Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

# 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:

Ptot = ∑Pi   = P1 + P2 + P3 ...

Where

Ptot = the total pressure

Pi = 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,

Ptot = ntotRT/V      and Pi = niRT/V

where

ni = the number of moles of component i

ntot = the total number of moles in the gas mixture, which is the sum of all ni.

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:

Pi /Ptot  =  (niRT/V)/(ntotRT/V)  = ni /ntot

We can express the concentration of one gas in the gas mixture as the mole fraction, Xi:

Xi = ni/ntot

and then

Pi/Ptot = Xi  or  Pi = XiPtot

### 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:

nN2 = 100[g] * 0.7547 /28.02 [g/mol] = 2.693 mol N2

nO2 = 100[g] * 0.2320 /32.00 [g/mol] = 0.725 mol O2

nAr = 100[g] * 0.0128 /39.95 [g/mol] = 0.032 mol Ar

nCO2 = 100[g] * 0.00046 /44.01 [g/mol] = 0.001 mol CO2

ntot = nN2 + nO2 + nAr + nCO2 = 3.451 mol gas

Then, assuming the gas mixture behaves ideally, we have:

The total pressure, Ptot = ntotRT/V = 3.451 [mol]* 0.08206 [L atm/mol K]* (273+120) [K] / 50 [L] = 2.226 atm

PN2= XN2*Ptot = nN2/ntot *Ptot = (2.693[mol]/3.451[mol])*2.226 atm = 1.737 atm

PO2= XO2*Ptot = nO2/ntot *Ptot = (0.725[mol]/3.451[mol])*2.226 atm = 0.468 atm

PAr= XAr*Ptot = nAr/ntot *Ptot = (0.032[mol]/3.451[mol])*2.226 atm = 0.021 atm

PCO2= XCO2*Ptot = nCO2/ntot *Ptot =(0.001[mol]/3.451[mol])*2.226 atm = 0.0006 atm

## Related Topics

• ### Basics

The SI-system, 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.
• ### Non-ideal gas - Van der Waal's Equation and Constants

The van der Waals constants for more than 200 gases used to correct for non-ideal 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.

## Engineering ToolBox - SketchUp Extension - Online 3D modeling!

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with older versions of the amazing SketchUp Make and the newer "up to date" SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp Make/Pro from the Extension Warehouse !

We don't collect information from our users. More about

## Citation

• The Engineering ToolBox (2017). Total and Partial Pressure - Dalton's Law of Partial Pressures. [online] Available at: https://www.engineeringtoolbox.com/partial-pressure-ideal-gas-law-total-mixture-blending-d_1968.html [Accessed Day Month Year].

Modify the access date according your visit.

10.2.10