Gases and the Ideal Gas Law Lecture Notes

Lecture Date: 11/7/25
Topic: Gases and the Ideal Gas Law
Importance: Understanding gases in atomic-level and macroscopic perspectives.
- Goals: Describe gas behaviors, ideal gas law assumptions, and perform calculations using the ideal gas law.

Characteristics of Gases:
- Abundant in the environment.
- Can expand infinitely; occupy containers uniformly and completely.
- Diffuse and mix rapidly.
- Intermolecular forces and gases' volume are negligible for ideal gases.
Types of Gases:
- Gases can be monatomic (e.g., Noble gases like Helium He, Neon Ne, Argon Ar) or polyatomic (e.g., Hydrogen H₂, Oxygen O₂).
Chemical Formulas for Common Gases:
- Monatomic: He, Ne, Ar, Kr, Xe, Rn
- Polyatomic: H₂, O₂, N₂, F₂, NH₃, Cl₂, CO, CO₂.
Condensation of Gases: All gases can be condensed under suitable conditions (listed boiling points in Kelvin).

Constituents of Air:
- Nitrogen (N₂): 78.09% volume, 75.52% mass
- Oxygen (O₂): 20.95% volume, 23.14% mass
- Argon (Ar): 0.93% volume, 1.29% mass
- Carbon Dioxide (CO₂): 0.03% volume, 0.05% mass

Pressure Defined:
- Result of gas particles colliding with container walls. Increases with more particles hitting walls or harder impacts.
Pressure at High Altitudes:
- Decreases with elevation.
- Example Data:
- Top of Mt. Everest (29,028 ft): 240 Torr, Boiling Point 70 °C
- Top of Mt. McKinley (20,320 ft): 340 Torr, Boiling Point 79 °C
- Location Data also includes altitudes and boiling points for various places.
Pressure Formula:
$\text{Pressure} = \frac{\text{Force}}{\text{Area}} = \frac{\text{mass} \cdot \text{acceleration}}{\text{Area}}$
Pressure Units:
- 1 Pa = 1 kg m$^{-1}$ s$^{-2}$
- 1 bar = 10$^{5}$ Pa; 1 atm = 1.01325 x 10$^{5}$ Pa = 101.325 kPa
- 1 atm = 760 Torr; 1 atm = 14.7 lb/in$^{2}$ (psi)

Ideal Gas Equation:
$PV = nRT$
- Where:
- V = volume (L)
- T = temperature (K)
- n = amount (moles)
- P = pressure (atmospheres)
- R = Gas Constant
  - $R = 0.082057$ L atm/(K mol)
  - Other conditions: $R = 8.3145$ L kPa/(K mol), $R = 62.364$ L Torr/(K mol)
Usage of Ideal Gas Law:
- Can calculate properties when any variable changes (pressure, volume, moles, temperature).

Approximations:
- Intermolecular forces are negligible.
- Volume of gas particles is negligible which fails at high pressures and low temperatures.
Expected Behaviors:
- Breaks down at low temperatures (strong intermolecular forces) and high pressures (volume importance).

Statement: At constant n and T, $PV = ext{constant}$ .
- Inverse relationship: If the volume decreases, pressure increases due to more collisions with walls.

Statement: At constant n and P, $V \propto T$
- If temperature increases, volume increases.

Statement: At constant T and P, $V \propto n$
- Equal volumes of gases at the same T and P contain the same number of molecules.

Definition: The total pressure in a mixture is equal to the sum of the partial pressures of its components.
- $P<em>{total} = P</em>{A} + P_{B} + …$
- Important for calculating gas mixtures, correcting for vapor pressures.

Conversion examples between different units and finding values: e.g., $PV = nRT$ for different conditions; how moles and pressure change with temperature changes.

Definition: Gas diffusion rates inversely proportional to the square root of their molar mass.
Example: Comparing diffusion rates of different gases (e.g., NH₃ and HCl).

Gases exhibit unique properties and behaviors under varying conditions outlined by gas laws.
Ideal behaviors are often assumptions applicable under specified conditions, while real gases deviate significantly in real-world scenarios, especially under extreme conditions.