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

🧠 How to Know Which Law to Use

🧪 Problem-Solving Strategy

1. Identify what's changing: P, V, T, or n?
2. Convert all units:
   • Temp → Kelvin
   • Volume → Liters
   • Mass → Moles (if needed)
3. Choose correct gas law.
4. Plug values into formula.
5. Solve for unknown.
6. 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)