I'm sorry for this, I'm kind of rambly. Prepare yo'self.
So for active ingredients, let's say acids. We know here that they are pH dependent to function well on your skin. For the discussion portion of your project you could explain about acids and bases, the OH- hydroxide ions or H+ hydrogen ion.
If something is more acidic, it's because it has a higher concentration of H+ ions. You may have already learned that acids and bases dissociate in aqueous solution. It's a fancy way of saying they "come apart" in water mixtures. So hydrochloric acid, a very strong acid, has a chemical structure of HCl. In water it goes to H+ ions and Cl- ions.
Now talking conditions, you could talk about concentrations. Do you know how to calculate pH of a solution? In your calculator you'd enter -log[H+]. The term in the brackets would be the concentration of H+ ions. It would look something like 10-7 in scientific notation. When you look at acid containing products, OST says 20% or the new one for 21.5%. They don't refer to the H+. I can't remember if it's by volume or by molarity etc. You'll need to look into that.
For an example experimental procedure (I am totally making up numbers here, use whatever you want) you could try to simulate the pH of a freshly washed face before and after applying vitamin C or glycolic acid or lactic acid or salicylic acid. Pick one acid. Let's go with LAA, L-ascorbic acid which is vitamin C. Have 6 beakers with 1000 mL deionized water each. Test pH and record to confirm neutral pH starting point. Pick 5 different cleansers of varying pH. Add 1 mL or however many mL of the cleanser you want. First beaker we chose to add 1 mL cleanser A. Mix well, test the pH, record. Second one add 1 mL cleanser B. Mix well test pH, record... Do this with 5 beakers. With the 6th beaker do not add cleanser. This is something to compare your results to. Then take your acid and add 1 mL to each of all 6 beakers. Mix well, take pH, record results. Round two, repeat, go as many times as it takes to get enough data that represents a good pH change curve. If 1ml at a time is too slow you could do 2ml at a time etc. You could make each beaker start out with like 500 ml water instead, up to you. You don't want the water amounts too small though because you won't get to see that gradual change in pH. Plus it allows more room for error when you add slightly more or less than 1ml at at a time.
When you look at your results, compare if there is a significant change in pH between different cleansers + acid mixtures. Did one cleanser make your "face" more resistant to returning to a normal pH if it was a very basic cleanser?
There are lots of ways you could do this experiment. Maybe you could use one cleanser, and compare five different acids. Or one cleanser, one acid at 5 different concentrations. Maybe you wanna see if that Mizon AHA/BHA after the cleanser then followed by acid changes anything.
note Btw, sometimes you will see H3O+ instead of H+. They're used interchangeably. The H+ would typically react with water to form H3O+.