# 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:

p_{total}= p_{1}+ p_{2}+ .. + p_{n }

= Σp_{i}(1)

where

p_{total}= total pressureof mixture (Pa, psi)

p_{i}= 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

*p _{i} = n_{1} R T / V (2)*

*where *

*p _{i} = pressure (Pa, psi)*

*n _{1} = the number of moles of the gas*

*R = universal gas constant (J/(mol K), lb _{f} ft/(lb mol ^{o}R), 8.3145 (J/(mol K))*

*T = absolute temperature (K, ^{o}R)*

*V = volume (m ^{3}, ft^{3}) *

### Example - Partial Pressure of single Gas

If there is *2 moles* of gas in *0.005 m ^{3} *volume (

*5 litre*) with temperature

*27°C*(

*300 K*) - the partial pressure of the gas can be calculated as

*p _{i} = (2) (8.3145 J/(mol K)) (300 K) / (0.005 m^{3})*

* = 997740 Pa *

* = 997 kPa *