# Can a homogeneous chemical solution really not be split by centrifuge?

Assuming I have a homogeneous solution such as salt in water. My intuition tells me that gravity or centrifugal forces would affect sodium ions more than water molecules. Theoretically, if I could centrifuge salt water fast enough for the pulling forces to surpass the forces of the hydrogen bonds between salt and water, would I be able to seperate it? Or is there some theoretical reason for why no amount of centrifugal force would be able to split it up?

Sedimentation equilibrium happens when a suspension of particles needs up in an equilibrium where the sedimentation rate equals the diffusion rate. The volume fraction of the particles is given by the Laplace-Perrin equation: $$\Phi(z)=\Phi_0 \exp\left(-\frac{4 \pi g \Delta \rho R^3}{3 k_B T} z \right)$$ Here $$\Delta \rho$$ is the density difference - in this case at most a few times, and $$R$$ the radius of the particle. Note that if $$R$$ is very small, then the fraction in the exponential becomes very small, and the concetration changes very slowly with $$z$$. A criterion is that if $$\frac{3 k_B T}{4 \pi g \Delta \rho R^3} \gg R$$ there will not really be any sedimentation since diffusion dominates. This seems likely here, unless the centrifuge can make $$g$$ very large.
• @David - Yes, I was aware of the hydration. I actually looked for estimates of the local density of a hydrated ion complex, but did not find any good data then. This paper sciencedirect.com/science/article/pii/S0921452697004997 seems to suggest $\Delta \rho \sim 2$. Feb 21 at 13:50