How does vander waals equation differ from ideal gas equation
Answers
Answer:
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-1K-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
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.
Difference Between Ideal Gas Law and Van der Waals Equation
Figure 01: Real Gases behave differently from that of Ideal Gases
Volume Correction
The volume of a real gas molecule is not negligible (unlike in ideal gases). Therefore, the volume correction is done. (V-b) 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).
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.