Concept of Ideal Gas Equation

Known as Ideal gas law in thermodynamics, it is a well-defined approximation of the behaviour of many gases under a wide range of conditions. The Ideal Gas Equation is a combination of empirical laws such as Charle’s law, Boyle’s law, Gay-law, Lussac’s and Avogadro’s law that describe the behaviour of gases.

The Ideal Gas Equation is a mathematical expression for the states of hypothetical gases that is defined by the mathematical combination of empirical and physical constants. The general gas equation is another name for this equation. It can be summed up as follows:

The ideal gas law is the equation of state for a hypothetical ideal gas, and it is defined as follows: An ideal gas is a theoretical gas that is composed of a collection of point particles that are randomly moving and interact only through elastic collisions.

Define Ideal Gas Equation

Ideal gases are generally defined as those in which all collisions occur between atoms, or we can say that the molecules are perfectly elastic and in which there are no attractive forces between molecules. You can visualise it as being composed of perfectly hard spheres that collide but do not interact with one another in any other way, which is to say they do not interact with one another. A gas with kinetic energy as its internal energy has a temperature that changes in response to a change in internal energy, and any change in internal energy causes a change in temperature.

An ideal gas can be easily described by three state variables: the absolute pressure denoted by P, the volume denoted by V, and the absolute temperature denoted by T. The absolute pressure denoted by P, the volume denoted by V, and the absolute temperature denoted by T.

The ideal gas law is as follows: PV = nRT = NkT

• n is the number of moles present.
• R is the universal gas constant, which is equal to 8.3145 J/mol K.
• N is the number of molecules in a molecule.

the Boltzmann constant = 1.38066 x 10-23 J/K = 8.617385 x 10-5 eV/K is the Boltzmann constant

= is the R/NA ratio

Avogadro’s number = 6.0221 x 1023 /mol is represented by NA.

It is possible, however, to assert that there is also a statistical element involved in the calculation of the average kinetic energy of those molecules. The idea of kinetic temperature is invoked by the temperature that is said to be proportional to this average kinetic energy and is taken to be proportional to this average kinetic energy. One mole of ideal gas, which is also available at STP, takes up 22.4 litres of space.

According to this definition, the equation of state for a hypothetical ideal gas serves as an illustration of the law of ideal gas. Only elastic collisions are permitted in an ideal gas because there is no molecule-to-molecule interaction, as we can see in the diagram. It is considered to be a good approximation because it represents the behaviour of many gases under a variety of conditions, despite the fact that it has several limitations. Émile Clapeyron published the first statement of the law in 1834, which was a combination of Boyle’s law and Charles’ law.

What is an Ideal Gas?

In mathematics, an ideal gas is defined as a theoretical gas that does not exist in reality but is assumed to exist for the purposes of simplifying calculations. Another way to put it is that it serves as a point of reference against which the behaviour of other gases can be studied more generally.

In this case, we can say that the collisions are assumed to be perfectly elastic, which means that none of the particles’ energy is wasted.

But in reality, when the gas, which is composed of actual gas particles, collides with one another, some of their energy is lost in the process of changing directions and overcoming friction. However, we can state that under the STP conditions, which were previously defined, the majority of natural gases that behave exactly like an ideal gas are subject to reasonable limitations.

Derivation of ideal gas equation:

Using mathematical notation, the following is how this law is represented:

The fact that P = 1/V or that PV = K

Where P denotes the pressure of the gas, V denotes the volume of the gas, and K denotes the constant. Essentially, it means that at a constant temperature, both the volume and pressure of a given mass of gas are inversely proportional to one another. We can also say that it expresses that for any given gas, the product of pressure and volume remains constant, and that it can be used to study the comparison of a gas under various conditions, such as, for example, the following:

P’V’ = P”V”

in which both products are made from the same gas but are produced under different volumes and pressures

“When the pressure of a sample of air is held constant, we can say that the volume of the gas is directly proportional to its temperature,” says Charles’ law, which is written as V t where V is the volume of a sample of air and T is the absolute temperature. The most straightforward way to put it is that gases expand during heating and contract during cooling conditions.

“Equal volumes” of all gases at the same pressure and temperature, according to Avogadro’s law, equals “equal numbers of molecules.” It is written as V n or V/n =K, where V denotes the volume of the gas and n denotes the number of moles (1 mole=6.022 x 1023 molecules) in the gas.

Conclusion

It is possible to understand the behaviour of gases under different conditions using the kinetic theory of gases. The kinetic theory of gases states that gases are composed of particles that are constantly moving and that are attracted to one another by attractive forces. In the case of a gas, the pressure is a measure of the number of collisions that occur between the gas particles and with the sides of the container in which they are contained. The average kinetic energy of the particles in a substance is measured by the temperature of the substance. An ideal gas consists of identical particles with the same volume, and there are no intermolecular forces between any of the particles. In an ideal gas, all of the atoms or molecules move at the same speed. The behaviour of a real gas is similar to that of an ideal gas, with the exception of high pressures and low temperatures. Because of the strong forces between molecules, when the temperature drops below a certain point, the gas will begin to liquefy. When the particles are subjected to high pressures, their volume becomes significant.

Avogadro’s law states that equal volumes of gases, at the same temperature and pressure, contain the same number of molecules, regardless of their composition.