Key Difference – Ideal Gas Law vs Van der Waals Equation
The ideal gas law is a fundamental law whereas Van der Waals equation is the modified version of the ideal gas law. The key difference between ideal gas law and van der Waals equation is that ideal gas law equation is used for ideal gases whereas Van der Waal equation can be used for both ideal gases and real gases.
Gases are compounds that exist in the gaseous phase of matter. In order to understand the behaviour and properties of a gas, gas laws are used. These gas laws are used to describe the properties of ideal gases. An ideal gas is a hypothetical gaseous compound that has unique characteristics, i.e. there are no attraction forces between ideal gas molecules. However, real gases are very different from ideal gases. But some real gases behave as ideal gases when proper conditions (high temperatures and low pressures) are provided. Therefore, gas laws are modified before using them with real gases.
CONTENTS
1. Overview and Key Difference
2. What is Ideal Gas Law
3. What is Van der Waals Equation
4. Side by Side Comparison – Ideal Gas Law vs Van der Waals Equation in Tabular Form
5. Summary
What is Ideal Gas Law Equation?
Ideal gas law equation is a fundamental law in chemistry. The ideal gas law indicates that the product of pressure and volume of an ideal gas is directly proportional to the product of temperature and the number of gas particles of the ideal gas. The ideal gas law equation can be given as below.
PV = NkT
Where P is the pressure, V is the volume, N is the number of gas particles, and T is the temperature of the ideal gas. “k” is a proportionality constant known as Boltzmann’s constant (value of this constant is 1.38 x 10^{23} J/K). However, the most common form of this equation is as follows.
PV = nRT
Where P is the pressure, V is the volume, n is the number of moles of the gas and T is the temperature of the gas. R is known as the universal gas constant (8.314 Jmol^{1}K^{1}). This equation can be obtained as follows.
Boltzmann’s constant (k) = R/N
By applying this relationship to the fundamental equation,
PV = N x (R/N) x T
PV = RT
For “n” number of moles,
PV = nRT
What is Van der Waals Equation?
Van der Waal equation is the modified version of the ideal gas law. This equation can be used for ideal gases as well as for real gases. The ideal gas law cannot be used for real gases because the volume of gas molecules is considerable when compared to the volume of the real gas, and there are attraction forces between real gas molecules (ideal gas molecules have a negligible volume compared to the total volume, and there are no attraction forces between gas molecules). The Van der Waal equation can be given as below.
(P + a{n/V}^{2}) ({V/n} – b) = nRT
Here, “a” is a constant that depends on the type of gas and b is also a constant that gives the volume per mole of gas (occupied by the molecules of gas). These are used to as corrections of the ideal law equation.

Volume Correction
The volume of a real gas molecule is not negligible (unlike in ideal gases). Therefore, the volume correction is done. (Vb) is the volume correction. This gives the actual volume that is available for the gas molecule to move (actual volume = total volume – effective volume).

Pressure Correction
The pressure of a gas is the pressure exerted by gas molecule on the wall of the container. Since there are attraction forces between real gas molecules, the pressure is different from that of ideal behaviour. Then a pressure correction should be done. (P + a{n/V}^{2}) is the pressure correction. (Ideal pressure = observed pressure + pressure correction).
What is the Difference Between Ideal Gas Law and Van der Waals Equation?
Ideal Gas Law vs Van der Waals Equation 

Ideal gas law equation is a fundamental law in chemistry.  Van der Waal equation is the modified version of the ideal gas law. 
Equation  
Ideal gas law equation is PV = NkT  Van der Waal equation is (P + a{n/V}^{2}) ({V/n} – b) = nRT 
Nature  
Ideal gas law equation is not a modified version.  Van der Waal equation is a modified version with some corrections for pressure and the volume of a real gas. 
Components  
Ideal gas law equation is given for ideal gases.  Van der Waal equation can be used for both ideal gases and real gases. 
Summary – Ideal Gas Law vs Van der Waals Equation
Gaseous state is one of the three main phases of matter. The behavior and properties of a gas can be determined or predicted using gas laws. Ideal gas law is a fundamental law that can be used for ideal gases. But when considering real gases, the ideal gas law equation should be modified. The difference between ideal gas law and van der Waals equation is that, ideal gas law equation is given for ideal gases whereas Van der Waal equation can be used for both ideal gases and real gases.
Reference:
1.“Real Gases.” Chemistry LibreTexts, Libretexts, 1 Feb. 2016. Available here
2.Nave, C R. “Van Der Waals Equation of State.” HyperPhysics, 2016. Available here
3.Poudel, Subash. “Van der waalâ��s equation” Science HQ. Ed. Rod Pierce. 18 Feb 2013. 22 Mar 2018. Available here
Image Courtesy:
1.’Ideal Gas Law’ By BlyumJ – Own work, (CC BYSA 4.0) via Commons Wikimedia
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