Question

what is the unit and dimension of van der waals constants?

Answer 1

$$\begin{gathered} \mathrm{Vander}\mathrm{Waal}\text{'}\mathrm{s}\mathrm{equation}\mathrm{for}\mathrm{gas}\mathrm{is}\mathrm{given}\mathrm{by} \\ \left(P+\frac{n\mathrm{a}}{V^2}\right)\left(V-n\mathrm{b}\right)=nRT \\ \mathrm{Now},\mathrm{From}\mathrm{the}\mathrm{principle}\mathrm{of}\mathrm{homogeneity}\mathrm{of}\mathrm{dimensions}, \\ \mathrm{we}\mathrm{have} \\ \therefore P=\frac{a}{V^2} \\ \Rightarrow a=P{V}^2=\left[{\mathrm{ML}}^{-1}{\mathrm{T}}^{-2}\right]{\left[{\mathrm{L}}^3\right]}^2=\left[{\mathrm{ML}}^5{\mathrm{T}}^{-2}\right] \\ V=b=L^3=\left[{\mathrm{M}}^0{\mathrm{L}}^3{\mathrm{T}}^0\right] \\ \mathrm{Unit}\mathrm{of}\mathrm{a}\mathrm{will}\mathrm{be}{\mathrm{PaL}}^2{\mathrm{mol}}^{-2} \\ \mathrm{Unit}\mathrm{of}\mathrm{b}\mathrm{will}\mathrm{be}{\mathrm{Lmol}}^{-1} \end{gathered}$$