Question

A solution is made by mixing 31.0 mL of ethanol, C 2 H 6 O , and 69.0 mL of water. Assuming ideal behavior, what is the vapor pressure of the solution at 20 ∘ C? The relevant values at 20 ∘ C are included in the table.

Liquid Density (g/mL) Vapor Pressure, ?∘ (Torr)

ethanol 0.789 43.9

water 0.998 17.5

Answer 1

Mass ( C2H6O) = density * volume
= 0.789 g/mL * 31.0 mL
= 24.46 g

Mass (H2O) = density * volume
= 0.998 g/mL * 69.0 mL
= 68.86 g

Molar mass of C2H6O,
MM = 2*MM(C) + 6*MM(H) + 1*MM(O)
= 2*12.01 + 6*1.008 + 1*16.0
= 46.068 g/mol


Molar mass of H2O,
MM = 2*MM(H) + 1*MM(O)
= 2*1.008 + 1*16.0
= 18.016 g/mol

n(C2H6O) = mass/molar mass
= 24.46/46.068
= 0.531

n(H2O) = mass/molar mass
= 68.86/18.016
= 3.822

n(C2H6O),n1 = 0.531 mol
n(H2O),n2 = 3.822 mol

Total number of mol = n1+n2
= 0.531 + 3.822
= 4.353 mol

use:
Mole fraction of each components are
X(C2H6O) = n1/total mol
= 0.531/4.353
= 0.122

use:
X(H2O) = n2/total mol
= 3.822/4.353
= 0.878


According to Raoult’s law:
P(C2H6O) = Po(C2H6O)*X(C2H6O)
P(C2H6O) = 43.9 torr*0.122
P(C2H6O) = 5.3545 torr


According to Raoult’s law:
P(H2O) = Po(H2O)*X(H2O)
P(H2O) = 17.5 torr*0.878
P(H2O) = 15.3655 torr

total pressure = sum of individual pressures
total pressure = 5.3545 torr + 15.3655 torr
total pressure = 20.72 torr
Answer: 20.7 torr