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**Gay-Lussac’s law formula**, which is expressed as P_{1}/T_{1} = P_{2}/T_{2}, relates the pressure and temperature of a gas. In this formula, P_{1} and T_{1} represent the initial pressure and temperature of the gas, while P_{2} and T_{2} 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.

## 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, P
_{1}= 2 atm - Initial temperature of the gas, T
_{1}= 20 ℃ = 293 K - Final pressure of the gas, P
_{2}= ? - Final temperature of the gas, T
_{2}= 60 ℃ = 333 K

Applying the formula:

- P
_{1}/T_{1}= P_{2}/T_{2} - P
_{2}= (P_{1}× T_{2}) ÷ T_{1} - P
_{2}= (2 × 333) ÷ 293 - P
_{2}= 666 ÷ 293 - P
_{2}= 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, P
_{1}= 5 atm - Final temperature of the gas, T
_{2}= 90 ℃ = 363 K - Final pressure of the gas, P
_{2}= 6 atm - Initial temperature of the gas, T
_{1}= ?

Applying the formula:

- P
_{1}/T_{1}= P_{2}/T_{2} - T
_{1}= (P_{1}× T_{2}) ÷ P_{2} - T
_{1}= (5 × 363) ÷ 6 - T
_{1}= 1815 ÷ 6 - T
_{1}= 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, T
_{1}= 25 ℃ = 298 K - Final temperature of the gas, T
_{2}= 80 ℃ = 353 K - Final pressure of the gas, P
_{2}= 12 atm - Initial pressure of the gas, P
_{1}= ?

Applying the formula:

- P
_{1}/T_{1}= P_{2}/T_{2} - P
_{1}= (P_{2}× T_{1}) ÷ T_{2} - P
_{1}= (12 × 298) ÷ 353 - P
_{1}= 3576 ÷ 353 - P
_{1}= 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, P
_{1}= 3 atm - Initial temperature of the gas, T
_{1}= 30 ℃ = 303 K - Final pressure of the gas, P
_{2}= 4 atm - Final temperature of the gas, T
_{2}= ?

Applying the formula:

- P
_{1}/T_{1}= P_{2}/T_{2} - T
_{2}= (P_{2}× T_{1}) ÷ P_{1} - T
_{2}= (4 × 303) ÷ 3 - T
_{2}= 1212 ÷ 3 - T
_{2}= 404 K = 131 ℃

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

## 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

## External links

- Gay Lussac’s Law – ChemTalk
- 14.5: Gay-Lussac’s Law – Chemistry LibreTexts
- Gay-Lussac’s Law Calculator – Omni Calculator
- Gay-Lussac’s Law — Overview & Formula – Expii
- Gay-Lussac’s Law of Ideal Gasses Study Guide – Inspirit VR
- Gay-Lussac’s Gas Law | Equation and Examples – Study.com
- Gay-Lussac’s law – Wikipedia
- Gay-Lussac’s Gas Law Examples – ThoughtCo
- Gay Lussac’s Law – Concept – Chemistry Video – Brightstorm
- Gay-Lussac’s Law – Chemistry Steps
- Gay-Lussac’s Law: Example & Equation – Vaia
- Lesson Explainer: Gay-Lussac’s Law Physics – Nagwa Limited
- Gay-Lussac’s Law Calculator P1/T1=P2/T2 – SensorsONE
- Gay-Lussac’s Law Formula – SoftSchools.com
- Gay-Lussac’s Law – Definition, Formula, Examples – Science Notes and Projects
- Gay-Lussac’s Law Calculator – Top Online Tool
- Gay-Lussac’s Law Calculator – CalcTool
- High School Chemistry : Using Gay-Lussac’s Law – Varsity Tutors

Deep

Learnool.com was founded by Deep Rana, who is a mechanical engineer by profession and a blogger by passion. He has a good conceptual knowledge on different educational topics and he provides the same on this website. He loves to learn something new everyday and believes that the best utilization of free time is developing a new skill.