Solved Examples on Boyle’s Law

Example 1: Find the pressure required to compress 600 dm³ of air at 1 Bar to 200 dm³ at 30^oC.

Solution:

At constant temperature of 30^oC

V₁  = 600 dm³, P₁ = 1 bar, V₂  = 600 dm³ and P₂ = ?

Using Boyle’s Law, P₁V₁ = P₂V₂

1 Bar × 600 dm³ = P₂ × 200 dm³

P₂ = 600/200

P₂ = 3 Bar

Example 2: Calculate the pressure required to reduce 400 mL of gas at 700 mm pressure to 300 mL at the same temperature.

Solution:

At constant temperature

V₁  = 400 mL, P₁ = 700 mm, V₂  = 300 mL and P₂ = ?

Using Boyle’s Law, P₁V₁ = P₂V₂

700 mm × 400 mL = P₂ × 300  mL

P₂ = 280000/300

P₂ = 933.33 mL

Example 3: A gas is expanded, at a constant temperature, from a volume of 500 mL to a volume of 1.5 litre, where its final pressure is 150 mm of Hg. What was the original pressure?

Solution:

At constant temperature,

V₁  = 500 mL, P₂ = 150 mm of Hg, V₂  = 1.5 L and P₁ = ?

Convert 1.5 L to mL.

1 L = 1000 mL

1.5 L = 1.5 × 1000 mL = 1500 mL

Using Boyle’s Law, P₁V₁ = P₂V₂

P₁ × 500 mL = 150 mm × 1500  mL

P₁ = 225000/500

P₁ = 450 mL

Example 4: Find the volume of a sample of nitrogen at a pressure of 1.50 atm, if its volume is 3.15 L at 1.00 atm and the temperature is constant.

Solution:

At Constant Temperature,

V₁  = 3.15 L, P₁ = 1 atm, P₂  = 1.5 atm and V₂ = ?

Using Boyle’s Law, P₁V₁ = P₂V₂

1 atm × 3.15 L = 1.5 atm × V₂

V₂ = 3.15/1.5

V₂ = 2.1 L

The English chemist Robert Boyle (1627–1691), widely regarded as one of the pioneers of the modern experimental science of chemistry, is commonly credited with this development. He found that increasing the pressure of a sample of contained gas by two times while holding its temperature constant reduced the gas volume by half. According to Boyle’s law, a gas’s volume changes inversely with pressure when the temperature is held constant. This is an illustration of an inverted relationship. The second variable drops when one variable rises in value.