Question

Calculate pH A decrease of one unit on the pH scale means a solu-
tion is ten times more acidic. A decrease of two units means the
solution is 100 times more acidic. How much more acidic is acid
precipitation (pH = 4.0) than pure water (pH = 7.0)?

Answer 1

Answer:

• 1,000 times

Explanation:

Lower pH means that the solution is more acidic

A decrease of two units means that the new solution is 100 times more acidic than the original one:

            $pH=-log[H_3O^+]}\\\\pH_2-pH_1=2\\\\-log[H_3O^+]_2-(-log[H_3O^+]_1})=2\\\\-log[H_3O^+]_2+log[H_3O^+]_1})=2\\\\\\\log\dfrac{[H_3O^+]_2}{[H_3O^+]_1}=2\\ \\ \\ \dfrac{[H_3O^+]_2}{[H_3O^+]_1}=10^2\\ \\\\ \dfrac{[H_3O^+]_2}{[H_3O^+]_1}=100$

The final equality means that the when the pH decreases two units, the new solution is 100 times more acidic.

Use the same when the pH decreases from 7.0 to 4.0, which is three units of decrease:

             $pH_2-pH_1=7.0-4.0\\\\-log[H_3O^+]_2-(-log[H_3O^+]_1})=3.0\\\\-log[H_3O^+]_2+log[H_3O^+]_1})=3.0\\\\\\\log\dfrac{[H_3O^+]_2}{[H_3O^+]_1}=3.0\\ \\ \\ \dfrac{[H_3O^+]_2}{[H_3O^+]_1}=10^3\\ \\\\ \dfrac{[H_3O^+]_2}{[H_3O^+]_1}=1000$

That means that the acid precipiation (pH = 4.0) is 1,000 times more acidic than pure water (pH = 7.0)