The unit of the van der Waals gas equation

Question:

The unit of the van der Waals gas equation

parameter 'a' in $\left(\mathrm{P}+\frac{\mathrm{an}^{2}}{\mathrm{~V}^{2}}\right)(\mathrm{V}-\mathrm{nb})=\mathrm{nRT}$ is :

  1. $\mathrm{kg} \mathrm{m} \mathrm{s}^{-2}$

  2. $\mathrm{dm}^{3} \mathrm{~mol}^{-1}$

  3. $\mathrm{kg} \mathrm{m} \mathrm{s}^{-1}$

  4. atm $\mathrm{dm}^{6} \mathrm{~mol}^{-2}$


Correct Option: , 4

Solution:

$\frac{\mathrm{an}^{2}}{\mathrm{~V}^{2}}=\mathrm{atm} \Rightarrow \mathrm{a}=\mathrm{atm} \times \frac{\mathrm{dm}^{6}}{\mathrm{~mol}^{2}}$

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