Find the dimensions of the gas constant R . An equation involving...

The ideal gas equation is given by $PV = nRT$.

Rearranging for the gas constant $R$, we get:

$R = \dfrac{PV}{nT}$

The dimensions of pressure $P$ (Force/Area) are $[M L^{-1} T^{-2}]$.

The dimensions of volume $V$ are $[L^3]$.

The dimensions of number of moles $n$ are $[\text{mol}]$ and temperature $T$ are $[K]$.

Substituting these dimensions into the equation for $R$, we get:

$[R] = \dfrac{[M L^{-1} T^{-2}][L^3]}{[\text{mol}][K]}$

$[R] = [M L^2 T^{-2} K^{-1} (\text{mol})^{-1}]$