# Ideal Gas Equation

## What is Ideal Gas Equation?

In thermodynamics, Ideal gas law is a well-defined approximation of the behavior of many gases under diverse conditions. Ideal Gas Equation is the combination of empirical laws like Charle’s law, Boyle’s law, Gay-Lussac’s law, and Avogadro’s law.

Ideal Gas Equation is the equation defining the states of the hypothetical gases expressed mathematically by the combinations of empirical and physical constants. It is also called the general gas equation. It can be defined as:

“The ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation of the behaviour of many gases under many conditions, although it has several limitations”.

## Equation of Ideal Gas Law

The state of an ideal gas is determined by the macroscopic and microscopic parameters like pressure, volume, temperature.

Thus, the ideal gas equation is often written as:

 PV = nRT

Where,

• P is the pressure of the ideal gas.
• V is the volume of the ideal gas.
• n is the amount of ideal gas measured in terms of moles.
• R is the gas constant.
• T is the temperature.

The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics. To check the Derivation of Ideal Gas Equation, click the link.

## Ideal Gas Equation Units

The Ideal gas equation units, terms, and corresponding definitions can be expressed as follows:

 Terms Symbol Definition Units Pressure P Force per units area Pa or N/m2 Volume V Three-dimensional space enclosed by the closed surface m3 Amount of substances/number of moles n The ratio of the mass of the gas(m) to its molar mass(M). Mole Ideal gas constant R Physical constant relating the average kinetic energy of an ideal gas with temperature. It is expressed in units of energy per temperature increment per mole 8.3144598(48) J.K-1.mol-1 Temperature T Measure of heat K or 0C

## What is Ideal gas?

Ideal gas does not exist in reality. It is a hypothetical gas proposed to simplify the calculations.

An ideal gas is a theoretical gas composed of a set of randomly-moving point particles that interact only through elastic collisions.

• In Ideal gas, the gas molecules move freely in all directions, and collision between them is considered to be perfectly elastic, which implies no loss in the kinetic energy due to the collision.
• Although there is no ideal gas, all real gas tends to approach that property when the density gets low enough. This is possible because the molecules of the gas are so far apart from one another that they do not interact with each other. Thus, the ideal gas concept helps us in studying real gases.

## Ideal Gas Equation – Explained

To study the property of gases we need to have a standard gas to study, but which gas should it be? Hydrogen, oxygen, helium, nitrogen, carbon dioxide to name a few, and there are thousands of other gasses we could study.

The researchers have found that no matter what gas you study if you take a one-mole sample of that gas and put it in the same container and maintain a constant temperature, the pressure is almost the same, and at lower densities, even those tiny differences in the measurements also disappear.

Thus, at really low densities, all the real gases tend to obey one universal law called ideal gas law.

This law is described by an equation known as the Ideal gas equation:

 PV = nRT

### Limitations:

Although the ideal gas equation has many limitations.

• This equation holds well as long as the density is kept low.
• This equation is applicable for single gas or even a mixture of multiple gasses where ‘n’ will stand for the total moles of gas particles in the given mixture.

## Ideal Gas Equation of States

The Equation of States of an ideal gas explains the simple relation between the parameters or properties that are very generic and accurate. In general, an equation relating the relation between P, V, T of an ideal gas is called Equation of States. Sometimes the relation involving other parameters of a substance at equilibrium state is also referred to as the Equation of States.

The simplest equation of state for substances in the gas phase is the ideal-gas equation of state as:

 PV =RT

## Ideal Gas Equation in Other Forms

The ideal gas equation can be rewritten in multiple ways depending upon the disciplines. Some of them are given below:

### Common Form:

Most frequently used form of the ideal gas equation is-

 PV = nRT = NkBT

Where,

• P is the pressure of the ideal gas.
• V is the volume of the ideal gas.
• n is the amount of ideal gas measured in terms of moles.
• R is the gas constant.
• T is the temperature.
• N is the number of gas molecules (N=NAn)
• kB is the Boltzmann constant.
• NA is the Avogadro’s constant.

### Molar form:

This alternate form of the ideal gas equation is useful because it specifies the amount of gas accurately. Here instead of the mass of the gas molecules its chemical equivalent mass is used. Thus, the molar form is given as:

 Pv = RspecificT

Where,

• P is the pressure of the ideal gas
• v is the specific volume given by $v=\frac{1}{\rho }=\frac{1}{\left ( \frac{m}{V} \right )}$
• Rspecific is the specific gas constant given by $R_{specific}=\frac{R}{M }$
• T is the temperature

### Statistical Mechanics:

In statistical mechanics, the ideal gas equations are given by:

 $P=\frac{k_{B}}{\mu m_{u}}\rho T$

Where,

• P is the pressure of the ideal gas
• T is the temperature.
• μ average particle mass
• mu is the atomic mass constant
• ρ is the density given by ρ = m/V = nμmu
• kB is the Boltzmann constant.

## Frequently Asked Questions on Ideal Gas Equation

### What is Ideal gas?

Ideal gas does not exist in reality. It is a hypothetical gas proposed to simplify the calculations. In Ideal gas, the gas molecules move freely in all directions, and collision between them is considered to be perfectly elastic, which implies no loss in the Kinetic energy due to the collision.

### What is the shape of the P-T curve for an ideal gas?

The shape of the P-T curve for an ideal gas is a straight line.

### What is the shape of the V-T curve for an ideal gas?

The shape of the V-T curve for an ideal gas is a straight line.

### What is the compressibility factor of an ideal gas?

It is always 1.

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#### 1 Comment

1. Rahul and tina

Super