The Ideal Gas Equation
PV = nRT
Van dear Waal’s Equation of State
Definition
The ideal Gas equation adapted for real gases
Van dear Waal’s Equation of State
Equation
(P + an²/V²)*(V - bn) = nRT
P = pressure V = volume n = number of Moles R = molar gas constant T = temperature b = actual volume of one mole of gas molecules a = pressure per unit volume, depends on the gas and is small for inert gases
Van dear Waal’s Equation of State
Explanation
(P + an²/V²)*(V - bn) = nRT
- V is lower than measured since the Gas molecules themselves take up volume, the free volume for the molecules to move into is the volume of the container, V minus the volume of the molecules, bn
- P is her than measured, as a molecule approaches the wall of the container it is attracted back by the other molecules with a force proportional to the density, n/V. But the number of molecules hitting the wall is also proportional to density thus the attractive force is actually proportional to (n/V)²
Density
Molar Equation
M / b
M = molar mass b = molar volume
Isotherm
Definition
Lines of constant temperature
Critical Isotherm
The first isotherm where P isn’t inversely proportional to V
Critical Temperature
The temperature of the critical isotherm
What is the critical temperature for water?
Tc = 647K
Saturated Vapour
A Vapour in equilibrium with its liquid
What happens when the volume of a Vapour is decreased?
- Pressure increases until a saturated vapour is formed and a maximum pressure, the saturation vapour pressure is reached
- Some vapour becomes liquid, the remaining vapour stays at saturation vapour pressure
- Eventually all of the vapour becomes liquid
- At this point pressure rapidly increases with even a small further decrease in volume
Cryogen
Definition
Gas that becomes liquified at low temperatures
Uses of Cryogens
Liquid Helium - cools superconducting magnets in MRI
Liquid Argon -
Melting
Fusion, solid -> liquid
Boiling
Vaporisation, liquid -> vapour
Sublimation
Solid -> vapour
Phase Diagrams
P & T
- the line TC shows vapour pressure with temperature
- moving along T towards C, liquid pressure decreases and vapour pressure increases
- at C, liquid and vapour are indistinguishable
Triple Point
-at triple point solid, liquid and vapour are in equilibrium
Gas vs. Vapour
- a vapour can be liquefied when compressed
- a gas when compressed will follow the relationship of P inversely proportional to V
Phase Diagram for Water
- water is unusual in that TB has a negative gradient
- melting temperature decreases with increasing pressure
Normal Boiling Point
Temperature at which vapour pressure is 1atm
Humidity
Relative Humidity =
PP of H2O/saturation vapour Pressure X 100%
Heat Capacity Equation
Q = CΔT
Q = heat added to system C = heat capacity ΔT = change in temperature
Specific Heat Capacity Equation
Q = mcΔT
Q = heat added to the system m = mass of the sample c = specific heat capacity of the material ΔT = change in temperature
