Ideal Gases

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Ideal Gas assumptions

• When describing an ideal gas, the following assumptions are made

1. The motion of all particles is random
   1. All particles are in constant, random motion
2. All particles travel in straight lines
3. intermolecular (electrostatic) and gravitational forces are negligible
4. All particles of a particular gas are identical and perfect spheres
5. Internal energy of the gas is entirely kinetic
6. All collisions between particles and the walls of the container are completely elastic (no loss of kinetic energy)
7. Particles take up negligible volume (pressure is due to mobility)
8. Newton’s Laws of Motion apply
   1. An object travelling at a constant velocity, or at rest, will remain at that constant velocity or at rest, unless acted upon by an external force. i.e., inertia
   2. Force is equal to the product of mass and acceleration
   3. Every action has an equal and opposite reaction

From Lucarelli

1. Gases are composed of particles in continuous rapid, random motion
2. Attraction and repulsion between particles in the gas is negligible
3. The particles of a gas are widely spaced such that the total volume of all the particles is negligible compared to the volume occupied by the gas
4. The average kinetic energy of the particles of a gas is proportional to its temperature, and is the same for all gases at the same temperature
5. Particle collisions are elastic (and collisions with the container walls)
   1. i.e. over time, as particles collide, they do not lose speed or slow down, thus particles do not lose kinetic energy (i.e. cool down) due to their collisions

Gas Laws

• Describe how gases behave
• Can be predicted by the kinetic theory
• Kinetic theory: all matter consists of tiny particles that are in constant motion
• Real Gases
  • Do have volume
  • Attraction between particles
  • Can condense or solidify
• Ideal Gases
  • No volume
  • No attraction between particles
  • Follows gas laws at all temperatures and pressures
• Real gases differ most from ideal gases at low temperatures and high pressures
• In order to completely describe a gas you need to measure 4 things
  1. Pressure
  2. Temperature
  3. Volume
  4. Number of particles

Gas Pressure

• Pressure: force per unit area
• Gas particles exert pressure when they collide with the walls of their container
• The SI unit of pressure is the pascal (Pa)
• However, there are several units of pressure
  • Pascal ()
  • Kilopascal (kPa)
  • Atmosphere (atm)

Temperature

• Average kinetic energy is directly proportionate to the Kelvin temperature
• At absolute 0 (0 degrees kelvin or -273.15 ˚ C), there is no molecular motion
• Standard temperature and pressure:
  • 0˚ C or 273.15 K
  • Standard pressure: 1 atm = 760 mm Hg = 760 torr = 101.3 kPa
• Kelvin = 273.15 + ˚C
• ˚C = Kelvin - 273.15

Ideal Gas Laws

• Given that the gas is ✨ideal✨

Boyle’s Law

• The pressure of a gas increases as its volume decreases, and vice versa
• $P_1{V}_1=P_2{V}_2$
• tldr: pressure is inversely proportional to volume
  • As volume decreases, pressure increases
    • Particles travel less
    • More collisions with walls of container
    • More force per unit area exerted
    • Alternatively, more energy is required to compress the gas, and thus the container can compress
  • As volume increases, pressure decreases
    • Particles travel more
    • Less collisions with walls of container
    • Less force per unit area exerted
    • Alternatively, less energy is required to compress the gas, and thus the container can expand
• We are assuming:
  1. Constant mass
  2. Constant temperature

Brownian Motion

• Gas particles move in an irregular, seemingly random path
• Example: smoke
  • When an air particle bombardes a smoke particle, the smoke particle moves to the original direction of the air particle
  • The air particle changes its direction to that of the smoke particle

Charle’s Law

• At a constant pressure, the volume of a gas increases as the temperature of the gas increases, and the volume decreases when the temperature decreases
• $\frac{V_1}{T_1}=\frac{V_2}{T_2}$
• Why?
  • Temperature increases
  • Increases average kinetic energy
  • Increases the speed of the particles
  • More collisions with the walls of the container
  • The walls of a flexible container expand

Gay-Lussac’s Law

• The pressure of a gas is directly proportional to its absolute temperature (Kelvin) at a constant volume
• $\frac{P_1}{T_1}=\frac{P_2}{T_2}$

Combined Law

$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_1}$

The Ideal Gas Equation

• One more gas law exists for changes in the gas properties as well as the amount of gas present in moles
• This law is referred to as the Ideal Gas Law because it accurately predicts gas properties of ideal gases
• Most gases at moderate conditions behaving like an ideal gas $PV=nRT$
• P = pressure (kPa)
• V = volume (L)
• n = moles (mol)
• R = 8.314 (universal gas constant)
  • 0.08314 if using litres, atm, mole and kelvin temperature
• T = temperature (K)

Avogardro’s Law

• Equal volumes of gases at the same temperature and pressure contain eqaul number of molecules
• 1 mole of any gas takes up a volume of 22.71 L at STP $n=\frac{V}{22.71}$