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# Dalton's Law

## Gibbs' Dalton's law of the total pressure of a mixture of gases.

The total pressure of a mixture of gases is made up by the sum of the partial pressures of the components in the mixture - also known from Gibbs'-Dalton's Law of Partial Pressures.

• the total pressure exerted by a mixture of gases is the sum of the partial pressures of the individual gases

The total pressure in a mixture of gases can be expressed as:

ptotal = p1 + p2 + .. + pn

= Σpi                                              (1)

where

ptotal = total pressure of mixture    (Pa, psi)

pi = partial pressure of individual gas   (Pa, psi)

Assuming that each gas behaves ideally - the partial pressure for each gas can calculated from the Ideal gas Law as

pi = n1 R T / V                     (2)

where

pipressure (Pa, psi)

n1 = the number of moles of the gas

R = universal gas constant (J/(mol K), lbf ft/(lb mol oR),  8.3145 (J/(mol K))

T = absolute temperature (K, oR)

V = volume (m3, ft3)

### Example - Partial Pressure of single Gas

If there is 2 moles of gas in 0.005 m3 volume (5 litre) with temperature 27°C (300 K) - the partial pressure of the gas can be calculated as

pi = (2) (8.3145 J/(mol K)) (300 K) / (0.005 m3)

=   997740 Pa

=  997 kPa

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