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).