Ideal Gas Law and Calculations

Overview

• Ideal Gas Equation: Relates pressure, volume, temperature, and moles: (PV = nRT)
  • Combines Boyle’s, Charles’s, Avogadro's, and Gay-Lussac's laws.
• Variables:
  • (P) = Pressure
  • (V) = Volume
  • (n) = Number of moles
  • (R) = Ideal gas constant
  • (T) = Temperature

Ideal Gas Constant (R)

• Common Value: (R = 0.08206) L atm / (mol K)
• Unit Dependence:
  • Different units for (P), (V), and (T) change (R).
  • Prefer using liters for volume and atmospheres for pressure.
• Conversions: Always convert units to match the gas constant.

Molar Volume at STP

• Standard Temperature and Pressure (STP): 0°C and 1 atm
• Molar Volume: 22.4 L for 1 mole of an ideal gas
• Calculation:
  • Rearrange ideal gas law to solve for (V).
  • Use (T) in Kelvin (273 K).

Calculations

Example Calculations

• Finding Moles (n):
  • Given (P), (V), and (T), use (n = \frac{PV}{RT}).
  • Convert (T) to Kelvin.
• Pressure Change with Temperature Change
  • Initial Conditions: (31.5^{\circ}C) to (-20.9^{\circ}C)
  • Calculate new (P) without changing (V) or (n).
  • Use (P_1/T_1 = P_2/T_2) for constant (n) and (V).

Temperature and Pressure Changes

• New Pressure Calculation:
  • Convert temperatures to Kelvin.
  • Use (P_1/T_1 = P_2/T_2) or rearrange ideal gas equation.

Volume and Temperature Changes (Constant Pressure)

• Volume Change Calculation:
  • Use (V_1/T_1 = V_2/T_2) when (P) is constant.
  • Convert (T) to Kelvin.

Key Points

• Unit Conversion: Always convert temperatures to Kelvin.
• Pressure P2 Calculations: Determine (P_2) using the rearranged formula for changes in (T).
• Volume Calculations: Follow conversions for (V) and use consistent units with (R).
• Absolute Temperatures: Use Kelvin to avoid nonsensical results (e.g., negative pressures).

Common Errors

• Celsius vs. Kelvin: Using Celsius in ideal gas law calculations results in errors.
• Pressure Unit Mismatch: Incorrect results if (R) units do not match pressure units.

Recap

• Ideal Gas Law: Central to calculations this semester.
• Conversions: Necessary for correct computations.
• Practice: Familiarity through repeated use of (PV = nRT).