The units of constant a in the Van der Waals | vedclass

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(A) The Van der Waals equation for $n$ moles of a gas is given by: $(P + \frac{n^2 a}{V^2})(V - nb) = nRT$. According to the principle of dimensional

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

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(A) The Van der Waals equation for $n$ moles of a gas is given by: $(P + \frac{n^2 a}{V^2})(V - nb) = nRT$. According to the principle of dimensional homogeneity,the term $\frac{n^2 a}{V^2}$ must have the same units as pressure $(P)$. Therefore,the unit of $\frac{n^2 a}{V^2} = 	ext{unit of } P = atm$. Substituting the units: $\frac{(mol)^2 \cdot a}{(L)^2} = atm$. Rearranging for $a$: $a = atm \cdot L^2 \cdot mol^{-2}$. Since $1 \, L = 1 \, dm^3$,then $L^2 = (dm^3)^2 = dm^6$. Thus,the unit of $a$ is $dm^6 \, atm \, mol^{-2}$.

Gas	$Ar$	$Ne$	$Kr$	$Xe$
$a / (atm \ dm^6 \ mol^{-2})$	$1.3$	$0.2$	$5.1$	$4.1$
$b / (10^{-2} \ dm^3 \ mol^{-1})$	$3.2$	$1.7$	$1.0$	$5.0$

The units of constant $a$ in the Van der Waals equation are:

Similar Questions

Under which conditions does a real gas show maximum deviation from ideal gas behavior?

Consider the van der Waals constants,$a$ and $b$,for the following gases:

Gas $Ar$ $Ne$ $Kr$ $Xe$

$a / (atm \ dm^6 \ mol^{-2})$ $1.3$ $0.2$ $5.1$ $4.1$

$b / (10^{-2} \ dm^3 \ mol^{-1})$ $3.2$ $1.7$ $1.0$ $5.0$

Which gas is expected to have the highest critical temperature?

When is deviation more in the behaviour of a gas from the ideal gas equation $PV = nRT$?

When does a gas deviate the most from its ideal behaviour?

$A$ real gas most closely approaches the behaviour of an ideal gas at

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