Amendments To Ideal Gas Equation Enabling Application To Real Gases

Compressibility factor and its relationship to the ideal equation.The gas compressibility factor is the ratio of the volume of gas at a given temperature and pressure to the volume gas will take up if it was ideal gas at the same temperature and pressure. The compressibility factor tells how much the given gas is deviating from the ideal gas at a specific temperature and pressure.

It is the ratio of the volume of gas to the volume of an ideal gas at the same pressure and temperature. For the ideal gas equation compressibility factor can be derived as follows.Here P is pressure, n is moles of gas, T is the absolute temperature and R is the gas constant.

According to Boyle's law pressure is inversely proportional to volume. So the product of pressure and volume is constant at equilibrium. It is at standard temperature. So for ideal gases at a constant temperature, PV remains constant despite pressure changes. But for the real gases, the PV Vs P graph will not be straight-line.

Because real gases have intermolecular forces so upon colliding with each other gas particles will slow down. So pressure will be less than the pressure in ideal gas conditions. So the graph for real gases will dip initially due to pressure increasing but then starts to rise.

More the dip if more the intermolecular forces between gas particles. This happens because real gas can only be compressed at a particular point and after that pressure, no decrease in volume occurs. So the graph for real gases is as follows.

Real Gases reaching Ideal Behavior at Low Pressure.Gases have very less intermolecular forces but these attractive forces are yet present. So real gases deviate from ideal gas behavior because ideal gases do not have intermolecular forces. At low pressure, real gases experience fewer intermolecular forces. At low pressure, gas molecules are very far away from each other and the size of molecules becomes less significant due to the space between them. So gases tend to behave more ideally at low pressure.

High Temperature. Real gases exhibit attractive forces between molecules which deviate them from ideal gases. As ideal gases have negligible attractive forces between them. By applying low-pressure and high-temperature real gases behave more like ideal gases. At high temperatures and low pressure, molecules are very far away from each other and intermolecular forces become negligible. So gases behave ideally at low pressure and high temperature. At this condition, gases obey Boyle's law and behave like ideal gases.

Van Der Waals Equation.This equation shows the relationship between pressure, volume, temperature, and amount of real gases. In this equation, the b constant is used for the correction of volume fraction in real gases. While a is used to measure the attractive forces between real gas molecules. Van der Waals equation has two constants with particular units.

For volume and pressure correction of real gases with constant to ideal gases Van der Waals equation is used. Graph Of P V Over R T Against P For A Mole Of Hydrogen At Different Temperatures.First, we see this graph for Hydrogen at a constant temperature. According to the graph, there is a straight-line for ideal gas conditions but Hydrogen is a real gas. And real gases do not hold two assumptions of ideal gases.

First, there is no attractive force between gas molecules but in real gases attractive forces are present. Second, the volume of gas molecules is negligible but real gas molecules have a particular volume. That is why the graph line for Hydrogen deviates from the ideal gas line.

Now we consider the same scenario at different temperatures. With the increase in temperature real gasses behave like ideal gases at constant low pressure. So by increasing the temperature graph line for Hydrogen will be more horizontal and nearby to the ideal gas line.But by decreasing temperature molecular attraction increases so real gas deviates more from ideal gas behavior.