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 = ∑P i = 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 = ntot RT/V      and Pi = ni RT/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 =  (ni RT/V)/(ntot RT/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 = Xi Ptot

See also Non-ideal 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 :

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 = ntot RT/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

    Basic engineering data. SI-system, unit converters, physical constants, drawing scales and more.

Related Documents

Search

Search is the most efficient way to navigate the Engineering ToolBox.

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

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 !

Translate this Page

Translate this page to Your Own Language .

About the Engineering ToolBox!

Privacy Policy

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

We use a third-party to provide monetization technologies for our site. You can review their privacy and cookie policy here.

You can change your privacy settings by clicking the following button: .

Citation

This page can be cited as

  • 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.

3D Engineering ToolBox - draw and model technical applications! 2D Engineering ToolBox - create and share online diagram drawing templates! Engineering ToolBox Apps - mobile online and offline engineering applications!

Unit Converter


















































11.25.10

.