Hydrogen and chlorine gas in water

[Kiara]

Say you've electrolyzed salt water, and that water is moving at a brisk pace through a tube. You want to combine the hydrogen and chlorine gas bubbles created by the electrolysis to make HCl which can then react with the NaOH produced by the electrolysis. If a bright UV light was installed in the tube with enough energy to break the Cl-Cl bond in the Cl2, would the Cl atoms react with H2 to make 2HCl?