Passing protons through cation-permeable membranes

Question

Protons are attached to a water molecule (making hydronium) in acidic solutions. If a container was split through the middle with a cation-permeable but anion impermeable membrane and, say, HCl was added to one side, what would happen?

I'd assume because of the concentration gradient, osmosis will cause hydronium ions to move to the less concentrated side until equilibrium is reached.

But that would also make charge very uneven on both sides, where one side is highly negatively charged and the other side is very positively charged. So, I am not sure osmosis alone could even lead to this state.

Considering the ions on either side are either electron deficient or have full shells, and have the same charge, I would not expect any gas to come out of solution.

If a negative electric current was applied to one side of the container, and a positive on the other, would that produce gas more efficiently than plain electrolysis? If it depends, then under what conditions?

Or am I wrong, and what will happen to the ions from the acid?

Answer 1

Without current you would establish an equilibrium situation in which a charge imbalance is created across the membrane interface that counteracts (via migration) diffusion of your protons through the membrane. This is what is described by the Donnan equilibrium.

You can pass current in such a system as well, you will find however that there's a potential drop (a resistance) across this membrane. This resistance is exactly (or more) what you would thermodynamically gain by having a higher proton concentration at one side. You sadly cannot cheat thermodynamics.

But will it work better? Depends. The rate of the different electrochemical reactions is not only dependent on the thermodynamic driving force but also on other factors such as the kinetics and mass transport. If the rate is highly dependent on the proton concentration you might benefit from this. People are working on such systems for water electrolysis, in which at the hydrogen side they want an acidic environment and at the anode an alkaline environment. These membranes are called bipolar membranes.