If one solution has 100 times more hydrogen ions than another, what is the difference in pH between the two solutions?
pH is calculated as pH = -log[H(3)O+]
What does this really mean? It means the difference in pH between each level of the pH scale is a power of 10.
pH H+ Relative to pure water Example
0 10 000 000 Battery Acid
1 1 000 000 Sulfuric Acid
2 100 000 Lemon Juice
3 10 000 Soda
I'll refrain from putting the entire chart on here to save space and time. As you can see, every move up or down the chart is to the positive or negative power of 10. Therefore, a 100 difference, or 10 x 10 is two levels difference between the two solutions.
A level 3 acid (10,000) times 100 will give you a level 1 acid (1,000,000). Conversely, if you divide by a factor of 100 you will get the base. So, if we continued this chart and take a level 3 acid to base, you would get a level 5 acid (coffee). Remember, as the level goes higher it becomes more basic. A level 5 divided would get you a level 7 (neutral), etc.