Exam

NTA Abhyas

Year

2020

Subject

Chemistry

Chapter

States of Matter

NTA Abhyas 2020 · Chemistry · States of Matter

For one mole of a van der Waals when b = 0 and T = 300 K, the PV...

For one mole of a van der Waals when b = 0 and T = 300 K, the PV vs. 1/V plot is shown below. The value of the van der Waals constant a (atm litre^{2} mol^{-2}) is:

Step-by-step solution

van der Waals equation for 1 mol of real gas is

$\left[\text{P} + \dfrac{\text{a}}{V^{2}}\right] \left[\text{V} - \text{b}\right] = \text{RT}$

Given that b = 0

$∴ \left(\text{P} + \dfrac{\text{a}}{V^{2}}\right) \left(\text{V}\right) = \text{RT}$

$∴ \text{PV} = \text{RT} - \dfrac{\text{a}}{\text{V}}$~ ........ (i)

Following y = mx + c for the curve $\text{PV vs} \dfrac{1}{\text{V}}$

$\text{Slope} = - \text{a}$

$\text{Slope} = \dfrac{\text{21.6} - \text{20.1}}{2 - 3} = - \text{1.5}$

$∴ \text{a} = \text{1.5}$