1.5 - Ideal Gases

ideal gas

a hypothetical gas that obeys the ideal gas law PV=nRT under all conditions

the particles have negligble volume and move in a random chaotic motion with no intermolecular forces

assumptions of an ideal gas

1. particles have negligible volume

2. no intermolecular forces

3. particles have a range of speeds and move randomly with no preferred direction

4. collisions are elastic

elastic

kinetic energy is conserved

reason for pressue of gas

gas particles colliding with walls of the container

-volume increases > particles travel greater distances between collisions > collide less frequently > lower pressure

real gas

• Finite molecular volume: Unlike ideal gases, which assume particles have no volume, real gas molecules have a physical volume. This volume becomes significant, especially when the gas is compressed, reducing the space available for molecules to move.

• Intermolecular forces: Real gas molecules are subject to both attractive and repulsive forces.

  • Attractive forces: These forces, such as van der Waals forces, pull molecules together and are more significant at moderate pressures.

  • Repulsive forces: At very close distances, molecules repel each other due to the Pauli exclusion principle, preventing them from inter-penetrating.

Deviation from ideal gas law: Due to these properties, real gases deviate from the ideal gas law ).

• High pressure: The volume occupied by the molecules becomes significant, and repulsive forces dominate, causing the gas to occupy more volume than predicted by the ideal gas law.

• Low temperature: Attractive forces become more significant, leading to a pressure that is lower than predicted by the ideal gas law.

kinetic theory of gases

-take up the space of their container

-negligible interparticle forces

-no fixed shape or volume

Boyles law - P&V

P proportional 1/V

PV= a constant

pascal (Pa)

SI unit for pressure

equivalent to 1 Nm-2

SI unit volume

m^3

Charles law -V&T

V proportional T(K)

V/T(K)=a constant

Gay Lussacs law - P&T

P proportional T(K)

P/T(K)= a constant

Kelvin Celsius relationship

K = C + 273

C=K-273

STP vs satp

standard temperature and pressure

0°C 273 K

100kPa

satp is Standard Ambient Temperature and Pressure

100kpa

and 25 degrees celsius (298.15) K

molar volume og a gas in STP

22.7dm^3 per mole

how to find number of moles of gas (n)

volume (V)/molar volume

ideal gas equation

PV=nRT

combined gas law

P1V1/T1=P2V2/T2

gas density =

mass / volume

temperature

the avergae kinetic energy of the particles

ideal gas law for molecular mass

M=(m/PV)RT

why low temperature causes deviation

• particles move slower

• intermolecular forces become significant

• gas particles are more likely to stick together

• pressure is lower than predicted by ideal gas law

why high pressure causes deviation

• 
  

particles are forced closer together

volume of particles is no longer negligible

pressure is higher than predicted by ideal gas law

what real gas corrections are used in the van der Waals ( pv=nrt) equation

1. 
   

1. add a term to account for intermolecular forces

2. subtract a term to account for particle volume
   (You do NOT need to memorize the formula in SL/HL, just know the ideas.)

relationship between kinetic energy and temperature

average kinetic energy of gas particles is directly proportional to temperature (in Kelvin)

molar volume at STP

22.7 dm³ per mole

SI unit for Volume

m³ (1 dm³ = 10⁻³ m³)

why gases have no fixed shape or volume

particles move randomly with negligible forces between them, spreading to fill container

SI unit for Pressure

Pa (1 kPa = 1000 Pa)

agrovado law

states that equal volumes of any two gases at the same temp and pressure contain equal numbers of particles

the molar volume of an ideal gas is a constant at specified temperature and pressure.

At STP the molar volume of a gas is equal to 22.7 dm³ mol^1

Boyle’s Law – Pressure and volume (explanation)

P ∝ 1/V

When volume decreases, gas particles have less space to move, so they collide with the container walls more frequently.
More collisions per second means greater pressure.
When volume increases, collisions are less frequent, so pressure decreases.

Charles’s Law – Volume and Temp (explanation)

When temperature increases, the average kinetic energy of gas particles increases.
Particles move faster and collide with the container walls with more force.
To keep pressure constant, the gas expands, increasing volume.

Gay-Lussac’s Law – Pressure and Temp (explanation)

At constant volume, increasing temperature increases the kinetic energy of particles.
They collide with the container walls more frequently and with greater force, increasing pressure.

Avogadro’s Law – Volume an d moles (n) (explanation)

At constant temperature and pressure, increasing the number of moles (n) adds more gas particles.
More particles cause more collisions with the container walls, so to keep pressure constant, the gas expands — increasing volume.

v1/n1 = v2/n2

ideal gas law – density relationship

starting from PV = (m/M)RT

rearrange to find density (ρ = m/V):
ρ = (PM) / (RT)

explanation:
since m/V is density, gases at higher pressure or with greater molar mass have higher density,
while increasing temperature lowers density because particles spread out.

m3 to dm3

1 m³ = 1000 dm

m3 to cm3

1 cubic meter (m³) is equal to 1,000,000 cubic centimeters (cm³). 

1 × 10^-6