How do the numbers on the pH scale compare? Example: is a pH of 4 twice as strong as a pH of 2? The pH scale is linear!

Question

I don't know anything about this and do not know how I would put it in words

Answer 1

pH = -log₁₀[H₃O⁺]

 

Now consider pH values of 2 and 4.

 

2 = -log₁₀[H₃O⁺]

 

-2 = log₁₀[H₃O⁺]

 

[H₃O⁺] = 10^-2 = 0.01

 

4 = -log₁₀[H₃O⁺]

 

-4 = log₁₀[H₃O⁺]

 

[H₃O⁺] = 10^-4 = 0.0001

 

Note the concentration of the ion in the solution of pH = 2 is 100 times the concentration of the ion in the solution of pH = 4.  Note also that 100 = 10^4-2, which is 10 elevated to the difference in pH.  You can see that the concentration of the ion varies exponentially with pH, not linearly.