# Physical Chemistry - Real Gases

### Real Gases

Introduction

This page relates to the physical properties of real gases.   The webpage Gas Properties includes some general physical properties of selected gases.  Thermodynamic and heat transfer relationships for fluids can be found on page Thermodynamics /Heat Transfer

The laws and rules for ideal gases are only reasonable accurate for gases at low pressures and moderately high temperatures...At pressures around 1 bara or less the ideal gases are generally reasonably accurate for real gases.

The main reasons for the divergence from the ideal gas laws are that molecules actually attract each other and that molecules have real volumes.  The ideal gas laws assume that the volume of a gas molecule can be discounted and that molecules do not attract each other.  It is also apparent that as molecules approach very close, the attraction changes to repulsion.. In 1873 van der Waals devised a crude simple equation to adapt the ideal gas laws to the behaviour or real gases

Van der Waals Equation

Considering a molecule in a container.  The molecule will be attracted to all other molecules when located in away from the container wall.  When local to the container wall there will be greater attraction towards the molecules within the centre of the container and its momentum will be reduced.  The higher the pressure greater the inward attract and the more significant is this effect.   The correction for pressure will depend on the number of molecules at the surface and the number within the body of the gas.  Both of these factors vary inversely with the volume V.  Van der Walls proposed that a compensatory factor a/V2 be added to the true pressure.

It is also true that the volume containing a gas within which the molecules are moving is reduced by the effective volume of the molecules.  This reduction is greater if the pressure is increased..Van der Walls proposed a factor b to allow for this reduction this factor is greater at higher pressures.
The Gas law as modified by Van der Waals for real gases is as follows >

Typical units are as follows

 p = Pressure = Atm or Pa (N/m 2) V = Volume = liter or m 3 Vm = volume of one l mole (litres) or volume of 1 kMole ( m 3) T = Absolute Pressure = deg Kelvin R = Universal Gas Constant = 8,314 J /mole.K or 8 314 J /kmole.K ( "," is my decimal point) n = Number of moles (kmoles)
Table of Van Der Waals Constants

 Substance a b Substance a b liter2.atm./mole2 (m3)2.Pa./kmole2 litre/mole= m3/kmole liter2.atm./mole2 (m3)2.Pa./kmole2 litre/mole= m3/kmole Hydrogen 0,245 2,48x104 2,67x 10-2 Hydrogen Chloride 3,8 3,85x105 4,1x 10-2 Helium 0,034 3.44x103 2,36x 10-2 Ammonia 4,0 4,05x105 3,6x 10-2 Nitrogen 1,380 1,4x105 3,94x 10-2 Acetylene 4,4 4,46x105 5,1x 10-2 Oxygen 1,32 1,34x105 3,12x 10-2 Ethylene 4,5 4,56x105 5,6x 10-2 Carbon Monxide 1,4911,51x105 4,00x 10-2 Chlorine 5,5 5,57x105 4,9x 10-2 Carbon Dioxide 3,603,65x105 4,28x 10-2 Sulfur Dioxide 6,7 6,79x105 5,6x 10-2

Critical Temperature

The critical temperature for a matter is the maximum temperature that a gas can be liquified is called the critical temperature for the gas.   The liquid state cannot exist above this temperature.

The pressure to cause liquifaction at this temperature is called the critical pressure. A vapor is really a gaseous state of a substance when its temperature is below the critical temperature.  A vapour can therefore by condensed to a liquid by increasing the pressure.

 Substance Critical Temp Critical Pressure Substance Critical Temp Critical Pressure Deg. K atm Deg. K atm He 5,2 2,26 H2S 373,5 89,0 H2 33,2 12,8 NH3 406,0 112,3 N2 126,0 33,5 Cl2 417,1 76,1 CO 133,6 35,5 SO2 430,3 77,6 O2 154,3 49,7 CCl4 556,2 45,0 CO2 304,2 73,0 C6H6 561,6 47,9 HCl 324,1 81,5 H2O 647,3 217,7

 Relevant Chemistry Sites.. Real Gases....Useful Lectures notes and Audio lectures Equations of State... A single page comprehensive set of notes. Equations of state... NASA information page -very clear Ideal and Real Gases... Notes comparing ideal and real gases. Useful