# Real Gases. The ideal gas equation of state is not sufficient to describe the P,V, and T behaviour of most real gases. Most real gases depart from ideal.

## Presentation on theme: "Real Gases. The ideal gas equation of state is not sufficient to describe the P,V, and T behaviour of most real gases. Most real gases depart from ideal."— Presentation transcript:

Real Gases

The ideal gas equation of state is not sufficient to describe the P,V, and T behaviour of most real gases. Most real gases depart from ideal behaviour at deviation from low temperature high pressure

Low Temperatures

The variation of the potential energy of two molecules on their separation. High positive potential energy (little separation) Repulsive interactions Intermediate separations attractive interactions dominate Large separations (on the right) the potential energy is zero and there is no interaction between the molecules.

High Pressures

Real gas molecules do attract one another (P id = P obs + constant) Real gas molecules are not point masses (V id = V obs - const.)

V id = V obs - nb b is a constant for different gases P id = P obs + a (n / V) 2 a is also different for different gases Ideal gas Law P id V id = nRT

Critical temperature (T c ) - the temperature above which a gas cannot be liquefied Critical pressure (P c ) – the minimum pressure that needs to be applied at T c to bring about liquefaction

The compression factor

For a perfect gas, the slope is zero Boyle temperature the slope is zero and the gas behaves perfectly over a wider range of conditions than at other temperatures.

At the critical point

Boyle temperature - for a van der Waal's gas, the Boyle temperature (T B ) is written

The reduced state variables are defined

Re-write the Van der Waals in terms of reduced variables

All substances obey the same equation of state in terms of the reduced variables. Degree of generality.

The chemical potential of a real gas is written in terms of its fugacity

The activity coefficient ( J ) relates the activity to the concentration terms of interest. In gaseous systems, we relate the fugacity (or activity) to the ideal pressure of the gas via

The fugacity (f) represents the chemical potential of a real gas. Define the fugacity coefficient = f / P For a real gas

Comparing the chemical potential of the real gas to the chemical potential of an ideal gas at the same pressure

The fugacity coefficients are obtained from the compression factors (Z) as shown below

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