The unit of the van der Waals gas equation pa | vedclass

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(D) In the van der Waals equation $(P + \frac{an^{2}}{V^{2}})(V - nb) = nRT$,the term $\frac{an^{2}}{V^{2}}$ is added to pressure $P$.According to the

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$atm \, dm^{6} \, mol^{-2}$

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(D) In the van der Waals equation $(P + \frac{an^{2}}{V^{2}})(V - nb) = nRT$,the term $\frac{an^{2}}{V^{2}}$ is added to pressure $P$.According to the principle of dimensional homogeneity,only quantities with the same units can be added.Therefore,the unit of $\frac{an^{2}}{V^{2}}$ must be the same as the unit of pressure ($atm$ or $bar$ or $Pa$).$\frac{an^{2}}{V^{2}} = 	ext{Pressure} \Rightarrow a = 	ext{Pressure} 	imes \frac{V^{2}}{n^{2}}$.Substituting the units: $a = atm 	imes \frac{(dm^{3})^{2}}{(mol)^{2}} = atm \, dm^{6} \, mol^{-2}$.

The unit of the van der Waals gas equation parameter $a$ in $(P + \frac{an^{2}}{V^{2}})(V - nb) = nRT$ is :

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