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In van dar Wall equation $$\left[P + \frac{a}{V^2}\right][V - b] = RT$$; $$P$$ is pressure, $$V$$ is volume, $$R$$ is universal gas constant and $$T$$ is temperature. The ratio of constants $$\frac{a}{b}$$ is dimensionally equal to:
In the van der Waals equation $$\left[P + \frac{a}{V^2}\right][V - b] = RT$$, we need to find the dimensions of $$\frac{a}{b}$$.
To begin, since $$\frac{a}{V^2}$$ is added to pressure $$P$$, it must have the same dimensions as pressure:
$$\frac{a}{V^2} = P \implies a = PV^2$$
Thus, $$[a] = [PV^2]$$.
Next, because $$b$$ is subtracted from volume $$V$$, it shares the same dimensions as volume:
$$[b] = [V]$$
Finally, combining these results gives
$$\frac{a}{b} = \frac{PV^2}{V} = PV$$
Therefore, the correct answer is Option C: $$PV$$.
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