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
[ K = °C + 273 ]
- Amount of gas (n): In moles
[ moles = \frac{mass (g)}{molar mass} ]
⚙️ The Major Gas Laws
1. Boyle’s Law — Pressure vs. Volume
- Formula: [ P_1 V_1 = P_2 V_2 ]
- Constant: Temperature, number of moles
- Relationship: Inverse
- When volume ↓, pressure ↑
- Use when: Temp is constant, P & V change
2. Charles’s Law — Volume vs. Temperature
- Formula: [ \frac{V_1}{T_1} = \frac{V_2}{T_2} ]
- Constant: Pressure, number of moles
- Temperature: Always in Kelvin
- Relationship: Direct
- Temp ↑ ⇒ Volume ↑
- Use when: Pressure is constant, V & T change
3. Gay-Lussac’s Law — Pressure vs. Temperature
- Formula: [ \frac{P_1}{T_1} = \frac{P_2}{T_2} ]
- Constant: Volume, number of moles
- Relationship: Direct
- Temp ↑ ⇒ Pressure ↑
- Use when: Volume is constant, P & T change
4. Combined Gas Law
- Formula: [ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} ]
- 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, temp, volume
- Can be rearranged:
- [ P = \frac{nRT}{V} ]
- [ V = \frac{nRT}{P} ]
- [ n = \frac{PV}{RT} ]
6. Avogadro’s Law — Moles vs. Volume
- Formula: [ \frac{V_1}{n_1} = \frac{V_2}{n_2} ]
- 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 (volume shouldn’t be negative, etc.)
📍 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)