= Solution
The SI <volume> <magnetic susceptibility> is the weak-field response $\chi_M=\partial M/\partial H$, or $M/H$ for a linear isotropic sample with no spontaneous moment. It is dimensionless; a molar susceptibility would be a different quantity. For weak <magnetization>, $B\simeq\mu_0H$. Neglect local-field and demagnetizing corrections in this independent-spin model.
A spin-$1/2$ ion has moment projections $\pm g\mu_B/2$. The requested coefficient assumes a spin-only $g\simeq2$, giving projections $\pm\mu_B$ and Zeeman energies $\mp\mu_BB$. With $x=\mu_BB/(k_BT)$, the one-ion <partition function> and <magnetization> are
$$
Z_1=e^x+e^{-x}=2\cosh x,\qquad
M=N\mu_B\frac{e^x-e^{-x}}{e^x+e^{-x}}=N\mu_B\tanh x.
$$
For $|x|\ll1$, $\tanh x\simeq x$, so
$$
\boxed{\chi_M\simeq\mu_0\frac{\partial M}{\partial B}
=\frac{N\mu_0\mu_B^2}{k_BT}.}
$$
Here $N$ is a <number density>, as specified, rather than total ion number. The small-field condition is
$$
\boxed{\mu_B|B|\ll k_BT,}
$$
meaning the Zeeman splitting $2\mu_BB$ is small compared with the thermal scale up to an irrelevant order-one convention. It is not a temperature-independent absolute upper bound on $B$. For a different $g$ value the coefficient contains $(g\mu_B/2)^2$ instead of $\mu_B^2$.
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