= Solution
For dilute nonrelativistic nucleons in thermal equilibrium, their <Maxwell-Boltzmann distribution> gives $n_j=g_j(m_jkT/2\pi\hbar^2)^{3/2}\exp[(\mu_j-m_jc^2)/kT]$. The <neutron> and <proton> spin degeneracies are equal, and their <mass> prefactor ratio is nearly one. Thus
$$
\frac{n_n}{n_p}\simeq\exp\left[\frac{\mu_n-\mu_p-Q}{kT}\right].
$$
Weak reaction equilibrium imposes $\mu_n+\mu_{\nu_e}=\mu_p+\mu_e$. Charge neutrality in an electron-positron plasma, together with the small <baryon> asymmetry, makes $\mu_e/kT$ very small. Assuming negligible neutrino lepton asymmetry also makes $\mu_{\nu_e}/kT$ small. Hence the difference, rather than the absolute <baryon> <chemical potentials>, is negligible, yielding
$$
\boxed{n_n/n_p\simeq e^{-Q/kT}.}
$$
A large neutrino <chemical potential> would invalidate this last approximation; it is an assumption about the lepton asymmetry, not a general rule that baryonic <chemical potentials> vanish.
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