Ideal Gas Law – A General Gas Equation

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Relationships between Boyle’s, Charles’s, Gay-Lussac’s, Avogadro’s, combined and ideal gas law, with the Boltzmann constant kB = R / NA = n R / N (in each law, properties circled are constant and properties not circled are variable)/Credit: Wikimedia Commons

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?

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An animated representation of an ideal gas law in terms of universal gas constant/Credit: Flickr

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.

Recommended, Top 6 Real-Life Gay Lussac Law Examples

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 m3, 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 m3)
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 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.o 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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I am a mechanical engineer by profession. Just because of my love for fundamental physics, I switched my carrier, and therefore I just completed my postgraduate degree in physics. Right now I am a loner (as like ever) and a Physics blogger too. My sole future goal is to do a Ph.D. in theoretical physics, especially in the field of cosmology. Because in my view, every part of physics comes within the range of cosmology. And I love traveling, especially the Sole one.

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