# Gay-Lussac’s law formula

Gay-Lussac’s law formula, which is expressed as P1/T1 = P2/T2, relates the pressure and temperature of a gas. In this formula, P1 and T1 represent the initial pressure and temperature of the gas, while P2 and T2 represent the final pressure and temperature, respectively. This formula can be used to calculate the pressure or temperature of a gas under different conditions, given the initial pressure and temperature of the gas.

Contents

## Practice problems

### Problem #1

A gas cylinder contains hydrogen gas at a pressure of 2 atm and a temperature of 20 ℃. What is the final pressure of the gas when the temperature of the cylinder is increased to 60 ℃?

Solution

Given data:

• Initial pressure of the gas, P1 = 2 atm
• Initial temperature of the gas, T1 = 20 ℃ = 293 K
• Final pressure of the gas, P2 = ?
• Final temperature of the gas, T2 = 60 ℃ = 333 K

Applying the formula:

• P1/T1 = P2/T2
• P2 = (P1 × T2) ÷ T1
• P2 = (2 × 333) ÷ 293
• P2 = 666 ÷ 293
• P2 = 2.27 atm

Therefore, the final pressure of the gas is 2.27 atm.

### Problem #2

A large balloon contains helium gas at a pressure of 5 atm. If the temperature of the gas increases to 90 ℃, the pressure of the gas increases to 6 atm. What was the initial temperature of the gas?

Solution

Given data:

• Initial pressure of the gas, P1 = 5 atm
• Final temperature of the gas, T2 = 90 ℃ = 363 K
• Final pressure of the gas, P2 = 6 atm
• Initial temperature of the gas, T1 = ?

Applying the formula:

• P1/T1 = P2/T2
• T1 = (P1 × T2) ÷ P2
• T1 = (5 × 363) ÷ 6
• T1 = 1815 ÷ 6
• T1 = 302.5 K = 29.5 ℃

Therefore, the initial temperature of the gas is 29.5 ℃.

### Problem #3

A cylinder is filled with argon gas at a temperature of 25 ℃. When the temperature is increased to 80 ℃, the pressure of the gas increases to 12 atm. What was the initial pressure of the gas?

Solution

Given data:

• Initial temperature of the gas, T1 = 25 ℃ = 298 K
• Final temperature of the gas, T2 = 80 ℃ = 353 K
• Final pressure of the gas, P2 = 12 atm
• Initial pressure of the gas, P1 = ?

Applying the formula:

• P1/T1 = P2/T2
• P1 = (P2 × T1) ÷ T2
• P1 = (12 × 298) ÷ 353
• P1 = 3576 ÷ 353
• P1 = 10.13 atm

Therefore, the initial pressure of the gas is 10.13 atm.

### Problem #4

A container is filled with hydrogen gas at a pressure of 3 atm and a temperature of 30 ℃. If the pressure of the gas is increased to 4 atm, what is the final temperature of the gas?

Solution

Given data:

• Initial pressure of the gas, P1 = 3 atm
• Initial temperature of the gas, T1 = 30 ℃ = 303 K
• Final pressure of the gas, P2 = 4 atm
• Final temperature of the gas, T2 = ?

Applying the formula:

• P1/T1 = P2/T2
• T2 = (P2 × T1) ÷ P1
• T2 = (4 × 303) ÷ 3
• T2 = 1212 ÷ 3
• T2 = 404 K = 131 ℃

Therefore, the final temperature of the gas is 131 ℃.