Total and Partial Pressure  Dalton's Law of Partial Pressures
How to calculate total pressure and partial pressures for gas mixtures from Ideal Gas Law.
The term partial pressure is used when we have a mixture of two or several gases in the same volume, and it expresses the pressure that is caused by each of the induvidual gases in the mixture.
The total pressure of the gas mixture is the sum of the partial pressure of the component gases:
P _{ tot } = ∑P _{ i } = P _{ 1 } + P _{ 2 } + P _{ 3 } ...
Where
P _{ tot } = the total pressure
P _{ i } = the pressure of component i ( i can vary from 1,2,3.....up to the number of different gases in the mixture)
From the Ideal Gas Law we have:
PV = nRT or P = nRT / V
Then,
P _{ tot } = n _{ tot } RT/V and P _{ i } = n _{ i } RT/V
where
n _{ i } = the number of moles of component i
n _{ tot } = the total number of moles in the gas mixture, which is the sum of all n _{ i } .
R = the gas constant = 8.3145 [J/mol K] = 0.08206 [L atm/mol K] = 62.37 [L torr /mol K]
T = absolute temperature [K]
V = volume [m3] or [L]
For a gas mixture, the temperature and the volume is the same for all gases, and the gas constant is always the same, and then we get:
P _{ i } /P _{ tot } = (n _{ i } RT/V)/(n _{ tot } RT/V) = n _{ i } /n _{ tot }
We can express the concentration of one gas in the gas mixture as the mole fraction, X _{ i } :
X _{ i } = n _{ i } /n _{ tot }
and then
P _{ i } /P _{ tot } = X _{ i } or P _{ i } = X _{ i } P _{ tot }
See also Nonideal gas  Van der Waal's equation and constants
Example 1.
Dry air consists mainly of nitrogen (78.09vol% or 75.47wt%),oxygen (20.95vol% or 23.20 wt%), argon (0.93vol% or 1.28wt%) and carbondioxide (0.03vol% or 0.046wt%).
If you have 100 g of dry air in a 50 liter closed container, what will the partial pressure of each gas be, and what will the total pressure be at 120°C?
First, we must find how many moles of each gas, using the weight fraction of each gas and molweight of the gases :
n _{ N2 } = 100[g] * 0.7547 /28.02 [g/mol] = 2.693 mol N _{ 2 }
n _{ O2 } = 100[g] * 0.2320 /32.00 [g/mol] = 0.725 mol O _{ 2 }
nAr = 100[g] * 0.0128 /39.95 [g/mol] = 0.032 mol Ar
n _{ CO2 } = 100[g] * 0.00046 /44.01 [g/mol] = 0.001 mol CO _{ 2 }
n _{ tot } = n _{ N2 } + n _{ O2 } + n _{ Ar } + n _{ CO2 } = 3.451 mol gas
Then, assuming the gas mixture behaves ideally, we have:
The total pressure, P _{ tot } = n _{ tot } RT/V = 3.451 [mol]* 0.08206 [L atm/mol K]* (273+120) [K] / 50 [L] = 2.226 atm
P _{ N2 } = X _{ N2 } *P _{ tot } = n _{ N2 } /n _{ tot } *P _{ tot } = (2.693[mol]/3.451[mol])*2.226 atm = 1.737 atm
P _{ O2 } = X _{ O2 } *P _{ tot } = n _{ O2 } /n _{ tot } *P _{ tot } = (0.725[mol]/3.451[mol])*2.226 atm = 0.468 atm
P _{ Ar } = X _{ Ar } *P _{ tot } = n _{ Ar } /n _{ tot } *P _{ tot } = (0.032[mol]/3.451[mol])*2.226 atm = 0.021 atm
P _{ CO2 } = X _{ CO2 } *P _{ tot } = n _{ CO2 } /n _{ tot } *P _{ tot } =(0.001[mol]/3.451[mol])*2.226 atm = 0.0006 atm
Related Topics

Basics
The SIsystem, unit converters, physical constants, drawing scales and more.
Related Documents

Air  Composition and Molecular Weight
Dry air is a mechanical mixture of nitrogen, oxygen, argon and several other gases in minor amounts. 
Air  Molecular Weight and Composition
Dry air is a mixture of gases where the average molecular weight (or molar mass) can be calculated by adding the weight of each component. 
Charles' Law
Volume of an ideal gas vs. temperature. 
Compression and Expansion of Gases
Isothermal and isentropic gas compression and expansion processes. 
Critical Temperatures and Pressures for some Common Substances
Critical temperatures and pressures for some common substances like air, alcohol, ether, oxygen and more. 
Density vs. Specific Weight and Specific Gravity
An introduction to density, specific weight and specific gravity. 
Elements of the Periodic System
The elements of the periodic system with names, symbols, atomic numbers and weights, melting and boiling points, density, electronegativity and electron affinity, and electron configuration. 
Gas Mixtures  Properties
Gas mixtures and the ideal gas law, mass calculations, the individual gas constant and density. 
Gases  Dynamic Viscosities
Absolute (dynamic) viscosities of some common gases. 
Gases  Ratios of Specific Heat
Ratios of specific heat for gases with constant pressure and volume processes. 
Gases  Specific Heats and Individual Gas Constants
Specific heat at constant volume, specific heat at constant pressure, specific heat ratio and individual gas constant  R  common gases as argon, air, ether, nitrogen and many more. 
Humid Air vs. the Ideal Gas Law
Pressure, temperature and volume in a perfect ideal gas like moist air (air with water vapor). 
Molecular Weight of Substances
Definition and molecular weight (molar mass) of some common substances. 
Nonideal gas  Van der Waal's Equation and Constants
The van der Waals constants for more than 200 gases used to correct for nonideal behavior of gases caused by intermolecular forces and the volume occupied by the gas particles. 
The Ideal Gas Law
The relationship between volume, pressure, temperature and quantity of a gas, including definition of gas density. 
Unit Converter with commonly used Units
Common converting units for Acceleration, Area, Density, Energy, Energy per unit mass, Force, Heat flow rate, Heat flux, Heat generation per unit volume and many more. 
Universal and Individual Gas Constants
The Universal and Individual Gas Constants in fluid mechanics and thermodynamics. Individual gas constants for the most common gases. 
Vapor and Steam
An introduction to vapor and steam.