@Andrew S.
You raise some good questions. Unfortunately, my background is in mechanical engineering and the questions you are posing are ideally for some with a chemical engineering background.
MIXING SOAP AND BLEACH
You thoughts on using soap with bleach make sense ... but I have always learned to work on the KISS principle. Mixing soap (which is a chemical) with bleach (which is also a chemical) could create some other "unknown and uncontrolled" substance that could be extremely harmful to products or people. Now you'd ask me ... which products? Which soaps, etc.? I can't tell you exactly. I can only speculate because I don't recommend it and I don't do it. Just know that the compounds in dish soaps vary from brand to brand. Consequently, the "chemical soup" that you'd create by mixing one brand with bleach would likely be very different than the soup you'd create when mixing bleach with another brand.
PROBLEMS CAN HAPPEN
I can offer this one example that a peer related to me a couple of years ago. His instructions to a maintenance engineer in a very large building was to use bleach to clean some very contaminated metal pipe fittings. These fittings were under the sink in a 30 story office building. He directed the engineer to wet a rag with a bleach/water solution and wipe the piping clean. They were trying to eliminate the possibility of bacteria from a previous leak under the sink. As I understood it, the directions to the engineer on the product and method were very specific. Now, knowing that bleach was good, and realizing also that ammonia is used as a disinfectant, the engineer was ready to mix them together and clean the piping. Fortunately, my friend revisited the building about 5 minutes before the engineer began his mixing/cleaning process. Had this mixture NOT been avoided, it would likely have killed or severely impacted every person on the 18th floor and may have affected others on adjoining floors. These 3 floors had about 400 people on them.
My point here is that I (personally) and most of my peers - choose to avoid the use of harmful chemicals at any point possible. Sure, you and your closest 50 friends are not harmed by exposure to bleach. What if you opened a bottle and started using it when that one person (in 50) who WAS reactive was nearby?
THE USE OF OXIDIZERS
Using bleach will (almost) always leave a residual. That residual produce can continue to cause oxidation to occur on metal surfaces, electrical wiring, galvanized studs, nails, etc.
Using hydrogen peroxide doesn't leave a residual. I can not explain the chemical process, but that is what has been explained, demonstrated, and drilled into me by countless educators.
Using bleach to "kill mold" usually means that the user plans to saturate a surface with bleach. Saturating a surface with a mixture of water and sodium hypochlorite REALLY sounds to me like they are going to "saturate the surface." That's why we don't like the use of bleach.
The use of soap and water asks the user to saturate the rag and wring it out. Next, you wipe the surface, turn the rag to a clean location, wipe the surface, turn the rag, wipe the surface, etc. The purpose of soap and water is NOT to saturate the walls. Rather, the soap increases the surfactantcy of the water (makes it wetter) and that allows a damp rag to better pick up mold spores, hyphal fragments, mold pieces, etc. Hence, this is the more effective method. It removes the mold better and does not saturate the wall.
SURFACTANTCY TIPS
Although this is not the purpose of my whole response, I'd like to share a brief tip that I learned from a painter years ago. It involves a BETTER METHOD to remove latex paint from brushes, rollers, and other paint tools when you're done for the day.
1) buy some liquid fabric softener
2) pour about 1/2 a cup into a 2-3 gallon pail of water
3) place your "paint loaded" brush into the water solution
4) actively move your brush to agitate the water for 10-20 seconds
5) remove your brush and briskly shake it to remove the water
6) note that there is NO paint left in or on your brush
NOTE: This is because the fabric softener dramatically increases the surfactantcy of the water. It makes the size of the water droplets dozens (or maybe hundreds) of times smaller. These smaller water droplets do a much better job cleaning your brush and help to remove paint in the smallest recesses of the brush, roller pad, etc. The embedded latex paint doesn't stand a chance when confronted with these hyper-small water droplets.
SURFACTANTCY WORKS FOR MOLD TOO
So my point in the surfactantcy example above is that when you use dish soap (which also increases the surfactantcy of water) you are able to pick up MORE of the smaller mold compounds (spores, hyphal fragments, etc.) without using a lot of "liquid live water" and without saturating the wall - as you do with bleach. This is why soap and water works so well. It's designed to remove mold without using a lot of water!
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As I said earlier, I advise AGAINST anybody creating custom compounds by mixing soap and bleach. This is because I am not a chemical engineer and because I do not know what new (and potentially dangerous) compounds you might be creating.
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Besides, my professional liability insurance does not cover me for suggestions outside of my professional training.
Travis West
Certified Indoor Environmental Consultant - CIEC #0609003; Board Certified by the American Council of Accredited Certification
Licensed Mold Assessment Consultant; MAC0325; Texas Department of State Health Services