What is Combined Gas Law?

S7-SA5-0304

Grade Level:

Class 12

AI/ML, Physics, Biotechnology, FinTech, EVs, Space Technology, Climate Science, Blockchain, Medicine, Engineering, Law, Economics

Definition

What is it?

The Combined Gas Law helps us understand how the pressure, volume, and temperature of a fixed amount of gas are all related. It's like a shortcut that combines Boyle's Law, Charles's Law, and Gay-Lussac's Law into one easy formula.

Simple Example

Quick Example

Imagine you have a football filled with air. If you take it from a cool room (lower temperature) and leave it in the hot sun (higher temperature), the air inside tries to expand. If the football can't expand, its internal pressure will increase because the gas particles move faster and hit the walls harder.

Worked Example

Step-by-Step

QUESTION: A gas in a balloon has a volume of 2.0 litres at 27 degrees Celsius and 1.0 atmosphere pressure. If the temperature changes to 77 degrees Celsius and the pressure increases to 1.5 atmospheres, what will be the new volume of the gas?

STEP 1: Convert temperatures to Kelvin. Remember, Kelvin = Celsius + 273.
Initial Temperature (T1) = 27 + 273 = 300 K
Final Temperature (T2) = 77 + 273 = 350 K
---STEP 2: Identify known values.
Initial Volume (V1) = 2.0 L
Initial Pressure (P1) = 1.0 atm
Final Pressure (P2) = 1.5 atm
---STEP 3: Write down the Combined Gas Law formula.
(P1 * V1) / T1 = (P2 * V2) / T2
---STEP 4: Rearrange the formula to solve for V2.
V2 = (P1 * V1 * T2) / (P2 * T1)
---STEP 5: Plug in the values and calculate.
V2 = (1.0 atm * 2.0 L * 350 K) / (1.5 atm * 300 K)
V2 = (700) / (450)
---STEP 6: Calculate the final volume.
V2 = 1.555... L
---ANSWER: The new volume of the gas will be approximately 1.56 litres.

Why It Matters

Understanding the Combined Gas Law is crucial for engineers designing engines and rockets, or for scientists working on climate models. It helps in predicting how gases behave under different conditions, which is vital in fields like Space Technology for rocket propulsion or in Medicine for oxygen tanks.

Common Mistakes

MISTAKE: Not converting temperature from Celsius to Kelvin. | CORRECTION: Always convert all temperatures to Kelvin (K = °C + 273) before using them in gas law calculations.

MISTAKE: Mixing up initial and final values (e.g., using P1 with V2). | CORRECTION: Clearly label all initial values (P1, V1, T1) and final values (P2, V2, T2) to avoid confusion.

MISTAKE: Forgetting to keep units consistent (e.g., using litres for one volume and millilitres for another). | CORRECTION: Ensure all pressure units are the same, all volume units are the same, and all temperature units are Kelvin.

Practice Questions

Try It Yourself

QUESTION: A gas occupies 10 litres at 300 K and 2 atm pressure. What is its volume at 400 K and 1 atm pressure? | ANSWER: 26.67 litres

QUESTION: A cylinder contains 5.0 L of air at 20 degrees Celsius and 3.0 atm. If the volume is compressed to 2.0 L and the temperature rises to 50 degrees Celsius, what is the new pressure? | ANSWER: 8.43 atm

QUESTION: A balloon has 4.0 litres of gas at 27 degrees Celsius and 100 kPa. If the balloon is moved to a place where the temperature is -3 degrees Celsius and the volume expands to 5.0 litres, what is the new pressure in kPa? | ANSWER: 79.9 kPa

MCQ

Quick Quiz

Which of the following remains constant in the Combined Gas Law?

Pressure

Volume

Temperature

Amount of gas (moles)

The Correct Answer Is:

The Combined Gas Law applies to a fixed amount of gas, meaning the number of moles (amount of gas) does not change. Pressure, volume, and temperature can all change.

Real World Connection

In the Real World

Think about scuba diving. As divers go deeper into the ocean, the water pressure increases, affecting the air in their tanks and lungs. The Combined Gas Law helps design breathing equipment and understand how gas in the body behaves under changing pressure and temperature, ensuring diver safety.

Key Vocabulary

Key Terms

PRESSURE: Force exerted by gas particles on container walls | VOLUME: Space occupied by the gas | TEMPERATURE: Measure of the average kinetic energy of gas particles | KELVIN: Absolute temperature scale used in gas laws | ATMOSPHERE (atm): A unit of pressure

What's Next

What to Learn Next

Great job learning about the Combined Gas Law! Next, you can explore the Ideal Gas Law. It builds on this concept by adding the 'amount of gas' into the equation, helping you understand even more complex gas behaviors.