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Dalton's law states that each gas in a mixture of ideal gases, has a partial pressure which is the pressure which the gas would have if it alone occupied the same volume at the same temperature. The total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture.

Henry's law states that at a constant temperature, the partial pressure of a gas in equilibrium with a liquid solution containing some of the gas is directly proportional to the concentration of that gas in the liquid solution.

Dalton's law of partial pressures

John Dalton, an English chemist, meteorologist and physicist, first propounded his law of partial pressures in 1803 and published it in 1805. His statement that the total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture can be expressed mathematically. For example, for a mixture of three ideal gases (denoted as gases a, b and c):

(1)     $p_{t}=p_{a}+p_{b}+p_{c}$

where:
$p_{t}$	= total pressure of the gas mixture
$p_{a}$	= partial pressure of gas a
$p_{b}$	= partial pressure of gas b
$p_{c}$	= partial pressure of gas c

Dalton's law applies only to gases that behave in accordance with the ideal gas law which is applicable for hypothetical gases with no intermolecular forces. The ideal gas law is a useful approximation for predicting the behavior of many gases over a wide range of temperatures and pressures.

However, real gases can deviate considerably from ideal gas behavior because of the intermolecular attractive and repulsive forces. The deviation is especially significant at low temperatures or high pressures. In other words, Dalton's law is not applicable for real gases at conditions where they deviate significantly from ideal gas behavior.

Dalton's law is also applicable only to gases at conditions under which they are mutually inert (i.e., they do not react with each other).

Ideal gas mixtures

The mole fraction of an individual gas component in an ideal gas mixture can be expressed in terms of the component's partial pressure or the moles of the component:

(2)     $x_{i}={\frac {p_{i}}{p_{t}}}={\frac {n_{i}}{n}}$

and the partial pressure of an individual gas component in an ideal gas can be obtained using this expression:

(3)     $p_{i}=x_{i}\cdot p_{t}$

where:
$x_{i}$	= mole fraction of any individual gas component in a gas mixture
$p_{i}$	= partial pressure of any individual gas component in a gas mixture
$p_{t}$	= total pressure of the gas mixture
$n_{i}$	= moles of any individual gas component in a gas mixture
$n$	= total moles of the gas mixture

The mole fraction of a gas component in a gas mixture is equal to the volumetric fraction of that component in a gas mixture.

Henry's Law and the solubility of gases

Gases will dissolve in liquids to an extent that is determined by the equilibrium between the undissolved gas and the gas that has dissolved in the liquid (called the solvent). The equilibrium constant for that equilibrium is:

(4)     $k={\frac {p_{x}}{C_{x}}}$

where:
$k$	=  the equilibrium constant for the solvation process
$p_{x}$	=  partial pressure of gas $x$ in equilibrium with a solution containing some of the gas
$C_{x}$	=  the concentration of gas $x$ in the liquid solution

The form of the equilibrium constant shows that the concentration of a solute gas in a solution is directly proportional to the partial pressure of that gas above the solution. This statement is known as Henry's Law and the equilibrium constant $k$ is quite often referred to as the Henry's Law constant.

Henry's Law is sometimes written as:

(5)     $k'={\frac {C_{x}}{p_{x}}}$

where $k'$ is also referred to as the Henry's Law constant. As can be seen by comparing equations (1) and (2) above, $k'$ is the reciprocal of $k$. Since both may be referred to as the Henry's Law constant, readers of the technical literature must be quite careful to note which version of the Henry's Law equation is being used.

Henry's Law is an approximation that only applies for dilute, ideal solutions and for solutions where the liquid solvent does not react chemically with the gas being dissolved.

Equilibrium constants of reactions involving gas mixtures

It is possible to work out the equilibrium constant for a chemical reaction involving a mixture of gases given the partial pressure of each gas and the overall reaction formula. For a reversible reaction involving gas reactants and gas products, such as:

(6)     $a\,A+b\,B\leftrightarrow c\,C+d\,D$

the equilibrium constant of the reaction would be:

(7)     $K_{P}={\frac {P_{C}^{c}\,P_{D}^{d}}{P_{A}^{a}\,P_{B}^{b}}}$

where:
$K_{P}$	=  the equilibrium constant of the reaction
$a$	=  coefficient of reactant $A$
$b$	=  coefficient of reactant $B$
$c$	=  coefficient of product $C$
$d$	=  coefficient of product $D$
$P_{C}^{c}$	=  the partial pressure of $C$ raised to the power of $c$
$P_{D}^{d}$	=  the partial pressure of $D$ raised to the power of $d$
$P_{A}^{a}$	=  the partial pressure of $A$ raised to the power of $a$
$P_{B}^{b}$	=  the partial pressure of $B$ raised to the power of $b$

For reversible reactions, changes in the total pressure, temperature or reactant concentrations will shift the equilibrium so as to favor either the right or left side of the reaction in accordance with Le Chatelier's Principle. However, the reaction kinetics may either oppose or enhance the equilibrium shift. In some cases, the reaction kinetics may be the over-riding factor to consider.

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 calculated as:

partial pressure = total absolute pressure x volume fraction of gas component

For the component gas "i":

ppi = P x Fi

For example, at 50 metres (164 feet), the total absolute pressure is approximately 6 bar (600 kPa) and the partial pressures of the main components of air, oxygen 21% by volume and nitrogen 79% by volume are:

ppN2 = 6 bar x 0.79 = 4.7 bar absolute

ppO2 = 6 bar x 0.21 = 1.3 bar absolute

where:
ppi	= partial pressure of gas component i  = $P_{\mathrm {i} }$ in the terms used in this article
P	= total pressure = $P$ in the terms used in this article
Fi	= volume fraction of gas component i  =  mole fraction, $x_{\mathrm {i} }$, in the terms used in this article
ppN2	= partial pressure of nitrogen  = $P_{{\mathrm {N} }_{2}}$ in the terms used in this article
ppO2	= partial pressure of oxygen  = $P_{{\mathrm {O} }_{2}}$ in the terms used in this article

The minimum safe lower limit for the partial pressures of oxygen in a gas mixture is 0.16 bar (16 kPa) absolute. Hypoxia and sudden unconsciousness becomes a problem with an oxygen partial pressure of less than 0.16 bar absolute. The NOAA Diving Manual recommends a maximum single exposure of 45 minutes at 1.6 bar absolute, of 120 minutes at 1.5 bar absolute, of 150 minutes at 1.4 bar absolute, of 180 minutes at 1.3 bar absolute and of 210 minutes at 1.2 bar absolute. Oxygen toxicity, involving convulsions, becomes a risk when these oxygen partial pressures and exposures are exceeded. 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 absolute, based on an equivalent air depth of 35 metres (115 feet).

See also

• Vapor
• Gas, Ideal gas and Ideal gas law
• Mole fraction and Mole (unit)
• Dalton's law
• Henry's law
• Breathing gas