A solution is prepared by mixing 8.5 g of CH2Cl2 and 11.95 g of CHCl3. If vapour pressure of CH2Cl2 and CHCl3 at 298 K are 415 and 200 mm Hg respectively, the mole fraction of CHCl3 in vapour form is : (Molar mass of Cl = 35.5 g mol–1) (1) 0.162 Sol. 3 13. (2) 0.675 (3) 0.325 (4) 0.486

To find the mole fraction of CHCl3 in the vapor form, we need to first calculate the moles of each component in the solution and then use Raoult's Law to find the vapor pressures. Let’s break it down step by step.

Step 1: Calculate Moles of Each Component

The molar masses of the compounds are needed for this calculation. For CH2Cl2 (dichloromethane), the molar mass is calculated as follows:

• C: 12.01 g/mol
• H: 1.008 g/mol
• Cl: 2 × 35.5 g/mol = 71.0 g/mol

Thus, the molar mass of CH2Cl2 is:

Molar mass of CH2Cl2 = 12.01 + 1.008 + 71.0 = 84.018 g/mol

Now, for CHCl3 (chloroform), the molar mass is:

• C: 12.01 g/mol
• H: 1.008 g/mol
• Cl: 3 × 35.5 g/mol = 106.5 g/mol

So, the molar mass of CHCl3 is:

Molar mass of CHCl3 = 12.01 + 1.008 + 106.5 = 119.518 g/mol

Now that we have the molar masses, we can calculate the number of moles of each compound:

• Moles of CH2Cl2: 8.5 g / 84.018 g/mol ≈ 0.101 moles
• Moles of CHCl3: 11.95 g / 119.518 g/mol ≈ 0.100 moles

Step 2: Calculate Total Moles in the Solution

Now we add the moles of both components:

Total moles = Moles of CH2Cl2 + Moles of CHCl3 = 0.101 + 0.100 = 0.201 moles

Step 3: Calculate Mole Fractions

The next step is to find the mole fraction of CHCl3 in the solution:

Mole fraction of CHCl3 (X_CHCl3) = Moles of CHCl3 / Total moles = 0.100 / 0.201 ≈ 0.497

Step 4: Apply Raoult’s Law

According to Raoult's Law, the partial vapor pressure of each component is given by:

Partial Pressure of CHCl3 (P_CHCl3) = X_CHCl3 * P°_CHCl3

Where P°_CHCl3 is the vapor pressure of pure CHCl3, which is 200 mm Hg. Therefore:

P_CHCl3 = 0.497 * 200 mm Hg = 99.4 mm Hg

Step 5: Calculate the Total Vapor Pressure

Similarly, we calculate the partial pressure of CH2Cl2:

Partial Pressure of CH2Cl2 (P_CH2Cl2) = X_CH2Cl2 * P°_CH2Cl2

Where P°_CH2Cl2 is 415 mm Hg:

P_CH2Cl2 = (0.101 / 0.201) * 415 mm Hg = 207.6 mm Hg

Now, we can find the total vapor pressure (P_total):

P_total = P_CHCl3 + P_CH2Cl2 = 99.4 mm Hg + 207.6 mm Hg = 307 mm Hg

Step 6: Calculate Mole Fraction of CHCl3 in Vapor Form

Finally, the mole fraction of CHCl3 in the vapor can be calculated using the partial pressures:

Mole fraction of CHCl3 in vapor (Y_CHCl3) = P_CHCl3 / P_total

Y_CHCl3 = 99.4 mm Hg / 307 mm Hg ≈ 0.324

Final Result

The mole fraction of CHCl3 in the vapor form is approximately 0.325.

Thus, the correct answer from the options provided is (3) 0.325.