Charles's, Boyle's, and Gay-Lussac's Laws

Overview of Gas Laws

• Gas laws involve four variables: pressure, volume, temperature, and moles.
• Relationships:
  • Directly proportional: As one variable increases, the other also increases.
  • Inversely proportional: As one variable increases, the other decreases.

Boyle's Law

• Relationship: Inversely proportional between pressure and volume.
  • Example: Pressing a syringe decreases the volume inside it.
• Formula: ( P_1 V_1 = P_2 V_2 )
  • ( P ): Pressure, ( V ): Volume
  • Subscripts 1 and 2 denote initial and final states.
• Application: Given three variables, solve for the fourth using algebra.
• Example Problem:
  • Given: V1 = 1.1 L, P1 = 0.91 atm, V2 = 3.1 L
  • Find: P2
  • Solution: Use ( P_1 V_1 = P_2 V_2 ) and solve for P2.
  • Result: P2 = 0.32 atm

Charles's Law

• Relationship: Directly proportional between volume and temperature.
  • Example: A hot air balloon expands as temperature increases.
• Formula: ( \frac{V_1}{T_1} = \frac{V_2}{T_2} )
  • ( V ): Volume, ( T ): Temperature (in Kelvin)
• Key Point: Always convert temperature to Kelvin.
  • Conversion: Celsius to Kelvin = °C + 273.15
• Example Problem:
  • Given: V1 = 19.5 L, initial temperature T1 = 349 K (from 76°C)
  • Find: V2
  • Solution: Solve using Charles's Law.
  • Result: V2 = 17.4 L

Gay-Lussac's Law

• Relationship: Directly proportional between pressure and temperature.
  • Example: Increasing temperature in an aerosol can increases pressure.
• Formula: ( \frac{P_1}{T_1} = \frac{P_2}{T_2} )
  • ( P ): Pressure
• Key Point: Temperature must be in Kelvin.
• Example Problem:
  • Given: P1 = 35.2 PSI, initial temperature T1 = 298.2 K (from 25°C)
  • Find: T2
  • Solution: Use Gay-Lussac's Law.
  • Result: T2 = 309.16 K or 36°C

Tips for Solving Problems

• Units: Ensure all units are consistent (e.g., pressure in atm, temperature in Kelvin).
• Significant Figures: Maintain appropriate significant figures throughout calculations.
• Checks:
  • Boyle's Law: Volume up, pressure down (and vice versa).
  • Charles's and Gay-Lussac's Laws: What happens to one variable should happen to the other.
• Always label known and unknown variables before solving equations.