Real Gas PVT

Real Gas PVT | Chemistry Assignment Help

The PVT behaviour of real gases can be described by empirical modifications of PV = nRT.

So far, the PVT behaviour of gases has been presumed to follow Boyle’s law, to be a basis for an absolute temperature scale, and to confirm to Avogadro’s hypothesis. All this is summarized by conformity to the ideal-gas equation PV = nRT.

When measurements are extended to higher pressures, or even when very accurate measurements are made at ordinary pressures, the results do not confirm to Avogadro’s hypothesis. All this is summarized by conformity to the ideal-gas equation PV = nRT.

When measurements are extended to higher pressures, or even when very accurate measurements are made at ordinary pressures, the results do not confirm to this equation. The ideal-gas laws are not followed.

Any actual gas exhibits, to some extent, deviations from the ideal-gas laws. When these deviations are recognized, the gas said to behave as a real, non-ideal or imperfect gas.

For a sample of gas at a fixed temperature, ideal behaviour requires the product PV to be constant. Very accurate data for a few common gases at pressures up to about 1 bar under these conditions the product PV is nearby, but not exactly, constant.

The non-ideal behaviour can be described by modifying the PV = nRT expression to

PV = nRT (1 + bP)

The b term is an empirical constant that must be evaluated for each gas.

It is often convenient to deal with 1 mol of gas and to indicate this sample size by writing the volume of the sample as V. then the essentially straight-line relations can be described by the equation

PV = RT (1 + bP)

Equations such as PV = RT and PV = RT (1 + bP), that are written to describe the PVT behaviour of a 1-mol sample, or PV = nRT and PV = nRT (1 +bP) for n moles, are known as equations of state. One simple equation, PV = RT, or PV = nRT, is the equation of state for an ideal gas. A variety of equations, such as PV = RT (1 + b) with b evaluated for each gas, will be used as we try to describe the complex and highly individualistic behaviour of real gas.

Compressibility factor Z: real and ideal gases can be compared at various pressures and various temperatures by noting the extent to which the value of PV/(RT) deviates from 1. The quantity PV/(RT) is given by the symbol Z and the name compressibility factor. That is,

Z = PV/RT

Ideal behaviour requires Z to have a value of 1 at all pressures and temperatures. Any gas imperfection is immediately apparent as the difference between the observed value of Z and 1. The compressibility factor for methane at several temperatures and in several pressure ranges to any gas is immediately apparent.

Virial equations: the first step in developing an equation to represent real gas PVT behaviour was taken when we wrote PV = RT (1 + bP). We now write this equation as

PV/RT = 1 + bP

This is the first stage of a more complete expansion type equation known as a virial equation. One form of a virial equation is 

PV/RT = 1 + BPP + CPP2 + …..

The coefficients BP, CP… are known as virial coefficients. They are selected for each temperature to describe the way in which PV/(RT) varies with pressure at that temperature. The equation has a form that makes it a suitable base for the description of the PVT behaviour of real gases. Gases behave more nonideally and more individualistically the higher the pressure. At higher pressures more terms of the virial equation, and more constants, contribute to the calculation of the compressibility factor.

A virial equation made up of volume rather than pressure terms can also be written. Now we use the idea that more higher-order terms are needed to describe the PVT behaviour as the volume of the gas sample becomes smaller.