Ideal Gas Law or **General Gas Law** is one of the equations of state of the hypothetical Ideal Gas. When **Combined Gas Law **i.e the combination of **Boyle’s Law** (Constant Temperature), **Charles Law** (Constant Pressure), and, **Gay Lussac Law** (Constant Volume) is substituted with **Avogadro’s Law**** **yields Ideal Gas Law.

## What Is The Ideal Gas Law?

The ideal gas law is one of the Gas Laws that basically describe the behavior of an Ideal Gas. In other words, **when the temperature, volume, and pressure of an ideal gas are related, **their association is known as the ideal gas law**.**

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However, this gas law (also known as General Gas Equation) is also applicable to the Real Gases but under certain conditions such as Normal Temperature and Low Pressure. I mean, if these conditions are not followed, then real gases follow the **Van Der Waals gas equation**.

This general gas law was first proposed by the French Inventor, Physicist, and one of the founding members of Thermodynamics **Benoît Paul Émile Clapeyron **in 1834.

In fact, this general gas law can also be derived from the** Kinetic Molecular Theory Of Gas.**

## Formula For Ideal Gas Law

According to the ideal gas law definition, the ideal gas law formula can be represented in two different forms. Let us take a look at both equations one by one:

### Molar Mass Ideal Gas Law

In terms of molar mass, the mathematical expression of the ideal gas law is:

##### PV =nRT

where,

P = pressure of an ideal gas

V = volume of an ideal gas

n = amount of substance of gas (in moles)

R = where R in ideal gas law is the universal gas constant i.e 8.314 J⋅mol^{−1}⋅K^{−1} (which is the product of Boltzmann constant and Avogadro’s constant)

T = absolute temperature of an ideal gas (in Kelvin)

#### Ideal Gas Law Constant

Here comes the most confusing part. The most confusing part of the Ideal Gas Equation is choosing the right units at the right time

- If you are using R = 8.314 J/(K·mol). Then, you must use pressure (P) in units of pascals (Pa), Volume (V) in units of m
^{3}, and temperature in units of Kelvin (K). - If you are using R = 0.08206 L·atm/(mol·K). Then, you must use pressure (P) in units of atmospheres (atm), Volume (V) in the units of Liters (L), and Temperature in units of Kelvin (K).

### Molecular Form

In terms of molecular mass, the mathematical expression of the ideal gas law is:

##### PV =NKBT

where,

P = pressure of an ideal gas (in pascals Pa)

V = volume of an ideal gas (in m^{3})

N = number of gas molecules

KB = Boltzmann constant i.e 1.38×10^{−23} J/K

T = absolute temperature (in Kelvin)

### Other Form

Not to mention, there is one more way to mathematically write the ideal gas equation:

##### P1V1/T1 = P2V2/T2

where,

P1 and P2 = Pressure of gas

V1 and V2 = volume of gas

T1 and T2 = temperature of a gas

## Ideal Gas Law Example Problem

**8.2 liters of an ideal gas is contained at 4.0 atm and 27 °C. How many moles of this gas is present?**

ANS = In this question, we will use the Molar mass ideal gas law. Therefore,

PV =nRT

where,

P = 4.0 atm

V = 8.2 L

R = 0.08206 L·atm/(mol·K)

T = 300K (27 + 273)

n =?

Now, putting all the values in above Ideal Gas Equation, we get,

4 x 8.2 = n x 0.08206 x 300

on solving,

**No. of moles present in the gas (n) = 1.33 moles of the ideal gas is present in the system.**

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