In van dar Wall equation [P + a V ^ 2 ][V - b] = RT; P is pressure,...

In van dar Wall equation

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

is pressure,

V

is volume,

R

is universal gas constant and

T

is temperature. The ratio of constants

\dfrac{a}{b}

is dimensionally equal to :

Options

A $\dfrac{P}{V}$
B $\dfrac{V}{P}$
C $PV$
D $P{V}^{3}$

Correct answer

C. $PV$

Step-by-step solution

\left(P + \dfrac{a}{{V}^{2}}\right)\left(V - b\right) = nRT $</p><p>Dimensions of$ b $should be equal to dimensions of$ V $. Similarly, dimensions of$ a $will be equal to dimensions of$ P{V}^{2} $.</p><p>Therefore, dimensions of \left[\dfrac{a}{b}\right] = \left[\dfrac{P{V}^{2}}{V}\right] = \left[PV\right]$ .

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