Question

vapor pressure of CH2Cl2 is 133 torr at 25 degree C and vapor pressure of CH2Br2 is 11.4 torr at 25 degree C

A solution is prepared by mixing 3.50 mL of dichloromethane (CH2Cl2,84.93g/mol, 1.33 g/mL) with 3.50 mL of dibromethane (CH2Br2, 173.8 g/mol, 2.48 g/mL). By what factor is the vapor phase enroched in CH2Cl2 at 25 degree C?

Answer 1

Mass of CH2Cl2 = volume x density

= 3.50 mL x 1.33 g/mL

= 4.655 g

Moles of CH2Cl2 = mass/molecular weight

= 4.655g / 84.93g/mol

= 0.0548 mol

Mass of CH2Br2 = volume x density

= 3.50 mL x 2.48 g/mL

= 8.68 g

Moles of CH2Br2 = mass/molecular weight

= 8.68g / 173.8g/mol

= 0.04994 mol

Total Moles = 0.0548 + 0.04994 = 0.10474 mol

Mol fraction of CH2Cl2

X1 = moles of CH2Cl2 / total moles

X1 = 0.0548/0.10474 = 0.5232

Mol fraction of CH2Br2

X2 = 1 - X1 = 1 - 0.5232 = 0.4768

From Raoult’s law

Total vapor pressure

P = X1*Pv1 + X2*Pv2

= 0.5232*133 + 0.4768*11.4

= 75.02112 torr

Vapor phase fraction of CH2Cl2

Y1 = X1*Pv1 / P

= 0.5232*133 / 75.02112

= 0.9275 = 92.75%

Vapor phase fraction of CH2Br2

Y2 = 1 - Y1 = 1 - 0.9275 = 0.0725 = 7.25%

The factor is the vapor phase enroched in CH2Cl2 at 25 degree C

= 92.75 / 7.25

= 12.79