Gas Laws

Keypoints

• The 3 laws and the constant factor:
  * TB - Boyle, T constant
  * PC - Charles', P constant
  * TV - Third law, V constant
• Adiabatic change: referring to a thermodynamic process in which there is no gain or loss of heat between the system and its surroundings.
• Ideal gas equation: PV=nRT
• Avogadro's hypothesis: equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.
• Avogadro's number: 6.022 x 10²³
  * the number of molecules in 0.0120kg of pure carbon-12.
• Critical temperature: the temperature above which a substance cannot be liquefied however much pressure is applied.
• Pseudo-critical temperature: (for a mixture of gases at a specific pressure) the specific temperature at which the individual gases may separate from the gaseous phase.
• 1 mole of perfect gas at STPD = 22.4L
• 1 mole of gas at BTPS = 27.11L

The 3 Perfect Gas Laws

1st: Boyle's law

V = 1/P x k1

(TB - T constant)

At constant temperature, the volume of a given mass of gas varies with inversely with the absolute pressure

• Used to calculate O2 cylinder content

2nd: Charles' law (aka Gay Lussac's Law)

V = T x k2

(PC - P constant)

At a constant pressure, the volume of a given mass of gas varies directly with the absolute temperature (Kelvin)

3rd: The Third Perfect Gas Law

P = T x k3

(TV - V constant)

At a constant volume, the absolute pressure of a given mass of gas varies directly with the absolute temperature

Adiabatic change

... refers to a thermodynamic process in which there is no gain or loss of heat between the system and its surroundings.

• e.g. as gas rapidly expands, cooling occurs because energy is required to overcome the van der Waals forces.

However,

For Boyle's law to apply, heat must be added or taken from the system.
--> i.e. these conditions are NOT adiabatic

Ideal gas equation

PV = nRT

• n = number of moles
• R = universal gas constant
  = 8.314 JK^-1mol^-1
• T = temperature in Kelvin
• P = pressure in Pascal
• V = volume in cubic metre
  * NB: NOT litre

Other gas laws

Avogadro's hypothesis

(aka Avogadro's Law)

Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

NB:

• one mole of any gas occupies 22.4Ls at STP
• 2 g of H2, 32g of O2, or 44 g of CO2 are all 22.4L at STP

Mole

A mole is the quantity of a substance containing the same number of particles as there are atoms in 0.012kg of carbon-12

Avogadro's number

• The number of molecules in 0.0120kg of pure carbon-12.
• Equivalent to 6.0221367 x 10²³.

Critical temperature

... is the temperature above which a substance cannot be liquefied (and remains in gaseous form), no matter how much pressure is applied.

For example,

• Critical temperature for Nitrous oxide = 36.5 C
• Critical temperature for O2 = - 119 C

Pseudo-critical temperature

... (for a mixture of gases at a specific pressure), the specific temperature at which the individual gases may separate from the gaseous phase.

For example,

Entonox (50% N2O/50% O2) = -5.5 C at 117 bar

Gas vs vapour

Vapour is the gaseous form of a substance when the ambient temperature is below its critical temperature

Gas is the gaseous form of a substance when the ambient temperature is above its critical temperature