= Molar mass from sedimentation and diffusion
{title2=$M=R_{\rm gas}Ts/[D(1-\bar v\rho_s)]$}
Let $M$ be molar mass in $\mathrm{kg\,mol^{-1}}$, $\bar v$ partial specific volume, $\rho_s$ solvent density, and $N_A$ the <Avogadro constant>. The buoyant molecular mass is $m_b=M(1-\bar v\rho_s)/N_A$. Combining <sedimentation coefficient> $s=m_b/f_h$ and the thermal diffusion-friction relation $D=k_BT/f_h$ eliminates the unknown friction and proves the displayed formula, with $R_{\rm gas}=N_Ak_B$. Once friction is known, $R_h=f_h/(6\pi\eta)$ defines a <hydrodynamic radius> using <Stokes's law>. Mass and radius are different inferences: an extended molecule need not occupy the volume of that friction-equivalent sphere.
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