The van der Waals equation of state was designed to predict

The van der Waals equation of state was designed to predict the relationship between pressure p, volume Vand temperature T for gases better than the Ideal Gas Law pt a (y-nb) = nRT The van der Waals equation of state. R stands for the gas constant and n for the moles of gas. The van der Waals parameters a and b have to be determined for each gas by comparing to experimental data Consider the hypothetical gases X, Y and Z listed in the table below. Use the information provided to decide the relative size of the van der Waals parameters a and b boiling point OC particle diameter gas size of a size of b pm 242 193 217 (Choose one)V (Choose one) (Choose one) 6.1 (Choose one) (Choose one) 15.7 (Choose one)

Solution

In the Vanderwall\'s Equation ,

For n Moles of gas :

  ( P + a(n) / V² )( V - nb) = nRT .

Where \' a \' and \' b \' are the correction terms introduced by the Vanderwall to the ideal gas equation .

Two wrong assumptions were made in the Kinetic Theory of Gasses.

1. The Volume occupied by the gas molecules is negligible and tends to 0.

2.  The intermolecular force of attraction between the gas molecules is negligible.

So , Vanderwall introduced two correction terms \' a \' and \' b \' .

Where \' a \' is the measure of the Intermolecular forces between the particular gas molecules .

When the intermolecular forces are strong , value of \' a \' will be high and simultaneously the gas will have High boiling point.

Among the  gasses X ,Y & Z the vlaue of a will be high for gas Z and least for gas X and in between for Y.

X < Y < Z ***( Size of a )

In the Vanderwall\'s equation \' b \' is the measure of relative size of the gas molecule.

As the size of the molecule increases the value of \' b \' also increases .

Among the gases Value of \' b \' will be high for Gas X as it is having the largest diameter and Value of \' b \' will be least for gas Y as it is having the smallest diameter and Gas Z will have a Value in between the values of gas X and gas Y.

Y < Z < X ***( Size of b )