Sample Problems on Gas Laws

Example 5.1

A gas with volume 350 cm³ has a pressure of 650 mm of Hg. If its pressure is reduced to 325 mm of Hg, calculate what will be its new volume.

Data:

• V₁ = 350 cm³
• P₁ = 650 mm of Hg
• P₂ = 325 mm of Hg
• V₂ = ?

Solution:

By using Boyle's Law: PV = P₂V₂

Thus,
V₂ = (P₁ × V₁) / P₂
V₂ = (650 × 350) / 325 = 700 cm³

Thus, the volume of the gas is doubled by reducing the pressure to half.

Example 5.2

785 cm³ of a gas was enclosed in a container under a pressure of 600 mm Hg. If the volume is reduced to 350 cm³, what will be the pressure?

Data:

• V₁ = 785 cm³
• P₁ = 600 mm of Hg
• V₂ = 350 cm³
• P₂ = ?

Solution:

By using Boyle's equation: P₁V₁ = P₂V₂

Thus,
P₂ = (P₁ × V₁) / V₂
P₂ = (785 × 600) / 350 = 1345.7 mm of Hg

Converting to atm:
1345.7 / 760 = 1.77 atm

Thus, the pressure is increased by decreasing the volume.

Example 5.3

A sample of oxygen gas has a volume of 250 cm³ at -30°C. If the gas is allowed to expand up to 700 cm³ at constant pressure, find out its final temperature.

Data:

• V₁ = 250 cm³
• T₁ = -30°C = 243 K
• V₂ = 700 cm³
• T₂ = ?

Solution:

By using Charles's Law: V₁ / T₁ = V₂ / T₂

Thus,
T₂ = (V₂ × T₁) / V₁
T₂ = (700 × 243) / 250 = 680.4 K

Thus, the expansion is caused due to increasing temperature.

Example 5.4

A sample of hydrogen gas occupies a volume of 160 cm³ at 30°C. If its temperature is raised to 100°C, calculate what will be its new volume if the pressure remains constant.

Data:

• V₁ = 160 cm³
• T₁ = 30°C = 303 K
• T₂ = 100°C = 373 K
• V₂ = ?

Solution:

By using Charles's Law: V₁ / T₁ = V₂ / T₂

Thus,
V₂ = (V₁ × T₂) / T₁
V₂ = (160 × 373) / 303 = 196.9 cm³

Thus, the volume of the gas has increased by raising the temperature.