to convert it to atmospheres:
P = 760 mm Hg / 760 = 1 atm

The total volume of the system, including the round bottom flask and the distilling head, is 112 mL.
So, the volume of vapor will be:
V = 112 mL - 12 mL = 100 mL

Now, let's calculate the number of moles:
n = (1 atm * 100 mL) / (0.0821 atm * L/mol * K * 373.15 K)

Using the value for R, the ideal gas constant:
n = (100 / 0.0821) mol

Finally, we can calculate the mass of the vapor using the molar mass (MW = 200 g/mol):
mass = n * MW = (100 / 0.0821) * 200 g

And the volume of liquid that would recondense can be determined by dividing the mass by the density (0.9 g/mL):
volume = mass / density = (100 / 0.0821) * 200 / 0.9 mL

Simplifying the expression:
volume = (100 * 200 * 200) / (0.0821 * 0.9) mL

Calculating the result:
volume ≈ 546,924 mL

Therefore, approximately 546,924 milliliters of liquid (0.9 g/mL) would recondense into the distillation flask upon cooling.