Lecture Notes on Gas Laws

Introduction

• Focus on key formulas and equations for gas laws in chemistry.
• Importance of understanding units and conversions.

Pressure

• Definition: Pressure = Force / Area.
• Units:
  • Standard unit in physics: Pascal (Pa)
    • 1 Pascal = 1 Newton/m²
  • Chemistry unit: Atmosphere (atm)
  • Conversions:
    • 1 atm = 101,300 Pascals (101.3 kPa)
    • 1 atm = 760 mmHg = 14.7 psi

Ideal Gas Law

• Formula: PV = nRT
  • R (gas constant) = 0.08206 L atm/mol K or 8.3145 J/mol K
  • Units:
    • Pressure in atm or Pa
    • Volume in Liters or m³
    • Temperature in Kelvin
  • Temperature Conversion: Kelvin = Celsius + 273.15

Combined Gas Law

• Equation: ( \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} )
• Pressure and volume units must match; temperature in Kelvin.

Boyle's Law

• Equation: ( P_1V_1 = P_2V_2 )
• Relationship: Inverse relationship between pressure and volume.

Charles' Law

• Equation: ( \frac{V_1}{T_1} = \frac{V_2}{T_2} )
• Relationship: Direct relationship between volume and temperature.

Gay-Lussac's Law

• Equation: ( \frac{P_1}{T_1} = \frac{P_2}{T_2} )
• Relationship: Direct relationship between pressure and temperature.

Avogadro's Law

• Equation: ( \frac{V_1}{n_1} = \frac{V_2}{n_2} )
• Relationship: Direct relationship between volume and moles.

Molar Mass and Density

• Molar Mass: Replace n with m/MW in PV = nRT to get pressure, volume, and molar mass relation.
• Density: ( D = \frac{PM}{RT} )
  • Can calculate density or identify gas using molar mass and density.

Standard Temperature and Pressure (STP)

• Conditions:
  • Temperature: 273 K (0°C)
  • Pressure: 1 atm
  • 1 mole gas = 22.4 L at STP

Dalton's Law of Partial Pressures

• Concept: Total pressure = Sum of individual partial pressures.
• Equation: Partial pressure = Mole fraction x Total pressure.

Kinetic Theory

• Average Kinetic Energy: Proportional to temperature.
• Use R = 8.3145 J/mol K.

Root Mean Square Velocity

• Equation: ( v_{rms} = \sqrt{\frac{3RT}{MW}} )
  • MW in kg/mol, R = 8.3145 J/mol K._

Graham's Law of Effusion

• Equation: ( \frac{R_2}{R_1} = \sqrt{\frac{MW_1}{MW_2}} )
• Relationship: Rate of effusion inversely related to square root of molar mass.
  • Inverse relationship between time and rate.

Conclusion

• Reference to practice problems available for deeper understanding.