Gas Laws in Electrochemistry Lecture

Key Formulas and Units

Definition of Pressure

• Pressure: Force divided by Area
• Units:
  • Physics: Pascals (Pa), where 1 Pascal = 1 Newton/m²
  • Chemistry: Atmospheres (ATM), where:
    • 1 atm = 101.3 kilopascals (kPa) = 760 mmHg = 14.7 psi

Ideal Gas Law

• Equation: ( PV = nRT )
  • ( R ): Gas constant
    • Chemistry: 8.206 L atm/mol K
    • Physics: 8.3145 J/mol K
  • Units required:
    • Pressure in atmospheres (atm)
    • Volume in liters (L)
    • Temperature in Kelvin (K)
    • Moles (n)

Temperature Conversion

• Kelvin from Celsius: ( K = °C + 273.15 )
• Celsius from Fahrenheit: Use conversion formulas

Combined Gas Law

• Equation: ( \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} )
• Conditions: Number of moles constant; matching units for pressure and volume; temperature in Kelvin

Boyle's Law

• Equation: ( P_1 V_1 = P_2 V_2 )
• Relationship: Inverse between pressure and volume

Charles's Law

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

Gay-Lussac's Law

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

Avogadro's Law

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

Molar Mass and Density

• Molar Mass Formula: ( PV = \frac{m}{M} RT )
• Density Formula: ( \rho = \frac{PM}{RT} )

Standard Temperature and Pressure (STP)

• Conditions: 273 K (0°C) and 1 atm
• Volume: 1 mole of gas occupies 22.4 liters

Dalton's Law of Partial Pressures

• Total Pressure: Sum of partial pressures of individual gases
• Partial Pressure: Mole fraction x Total pressure

Kinetic Molecular Theory

• Average Kinetic Energy: Proportional to temperature
• Use ( R = 8.3145 ) J/mol K for calculations

Root Mean Square Velocity

• Formula: ( \text{Velocity} = \sqrt{\frac{3RT}{M}} )
• Units: Velocity in m/s, Molar mass in kg/mol

Graham's Law of Effusion

• Formula for Effusion Rate: ( \frac{R_2}{R_1} = \sqrt{\frac{M_1}{M_2}} )
• Relation: Inverse between rate and molecular weight
• Time Relation: Rate inversely related to time

Additional Resources

• Practice problems and detailed explanations available in provided links.