Separating Brown Gas into H2 and O2

I am looking to split brown gas into H2 and O2, since they are significantly safer(although still dangerous) when by themselves. The brown gas comes from an electrolysis chamber. I understand I could keep the gases separate when they are generated, but in order to maximize efficiency I want to put the electrodes as close together as possible.

Since the H2 and O2 should be ionized with opposing charges, would I be able to do something with charged electrodes?