Active mass of solids shouldn't necessarily be unity
Rather, active mass of solids need not necessarily be unity, but arbitrarily is unity with advantage. You do not have to know the molar mass nor density.
The common thermodynamic expressions like $K = \frac{[C][D]}{[A][B]}$
or kinetic ones like $\frac{\mathrm{d}[C]}{\mathrm{d}t} = k \cdot [A] \cdot [B]$
should be more exactly written as $K = \frac{a_\mathrm{C}] \cdot a_\mathrm{D}}{a_\mathrm{A} \cdot a_\mathrm{B}}$ or $\frac{\mathrm{d}[C]}{\mathrm{d}t} = k \cdot a_\mathrm{A} \cdot \cdot a_\mathrm{B}$
where $a_\mathrm{X}$ is unitless quantity called activity, defined by the chemical potential of the substance $ \mu_\mathrm{A} = \left( \frac {\partial G}{\partial n_\mathrm{A}} \right)_{T,p}$ by formula:
$$\mu_\mathrm{A} = RT \ln {a_\mathrm{A, unitless}}$$
If we implement the standard chemical potential, we can define unitless activity as ratio of the activity with unit and the standard activity with the unit value.
$$\mu_\mathrm{A} = \mu_\mathrm{A}^{\circ} + RT \ln \left( \frac {a_\mathrm{A}}{a_\mathrm{A}^{\circ}} \right)$$
where $a_\mathrm{A}^{\circ}$ is the activity at the standard chemical potential $\mu_\mathrm{A}^{\circ}$. We can consider the activity $a_\mathrm{A} = x\ \text{"whatever unit"}$ and the standard activity $a_\mathrm{A}^{\circ} = 1 \ \text{"whatever unit"}$.
If we arbitrarily choose $a^{\circ} = \pu{1 mol/L}$, then $a$ then more or less closely follow the respective concentration [A].
Chemical potential of the pure solid substance $\mu_\mathrm{A}^{\circ}$ does not depend on the amount of substance, so we arbitrarily choose $a^{\circ} = x_\mathrm{A}^{\circ}=1.0$ and $a$ then more or less follows the  molar fraction of substance $x_\mathrm{A}$.