Question

What is the significance of Van der Waals constants? Out of ${N_2}$ and $N{H_3}$ which one will have (i) larger values of a (ii) larger value of b.

Answer 1

Hint:
The Vander Waals equation is $\left( {P + \dfrac{{a{n^2}}}{{{V^2}}}} \right)\,\,\,\left( {v - nb} \right) = nRT$
Where a, b represents the Van der Waals constants and \[P,V,T,n\] are pressure volume, temperature and number of moles of gas.

Complete step by step answer:
Van der Waals equation is the relationship between pressure, volume, temperature and amount of real gases.
The Vander Waals equation is:
$\left( {P + \dfrac{{a{n^2}}}{{{V^2}}}} \right)\,\,\,\left( {v - nb} \right) = nRT$
Where,
\[P\] is pressure
\[V\] is volume
\[n\] is number of moles
\[T\] is temperature
\[a,b\] are Van Der Waals constants
\[R\] is gas constant
\[a,b\] Represents the Vander Waals constant in the equation. They are added to the equation keeping in mind the non – ideal behaviour of some gases.
The constants have positive values and are characteristics of the individual gas. If in case, the gas behaves ideally, then both a and b are taken as zero and the equation will become as:
\[\left( {P + \dfrac{{a{{\left( 0 \right)}^2}}}{{{V^2}}}} \right)\,\,\,\left( {v - \left( 0 \right)b} \right) = nRT\]
i.e. \[PV = nRT\] just like the ideal gas equation.
The constants have their own importance in the equation:
(i) The constant a provides the correction for intermolecular forces.
(ii) The constant b provides the volume occupied by a gas particle. It represents the correction for finite molecular size and its value is volume of one mole of the atoms or molecules.
The units of:
(A) Constant a is: \[atm\,\,{\text{litr}}{{\text{e}}^2}\,\,mo{l^{ - 2}}\]
(B) Constant b is: \[{\text{litre}}\,\,mo{l^{ - 1}}\]
Now out of \[{N_2}\] and \[N{H_3}\]since \[{N_2}\] is bigger than \[N{H_3}\] So, \[{N_2}\] will have larger value of b whereas as \[N{H_3}\] has strong hydrogen bonding. So, \[N{H_3}\] will have a greater value of a.

Note:Van der Waals equation is not only applicable to gases but also to all fluids. Moreover, this equation has the ability to predict the behaviour of gases better than the ideal gas equation.