🧪 Gas Laws: Complete Study Guide
⚠️ Foundational Concepts
Properties of Gases:
- Pressure (P): Force gas exerts per unit area (measured in atm, mmHg, torr, kPa).
- Volume (V): Space a gas occupies (usually in liters, L).
- Temperature (T): Always in Kelvin for gas laws.
Formula: K = °C + 273.
- Amount of gas (n): In moles.
Formula: moles = mass (g) / molar mass.
⚙️ The Major Gas Laws
1. Boyle’s Law — Pressure vs. Volume
- Formula: P1V1 = P2V2
- Constant: Temperature, number of moles.
- Relationship: Inverse
- When volume decreases, pressure increases.
- Use When: Temperature is constant, P & V change.
2. Charles’s Law — Volume vs. Temperature
- Formula: V1/T1 = V2/T2
- Constant: Pressure, number of moles.
- Temperature in Kelvin.
- Relationship: Direct
- As Temperature increases, Volume increases.
- Use When: Pressure is constant, V & T change.
3. Gay-Lussac’s Law — Pressure vs. Temperature
- Formula: P1/T1 = P2/T2
- Constant: Volume, number of moles.
- Relationship: Direct
- As Temperature increases, Pressure increases.
- Use When: Volume is constant, P & T change.
4. Combined Gas Law
- Formula: P1V1/T1 = P2V2/T2
- Use When: P, V, and T all change.
- Note: Must use Kelvin and consistent units.
5. Ideal Gas Law
- Formula: PV = nRT
- R (Gas constant): 0.0821 L·atm/mol·K
- Use When:
- Given or solving for moles, pressure, temperature, volume.
- Can be rearranged:
- P = nRT/V
- V = nRT/P
- n = PV/RT
6. Avogadro’s Law — Moles vs. Volume
- Formula: V1/n1 = V2/n2
- Relationship: Direct
- More moles = more volume (at same T & P).
🧰 Conversions You’ll Need
| Quantity | Convert to... | How |
|---|
| Temperature | Kelvin | °C + 273 |
| Pressure | atm | 1 atm = 760 mmHg = 101.3 kPa |
| Volume | Liters (L) | 1000 mL = 1 L |
| Moles | from grams | mass / molar mass |
🧠 How to Know Which Law to Use
| Problem Mentions... | Use This Law |
|---|
| Pressure & Volume change, temp constant | Boyle’s Law |
| Volume & Temp change, pressure constant | Charles’s Law |
| Pressure & Temp change, volume constant | Gay-Lussac’s Law |
| P, V, and T all changing | Combined Gas Law |
| Involves moles or gas amount | Ideal Gas Law |
🧪 Problem-Solving Strategy
- Identify what's changing: P, V, T, or n?
- Convert all units:
- Temp → Kelvin
- Volume → Liters
- Mass → Moles (if needed)
- Choose correct gas law.
- Plug values into formula.
- Solve for unknown.
- Check units & logic (e.g., volume shouldn’t be negative).
📍 Example Problem
Q: A gas occupies 3.50 L at 1.00 atm and 300 K. What volume will it occupy at 2.00 atm and 400 K?
A: Use the Combined Gas Law.
📚 Practice Topics to Master:
- Interpreting graphs of pressure vs. volume (inverse).
- Recognizing when to use Kelvin.
- Identifying whether relationships are direct or inverse.
- Using molar mass to convert grams to moles.
- Recognizing when a gas law question is a real-world scenario (e.g., balloons rising).