# Is osmosis stronger or weaker than gravity, and by how much?

Suppose you perpare a jar of salt water and another of sugar water and invert one on top of the other with a divider between them, and then carefully remove that divider so the liquids are in contact.

Will the concentrations of salt and sugar reach equilibrium, despite the fact that the salt or sugar in the bottom jar has to overcome gravity to rise into the upper jar? How would you calculate the relevant forces here?

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• I am calling Gorilla vs. shark on the title. yesterday
• @Wrzlprmft: I don't think so. Gorilla vs Shark is asking a subjective question, which ultimately comes down to personal taste. This question is about physical forces, which can in principle be calculated objectively. 15 hours ago
• Well, another aspect of gorilla vs. shark is that it strongly depends on context, just like the titular case. But then it turns out that your question is about something slightly different anyway. (Hence me only calling gorilla vs. shark on the title, not the entire question.) 14 hours ago

At equilibrium, the solute will have a very slightly higher concentration closer to the ground. The heavier the solute is, the more pronounced the gradient. If we treat the solution as an ideal solution, we can calculate the difference in concentrations explicitly using the Boltzmann distribution. For example, let's assume that each jar has a height of 10 cm. The mass of a sucrose molecule is $$5.68 \times 10^{-25}$$ kg. Let's assume an ambient temperature of 293 K. The ratio of probabilities for it to be found in the bottom jar rather than the top jar is $$\exp(\frac{mgh}{kT})$$ which comes out to about 1.000138. That means the sugar will be more concentrated in the bottom jar by a ratio of 1.000138; a very slight difference. You might be able to measure it using a very sensitive spectrophotometer.