Overview
This lecture explains the ideal gas law, its assumptions and limitations, and demonstrates how to use it for calculations, especially relating to the Hindenburg and gas behaviors under different conditions.
Ideal Gas Law and its Origins
- The ideal gas law combines Boyle's, Charles', and Avogadro’s laws into one equation: PV = nRT.
- Boyle’s law: Pressure times volume is constant at constant temperature for a closed system.
- Charles’ law: Volume divided by temperature is constant at constant pressure for a closed system.
- Avogadro’s law: Volume divided by the amount of gas (moles) is constant at constant temperature and pressure (not a closed system requirement).
- Dmitri Mendeleev combined these laws and established the universal gas constant (R = 8.3145 L·kPa/K·mol).
Assumptions and Limitations of the Ideal Gas Law
- Assumes gas particles have no size and do not attract each other.
- The law works best under normal conditions; high pressure, low temperature or high density can cause deviations.
- Real gases deviate from ideal behavior when particles interact or occupy significant space.
Calculations with the Ideal Gas Law
- At standard temperature and pressure (STP: 0°C or 273.15 K, 100 kPa), 1 mole of an ideal gas occupies 22.7 L.
- At 1 atmosphere (101.325 kPa), 1 mole occupies 22.4 L.
- The ideal gas law is used by plugging in known values and solving for the unknown (P, V, n, or T).
The Hindenburg Example
- The Hindenburg contained 211,890,000 L of H₂ at ~100 kPa, 10°C (283.15 K).
- Calculated moles of H₂: 9.00 x 10⁶ mol.
- Hydrogen's lower molar mass (2.016 g/mol) vs. helium (4.003 g/mol) allows it to carry 18 metric tons more than helium.
- A temperature rise (from 10°C in Germany to 18°C in New Jersey) increased internal pressure from 100 kPa to 103 kPa (assuming constant volume and moles).
Application and Demonstration
- Increasing air pressure in a confined space raises its temperature, as shown by igniting cotton in a fire piston.
Key Terms & Definitions
- Ideal Gas Law — Equation (PV = nRT) describing the relationship between pressure, volume, temperature, and moles of an ideal gas.
- STP (Standard Temperature and Pressure) — Defined as 0°C (273.15 K) and 100 kPa.
- Universal Gas Constant (R) — 8.3145 L·kPa/K·mol, the constant used in the ideal gas law.
- Mole (n) — Amount of substance used in gas calculations.
- Boyle’s Law — P × V = constant (at constant T, closed system).
- Charles’ Law — V / T = constant (at constant P, closed system).
- Avogadro’s Law — V / n = constant (at constant T and P).
Action Items / Next Steps
- Practice calculations using the ideal gas law with different values for P, V, n, and T.
- Review the conditions where real gases deviate from ideal behavior.
- Read about the van der Waals equation for corrections to the ideal gas law.