A solution is prepared by mixing 0.0400 mol CH2Cl2 and 0.0700 mol of CH2Br2 at 25°C. Assuming the solution is ideal, calculate the composition of the vapor (in terms of mole fractions) at 25°C. At 25°C, the vapor pressures of pure CH2Cl2 and pure CH2Br2 are 133 and 11.4 torr, respectively.

Question

A solution is prepared by mixing 0.0400 mol CH2Cl2 and 0.0700 mol of CH2Br2 at 25°C. Assuming the solution is ideal, calculate the composition of the vapor (in terms of mole fractions) at 25°C. At 25°C, the vapor pressures of pure CH2Cl2 and pure CH2Br2 are 133 and 11.4 torr, respectively.

Answer 1

XCH2Cl2 = 0.04/total moles.

XCH2Br2 = 0.07/total moles.

partial pressure CH2Cl2 = XCH2Cl2*133 = ??
partial pressure CH2Br2 = XCH2Br2*11.4
Total pressure = PCH2Cl2 + PCH2Br2 = ??
XCH2Cl2 in vapor = (partial pressure CH2Cl2/total P of vapor)
XCH2Br2 in vapor = (partial pressure CH2Br2/total P of vapor).

Answer 2

I did those steps and got .869 for CH2Cl2 and .130 CH2Br2 (assuming that both is in the correct number of sigfigs), but they don't seem to be right. I just want to know what I am doing wrong, or is this also the answer you got.

Answer 3

I obtained those numbers also. If you are keying your answer into a computer based "answer sheet" I suspect the problem is in the significant figures. Note that 0.04 and 0.07 have only 1 s.f. each. I would round the 0.870 value to 0.9 and the 0.130 value to 0.1

Answer 4

To calculate the composition of the vapor in terms of mole fractions, we need to use Raoult's law. According to Raoult's law, the vapor pressure of a component in an ideal solution is directly proportional to its mole fraction in the solution.

Let's start by calculating the mole fractions of CH2Cl2 and CH2Br2 in the solution.

Mole fraction of CH2Cl2 (X1) = moles of CH2Cl2 / total moles of the solution
= 0.0400 mol / (0.0400 mol + 0.0700 mol)
= 0.3636

Mole fraction of CH2Br2 (X2) = moles of CH2Br2 / total moles of the solution
= 0.0700 mol / (0.0400 mol + 0.0700 mol)
= 0.6364

Now, we can calculate the vapor pressures of the components in the solution using Raoult's law.

Partial pressure of CH2Cl2 (P1) = X1 * vapor pressure of pure CH2Cl2
= 0.3636 * 133 torr
= 48.1248 torr

Partial pressure of CH2Br2 (P2) = X2 * vapor pressure of pure CH2Br2
= 0.6364 * 11.4 torr
= 7.24416 torr

Finally, we can calculate the mole fractions of the vapor using the partial pressures.

Mole fraction of CH2Cl2 in the vapor (Y1) = P1 / (P1 + P2)
= 48.1248 torr / (48.1248 torr + 7.24416 torr)
= 0.8692

Mole fraction of CH2Br2 in the vapor (Y2) = P2 / (P1 + P2)
= 7.24416 torr / (48.1248 torr + 7.24416 torr)
= 0.1308

So, the composition of the vapor in terms of mole fractions is approximately 0.8692 for CH2Cl2 and 0.1308 for CH2Br2.