Question

Question 1

Acetone (CH3)2CO is a volatile Liquid that can be readily converted to vapour.
Calculate the density of acetone vapour at 100,000 Pa and 398 K in kg/m3. Assume
ideal behaviour and use R=8.314 J/mol.K.
Your Answer:
Answer

Answer 1

• 1.76 kg/m³

Step-by-step explanation:

1) Data:

a) Chemical formula: (CH₃)₂CO

b) P = 100,000 Pa

c) T = 398 K

d) D = ?

e) R = 8.314 J / mol.K

2) Principles and formulae:

a) Ideal behaviour of a gas means that it follows the ideal gas equation:

• PV = nRT

b) Density, D = mass / volume

c) mass in grams = n × molar mass

3) Solution:

a) Transform the ideal gas equation to solve for the density:

• PV = nRT ( n = mass in grass / molar mass)

• PV = (mass in grams / molar mass) RT

• (mass in grams / V) = P × molar mass / (RT)

• mass in kg × 1,000 (g/ kg) / V = P × molar mass / (RT)

• (mass in kg / V) = P × molar mass / (1,000RT)

• D = P × molar mass / (1,000RT)

b) Molar mass of (CH₃)₂CO: 58.08 g/mol

c) Substitute and compute:

• D = 100,000 Pa × 58.08 kg/mol / ( 1,000 × 8.314 J/mol.K × 398 K)

* (note that by dividing by 1,000 the molar mass is transformed from g/mol to kg/mol)

• D = 1.76 kg/m³← answer