= Solution
{c}
In weak <magnetic field> and the regime of <paramagnetism>, localized <magnetic moments> with total <angular momentum> $J$ and <Landé g-factor> $\widetilde g$ have SI <volume magnetic susceptibility>
$$
\chi_v=\frac{\mu_0 n_m(\widetilde g\mu_B)^2J(J+1)}{3k_B(T-\Theta)},
$$
within the <Curie–Weiss law>. Here $n_m$ counts magnetic <ions> per volume, $\mu_0$ is the <vacuum permeability>, $\mu_B$ is the <Bohr magneton>, and $\Theta$ is the <Weiss temperature>. The factor $J(J+1)/3$ is the zero-field average of the squared angular projection over $m_J=-J,\ldots,J$.
For one magnetic <ion> per formula unit, a molar volume $V_m$ contains $N_A$ magnetic <ions>, where $N_A$ is the <Avogadro constant>. Consequently $n_mV_m=N_A$, and the <molar magnetic susceptibility> is
$$
\chi_{\rm mol}=V_m\chi_v
=\frac{\mu_0N_A\mu_B^2}{3k_B}\,
\frac{\widetilde g^{\,2}J(J+1)}{T-\Theta}.
$$
Defining the dimensionless <effective paramagnetic moment> $m_{\rm eff}$ by $\mu_{\rm eff}=m_{\rm eff}\mu_B$, numerical substitution gives
$$
\frac{\mu_0N_A\mu_B^2}{3k_B}=1.5714\times10^{-6}\,
\mathrm{m^3\,K\,mol^{-1}},\qquad
\boxed{\chi_{\rm mol}=(1.57\times10^{-6}\,\mathrm{m^3\,K\,mol^{-1}})
\frac{m_{\rm eff}^2}{T-\Theta}.}
$$
The normalization is per mole of formula units, which here also means per mole of magnetic <ions>.
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