A solution is prepared by mixing 0.0433 mol CH2Cl2 and 0.0623 mol 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.
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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 partial pressure of each component in a mixture is proportional to its mole fraction in the liquid phase.
First, we need to calculate the total mole fraction of the solution. The total number of moles in the solution can be calculated by adding the moles of CH2Cl2 and CH2Br2:
Total moles = 0.0433 mol + 0.0623 mol = 0.1056 mol
The mole fraction of CH2Cl2 in the solution is given by:
Mole fraction of CH2Cl2 = moles of CH2Cl2 / total moles
Mole fraction of CH2Cl2 = 0.0433 mol / 0.1056 mol ≈ 0.4106
Similarly, the mole fraction of CH2Br2 in the solution is:
Mole fraction of CH2Br2 = moles of CH2Br2 / total moles
Mole fraction of CH2Br2 = 0.0623 mol / 0.1056 mol ≈ 0.5894
Now, we can calculate the partial pressure of each component in the vapor phase using Raoult's law.
Partial pressure of CH2Cl2 = Mole fraction of CH2Cl2 * Vapor pressure of CH2Cl2
Partial pressure of CH2Cl2 = 0.4106 * 133 torr ≈ 54.4938 torr
Partial pressure of CH2Br2 = Mole fraction of CH2Br2 * Vapor pressure of CH2Br2
Partial pressure of CH2Br2 = 0.5894 * 11.4 torr ≈ 6.7132 torr
Therefore, the composition of the vapor in terms of mole fractions is approximately:
Mole fraction of CH2Cl2 in the vapor = Partial pressure of CH2Cl2 / Total vapor pressure
Mole fraction of CH2Cl2 in the vapor = 54.4938 torr / (54.4938 torr + 6.7132 torr) ≈ 0.8905
Mole fraction of CH2Br2 in the vapor = Partial pressure of CH2Br2 / Total vapor pressure
Mole fraction of CH2Br2 in the vapor = 6.7132 torr / (54.4938 torr + 6.7132 torr) ≈ 0.1095
Therefore, the composition of the vapor in terms of mole fractions at 25°C is approximately 0.8905 for CH2Cl2 and 0.1095 for CH2Br2.