How is the pH level affected of a substance when it is mixed with a acid, base, or neutral?

I tried to mix diffrent acids and bases as well as neutral water with vinegar an acid to see how it would affect the vinegars pH level. The pH level did change when i mixed the other substance but i don't understand the pattern. Why did the pH level change, and why only a specific amount?How is the pH level affected of a substance when it is mixed with a acid, base, or neutral?
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Assuming water is 7, adding acid will lower the pH. Adding a base will increase the pH.



The amount that changes is based on the concentration (and reactivity) of acids and bases.



Molar/Molal concentrations will affect this as well, since a more concentrated, stronger acid/base will affect total PH more than a weaker reagent.



Also, the total volume of liquid affects the concentration as well.



Free hydrogen is acidic

Free hydroxide is basic

Since water is H20, things that react in water to make excess free hydrogen or peroxide react as above too.