Question

What is the unit of Van der Waals constant?

Answer 1

Hint: We know that the ideal gas law, also expressed as a general gas equation, can be considered as the equation of state of a hypothetical ideal gas. The Van Der Waals equation tends to take into consideration the molecular size and the molecular interaction forces which can be attractive or repulsive forces. It is used to examine the behaviour of gases in different conditions, but it has several limitations.

Complete answer:
Van Der Waals equation is an equation that is used to relate the relationship existing between the pressure, volume, temperature, and amount of real gases. The Van Der Waals equation is derived to make an approach to the ideal gas law \[PV=nRT\] because the value of these constants stands at zero. The constant A is meant for providing a correction for the intermolecular forces exerted. The constant B is meant for correcting the finite molecular size. The value of constant B is equal to the volume of one mole of the atoms or the molecules. Since we can use constant B for calculating molecular volume, thus it can be used to calculate the radius of an atom or a molecule.
Van der Waal was of the opinion that as the molecular volumes remain unchanged during expansion or contraction of gases, it must be excluded from the total volume of the gas, so the corrected volume of the gas is (for n mole of gas). And b is the constant for molecular volume. Now, we discuss the correction of molecular attraction. We know that attractive forces are always present among the gas molecules and they can be neglected only under certain conditions. Previously this attraction was ignored which resulted in a defect. $\left( P+\dfrac{a{{n}^{2}}}{{{V}^{2}}} \right)$ where a is constant for molecular attraction.
Thus, the van der Waals equation is; $\left[ P+\dfrac{a{{n}^{2}}}{{{V}^{2}}} \right]\left[ V-b \right]=RT$ where, P is pressure, V is volume, R is gas constant and T is temperature, b is the constant for molecular volume and a is constant for molecular attraction and n is number of moles of gas; $a=\dfrac{P{{V}^{2}}}{{{n}^{2}}}=\dfrac{Pressure\times {{\left( volume \right)}^{2}}}{{{\left( Moles \right)}^{2}}}$ The SI units of Van Der Waals constant are \[Pat{{m}^{6}}~~mo{{l}^{-2}}.\]

Note:
Remember that the Van Der Waal forces include attractions within various atoms, resulting from influenced dipoles. However, they also involve a repulsive interaction within molecules, arising from the overlapping of more than two atomic electronic clouds situated closer to each other.