# Ideal Gas Equation

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## Introduction to Ideal Gas Equation

In thermodynamics, we can say that the Ideal gas law is said to be a well-defined approximation of the behaviour that is of many gases under diverse conditions. The equation of Ideal Gas is the combination which is of empirical laws like Charle’s law and the Boyle’s law then the Gay-Lussac’s law and the law of Avogadro’s.

It can be defined as

The law of ideal gas which is the equation of state of a hypothetical ideal gas.

### What is the Ideal Gas Equation?

An ideal gas is generally defined as one in which all collisions are between the atoms or we can say that the molecules are perfectly elastic and in which there are no intermolecular attractive forces. One can visualize easily that it is a collection of perfectly hard spheres which collide but which otherwise we can say that they do not interact with each other. In such a gas, the internal energy is in the form of kinetic energy and any change in internal energy is accompanied by a change in temperature.

An ideal gas can be easily characterized by three state variables: that is the absolute pressure denoted by P volume denoted by V and absolute temperature denoted by T.

Ideal gas law: PV = nRT = NkT

• n = is the number of moles

• R = is the universal gas constant = 8.3145 J/mol K

• N = is the number of molecules

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

= is the R/NA

• NA = is the Avogadro's number = 6.0221 x 1023 /mol

But we can say that there is also a statistical element in the determination of the average kinetic energy of those molecules. The temperature which is said to be taken to be proportional to this average kinetic energy invokes the idea of kinetic temperature. One mole which is an ideal gas that too at STP occupies 22.4 litres.

The law of ideal gas is said to be the equation of state of a hypothetical ideal gas that is an illustration. In an ideal gas, there is no molecule-molecule interaction and we can say that only elastic collisions are allowed. It is said to be a good approximation which is the behaviour of many gases which are under many conditions although we can say that it has several limitations. In 1834 it was first stated by Émile Clapeyron as a combination of Boyle’s and Charles’ law.

### What is an Ideal Gas?

An ideal gas that is said to be a theoretical gas that does not exist in reality but is assumed to exist for the purpose of simplifying calculations. We can also say that It also generates a reference point in relation to which the behaviour of other gases generally can be studied.

We can say that these collisions are assumed to be perfectly elastic which means that no energy of either of these particles is wasted.

In reality, however, when the gas which is actual gas particles collide with each other some of their energy that is wasted in changing directions and overcoming friction. However, we can say that at STP that is defined earlier, conditions most natural gases that act just like an ideal gas are subjected to reasonable restrictions.

### Ideal Gas Law

In mathematical terms this law is represented as the following:

P ∝∝ 1/V or that  PV = K

Where P = Pressure of the gas, V = Volume of the gas and K = constant. It means that both of the volume and pressure of a given mass that is of gas are inversely proportional to each other at a constant temperature. Furthermore, we can say that  it also expresses that the product of pressure and volume that is for any gas is a constant and thus it can be used to study the comparison that is of the gas which is under different conditions as:

P’V’ = P”V”

where both the products are for the same as gas but under different volume and pressures.

The law of Charles’ states that ‘ When the pressure is of a sample of air is held constant and then we can say that the volume of the gas is directly proportional to its temperature‘, that is written as:

V ∝∝T

where V = Volume of a gas sample, T= Absolute temperature. Quite simply we can put as gases expand on heating and contract which is on cooling.

The law of Avogadro that states that ‘Equal volumes that are of all gases which are at conditions which are of same pressure and temperature have the same number of molecules’. It is written as follows:

V ∝∝ n or V/n =K

where V = volume of gas, n = Number of moles (1 mole=6.022 x 1023 molecules).

1. What does the ideal gas law assume?

The law of the ideal gas assumes that gases behave ideally that is meaning they adhere to the following characteristics: First,  the collisions occurring in between molecules are elastic and their motion is frictionless. It implies that the molecules do not lose energy.  Second, the total volume of the individual molecules is magnitudes smaller.

2. What is the ideal gas law?

The law which is of the ideal gas that is PV = nRT that relates the macroscopic properties which are of ideal gases. An ideal gas which we have learnt is a gas in which the particles that do not attract or repel one another and take up no space and have no volume.

3. Provide a real-life example of ideal gas law.

As an example, we can say that correcting the volume which is of gas at one temperature to its volume at another temperature. That is T1/T2 which is in Kelvin always to calculate the volume at the new temperature T2. Since as we have seen that the mass stays the same as well as this also gives you the new density at T2.

4. What are the properties of an ideal gas?

The gas particles which generally have negligible volume. We can say that the gas particles are equally sized and do not have intermolecular forces that are attraction or repulsion with other gas particles. The gas particles which we have seen move randomly in agreement with Newton's law of Motion. The gas particles which have perfect elastic collisions with no energy loss.