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# Partial pressure

Approximately, the partial pressure of a gas in atmospheres in a mixture or solution is what would be the pressure of that gas if all other components of the mixture or solution suddenly vanished without its temperature changing.

The partial pressure of a gas in a mixture is a measure of thermodynamic activity of gas molecules.

The pressure a gas exerts is proportional to the temperature and the concentration of the gas.

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## John Dalton's law of partial pressures

The pressure of an ideal gas in a mixture is equal to the pressure it would exert if it occupied the same volume alone at the same temperature. This is because ideal gas molecules are so far apart that they don't interfere with each other at all. Actual real-world gasses come very close to this ideal.

A consequence of this is that the total pressure of a mixture at equilibrium is equal to the sum of partial pressures of the gases present. For example, given the reaction:

N2 + 3H2 ↔ 2NH3

The total pressure is equal to the sum of the individual partial pressures of the gases in the mixture:

$P = P_{N_2} + P_{H_2} + P_{{NH}_3}$

Where P is the total pressure of the mixture and Px denotes the partial pressure of x.

If the volume of the container is decreased the total pressure of the gases increases. Because the reaction is reversible, the equilibrium position shifts to the side of the reaction with the least moles (in this case the product side, on the right). By Le Chatelier's Principle, this has the effect of increasing the fraction of the whole pressure available to the products, and decreasing the fraction available to the reactants (because there is more moles of reactant than product). The composition of the gases change so more ammonia is present. Similarly, changing the temperature of the system causes more reactants to be produced (because the reverse reaction is endothermic.)

The partial pressure of a gas is proportional to its mole fraction, which is a measure of concentration. This means that it is possible to work out the equilibrium constant for an equilibrium reaction involving a mixture of gases given the partial pressure of each and the chemical formula for the reaction. The equlibrium constant for gases is denoted KP. For a reaction:

aA + bB ↔ cC + dD

So the equilibrium constant, KP can be calculated with,

$K_P = \frac{P_C^c + P_D^d} {P_A^a + P_B^b}$

Although the composition of the gases change when the container is compressed, the equilibrium remains the same (assuming the temperature also remains constant).

## Fluid phase vs. gas phase

Partial pressure in the fluid is equal to that in the gas with which the fluid is in equilibrium.

When a liquid is exposed to a gas, molecules of the gas will dissolve in the liquid.

### Henry's law

Henry's law can be used to determine the partial pressure of a gas in a fluid.

$partial\ pressure = \frac{concentration\ of\ dissolved\ gas}{solubility\ coefficient}$

## Partial pressure vs. concentration

Gases dissolve, diffuse, and react according to their partial pressures, not necessarily according to their concentrations.

## Partial pressure in diving breathing gases

In recreational diving and professional diving the richness of individual component gases of breathing gases is expressed by partial pressure.

Using diving terms, partial pressure is caculated as:

 partial pressure = absolute pressure x fraction of gas


For the component gas "z":

 ppz = P x Fz


For example, at 50 metres, 165 feet, the absolute pressure is 6 bar (1 bar of atmospheric pressure + 5 bar of water pressure) and the partial pressures of the main components of air, oxygen 21% and nitrogen 79% are:

 ppN2 = 6 bar x 0.79 = 4.74 bar
ppO2 = 6 bar x 0.21 = 1.26 bar


A safe range of partial pressures of oxygen in a gas mixture is between 0.16 bar and 1.6 bar. Hypoxia and sudden unconsciousness becomes a problem with a ppO2 less than 0.16 bar. Oxygen toxicity, involving convulsions, becomes a risk with a ppO2 more than 1.6 bar. The partial pressure of oxygen determines the maximum operating depth of a gas mixture.

Nitrogen narcosis is a problem with gas mixes containing nitrogen. A typical planned maximum partial pressure of nitrogen for technical diving is 3.5 bar, based on an equivalent air depth of 35 metres / 110 feet.

Last updated: 05-07-2005 08:58:44
Last updated: 05-13-2005 07:56:04