Chem lab was too many years ago. I was thinking it was the chlorine ions that made it acid instead of the hydrogen ions and getting it confused with hydrochloric acid.
Acid-base chemistry can be very confusing, even when you're actually studying it. It doesn't help that there are multiple ways of defining an acid or base, let alone all those weird chemical names that sound so similar. Don't sweat it, UT.
That said, there
can be a use for mixing bleach with an acid. I can't find where I first read it, but since the disinfecting form of sodium hypochlorite is most available at lower (i.e. more acidic) pH levels there were some scientists who studied the disinfecting power of common bleach under different conditions. (And is why the most stable, unreactive form is in the highly alkaline pH state inside the bottle of bleach).
They found that getting the solution down to around a pH of 4 creates a potent santizing solution, for example, for cleaning up after a flood event. I was just reading an article recently that after Sandy, some other scientists were measuring the level of bacteria on household items that had been submerged in the NY area. The storm had damaged the underground pipes and sewage was mixing into the flood waters. Even after sitting out in the sun for a week, the scientists were still finding surprisingly high levels of bacterial contamination on the items that residents had dragged outside. The result doesn't necessarily mean that ALL bacteria were found at high levels, but it does suggest that harmful ones can stick around longer than most people expect, so people need to be careful with protective equipment and measures, like hand washing before eating after handling flood damaged debris, even this long after the event. Mold is another danger and health hazard.
Anyway, the scientsts say that a cup of bleach and a cup of vinegar diluted into a gallon of water makes a highly potent disinfecting solution. It can even destroy bacterial spores. The article didn't mention anything about chlorine gas being generated, so I think the solution is dilute enough to not produce chlorine in any significant quantity but even so, it's probably best to use in a well ventilated environment. Use this info at your own risk!
Oh, come to think of it, I think I originally read about this after the anthrax attacks. I believe the scientists were looking for cost effective ways to decontaminate large areas because that requires a lot of disinfecting solution, which can get very expensive for some commercial product that bills itself as being able to decontaminate bioterror agents.
Anyway, a bit beyond the level of "basic" bleach info.