The **Boyle’s law formula**, which is succinctly expressed as P_{1} V_{1} = P_{2} V_{2}, describes the relationship between the pressure and volume of a given quantity of gas. In this formula, P_{1} and V_{1} represent the initial pressure and volume of the gas, while P_{2} and V_{2} 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.

## 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, V
_{1}= 2 L - Initial pressure of the gas, P
_{1}= 5 atm - Final volume of the gas, V
_{2}= ? - Final pressure of the gas, P
_{2}= 10 atm

Applying the formula:

- P
_{1}V_{1}= P_{2}V_{2} - 5 × 2 = 10 × V
_{2} - V
_{2}= 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, V
_{1}= 3 L - Initial pressure of the gas, P
_{1}= 12 atm - Final volume of the gas, V
_{2}= 6 L - Final pressure of the gas, P
_{2}= ?

Applying the formula:

- P
_{1}V_{1}= P_{2}V_{2} - 12 × 3 = P
_{2}× 6 - P
_{2}= 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, P
_{1}= 2 atm - Final volume of the gas, V
_{2}= 5 L - Final pressure of the gas, P
_{2}= 8 atm - Initial volume of the gas, V
_{1}= ?

Applying the formula:

- P
_{1}V_{1}= P_{2}V_{2} - 2 × V
_{1}= 8 × 5 - 2 × V
_{1}= 40 - V
_{1}= 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, V
_{1}= 12 L - Final volume of the gas, V
_{2}= 2 L - Final pressure of the gas, P
_{2}= 6 atm - Initial pressure of the gas, P
_{1}= ?

Applying the formula:

- P
_{1}V_{1}= P_{2}V_{2} - P
_{1}× 12 = 6 × 2 - P
_{1}= 1 atm

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

## Related

## More topics

**Boyle’s law formula**- Charles law formula
- Gay-Lussac’s law formula
- Avogadro’s law formula
- Ideal gas law formula
- Dalton’s law formula
- Henry’s law equation
- Combined gas law formula