# Boyle’s law formula

The Boyle’s law formula, which is succinctly expressed as P1 V1 = P2 V2, describes the relationship between the pressure and volume of a given quantity of gas. In this formula, P1 and V1 represent the initial pressure and volume of the gas, while P2 and V2 represent the final pressure and volume, respectively. This formula is useful in calculating the pressure or volume of a gas under different conditions, given the initial pressure and volume of the gas.

Contents

## Practice problems

### Problem #1

A helium gas occupies a volume of 2 L at a pressure of 5 atm. Calculate the final volume of the gas if the pressure is increased to 10 atm.

Solution

Given data:

• Initial volume of the gas, V1 = 2 L
• Initial pressure of the gas, P1 = 5 atm
• Final volume of the gas, V2 = ?
• Final pressure of the gas, P2 = 10 atm

Applying the formula:

• P1 V1 = P2 V2
• 5 × 2 = 10 × V2
• V2 = 1 L

Therefore, the final volume of the gas is 1 L.

### Problem #2

A balloon is filled with 3 L of helium gas at a pressure of 12 atm. If the volume of the gas increases to 6 L, calculate the final pressure of the gas.

Solution

Given data:

• Initial volume of the gas, V1 = 3 L
• Initial pressure of the gas, P1 = 12 atm
• Final volume of the gas, V2 = 6 L
• Final pressure of the gas, P2 = ?

Applying the formula:

• P1 V1 = P2 V2
• 12 × 3 = P2 × 6
• P2 = 6 atm

Therefore, the final pressure of the gas is 6 atm.

### Problem #3

A large container initially contains a few liters of hydrogen gas at a pressure of 2 atm. When the gas is released into a small container, it occupies a volume of 5 L at a pressure of 8 atm. Calculate the initial volume of the gas.

Solution

Given data:

• Initial pressure of the gas, P1 = 2 atm
• Final volume of the gas, V2 = 5 L
• Final pressure of the gas, P2 = 8 atm
• Initial volume of the gas, V1 = ?

Applying the formula:

• P1 V1 = P2 V2
• 2 × V1 = 8 × 5
• 2 × V1 = 40
• V1 = 20 L

Therefore, the initial volume of the gas is 20 L.

### Problem #4

A container initially contains 12 L of argon gas at an unknown pressure. When released into a small container, the gas occupies a volume of 2 L at a pressure of 6 atm. Calculate the initial pressure of the gas.

Solution

Given data:

• Initial volume of the gas, V1 = 12 L
• Final volume of the gas, V2 = 2 L
• Final pressure of the gas, P2 = 6 atm
• Initial pressure of the gas, P1 = ?

Applying the formula:

• P1 V1 = P2 V2
• P1 × 12 = 6 × 2
• P1 = 1 atm

Therefore, the initial pressure of the gas is 1 atm.