A solution is prepared by mixing 0.0200 mol CH2Cl2 and 0.0500 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.

Question

A solution is prepared by mixing 0.0200 mol CH2Cl2 and 0.0500 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.

Answer 1

Convert moles CH2Cl2 to mole fraction.

moles fraction CH2Cl2 = moles CH2Cl2/total moles.
Convert CH3Br2 to mole fraction the same way.
Then calculate the partial pressure of each gas.
P_CH2Cl2 = X_CH2Cl2*P^{o^{_{(pure solvent)}.

Do the same for CH2Br2, then add the partial pressures to obtain the total pressure.}}

Answer 2

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 equal to the product of its mole fraction in the liquid phase and the vapor pressure of the pure component.

The mole fraction (X) of a component is expressed as the ratio of the number of moles of that component to the total number of moles in the solution.

Given:
Number of moles CH2Cl2 = 0.0200 mol
Number of moles CH2Br2 = 0.0500 mol
Vapor pressure of CH2Cl2 (P₁) = 133 torr
Vapor pressure of CH2Br2 (P₂) = 11.4 torr

First, we need to calculate the total number of moles in the solution:

Total number of moles = Number of moles CH2Cl2 + Number of moles CH2Br2
= 0.0200 mol + 0.0500 mol
= 0.0700 mol

Next, we can calculate the mole fraction of each component:

Mole fraction of CH2Cl2 (X₁) = Number of moles CH2Cl2 / Total number of moles
= 0.0200 mol / 0.0700 mol
= 0.2857

Mole fraction of CH2Br2 (X₂) = Number of moles CH2Br2 / Total number of moles
= 0.0500 mol / 0.0700 mol
= 0.7143

Now, we can use Raoult's law to calculate the partial pressure of each component in the vapor phase:

Partial pressure of CH2Cl2 (P₁') = X₁ * P₁
= 0.2857 * 133 torr
= 38 torr

Partial pressure of CH2Br2 (P₂') = X₂ * P₂
= 0.7143 * 11.4 torr
= 8.14 torr

Finally, we can express the composition of the vapor in terms of mole fractions:

Mole fraction of CH2Cl2 in the vapor phase = Partial pressure of CH2Cl2 / Total vapor pressure
= 38 torr / (38 torr + 8.14 torr)

Mole fraction of CH2Br2 in the vapor phase = Partial pressure of CH2Br2 / Total vapor pressure
= 8.14 torr / (38 torr + 8.14 torr)

Thus, the composition of the vapor (in terms of mole fractions) at 25°C is:
Mole fraction of CH2Cl2 = 0.823
Mole fraction of CH2Br2 = 0.177