calculate the boilinng point (at 1 atm) of a solution containing 116g of acetone

ID: 2997482 • Letter: C

Question

calculate the boilinng point (at 1 atm) of a solution containing 116g of acetone MW58 and 72g of water(MW=18) by using the following table assume that this mixture obeys Raoults law

T vapor pressure (atm) Acetone Vapor pressure (atm) water

60 1.14 0.198

70 1.58 0.312

80 2.12 0.456

90 2.81 0.694

Explanation / Answer

Calculate the boiling point (at 1 atm) of a solution containing 116 g of acetone (Mw = 58) and 72 g of water (Mw = 18) by using the following table:

Temperature
oC

Vapor pressure (atm)
Acetone

Vapor pressure (atm)
Water

1.14

0.198

1.58

0.312

2.12

0.456

2.81

0.694

A liquid starts to boil when its vapor pressure matches the atmospheric pressure (1 atm in this case). Thus, according to Raoult's law

P = xacetone Poacetone + xwater Powater = 1 atm

From the given data we can calculate the molar fractions

molesacetone = 116/58 = 2
moleswater = 72/18 = 4

total moles = 6

xacetone = 2/4 = 1/3

xwater = 4/6 = 2/3

thus

P = 2/3 Poacetone + 1/3 Powater= 1 atm

By trials, using the table, we can find the values of vapor pressure which satisfies the above equation. The best result is obtained by using the values at 80oC :

P = 2/3 0.456 + 1/3 2.12 = 1.01 atm

then the boiling point is about 80oC.