Gas Laws
1. Boyles law
At constant temperature, the volume of a given mass of gas is inversely ∝ to the absolute pressure.
V ∝ 1/P
or
P x V = K
(as one goes up the other goes down)
Can be used to calculate the volume of gas remaining in a cylinder.
P1 x V1 = P2 x V2 (as P x V is constant)
Size E cylinder is 10L so contains 10L of O2 at 13800 kPa (atmospheric pressure included as absolute pressure).
13800 x 10 = 138000
So at atmospheric pressure there would be 100 x ? = 138000
ie 1380 L
2. Charles’ law
At constant pressure, the volume of a given mass of gas is ∝ to the absolute temperature.
V ∝ T
or
V/T = K
At absolute zero a gas would have no volume.
3. Gay-Lussac
At constant volume, the absolute pressure of a given mass of gas is ∝ to its absolute temp.
P ∝ T
or
P/T = K
Universal gas law
Combining the 3 laws gives:
PV/T = K
For 1 mole of gas PV/T = R (the universal gas constant)
If the no of moles is n then
PV/T = nR
or
PV = nRT
In a gas cylinder V, R and T are constant so P ∝ n ie the pressure is ∝ to the quantity of gas in the cylinder.
Dalton’s law of partial pressures
The pressure exerted by a gas in a mixture equals the pressure it would exert if alone.
So partial pressure of a gas in a mixture is obtained by pressure x fractional concentration.
Eg air = 100 x 21% = 21 kPa for O2
Henry’s law
The amount of gas dissolved in a liquid is ∝ to the partial pressure above the liquid at constant temp.
At hyperbaric pressures O2 can be dissolved in significant amount and so provide a meaningful contribution to DO2.
Avogadro
Equal volumes of gas at the same temp and pressure contain equal no’s of molecules.
1 mole of gas at STP occupies 22.4 L
Can therefore use the weight of N2O to measure the volume of gas in a cylinder (MW N2O = 44g).