The chemical acidity of a solution is in units of pH: pH = -log[H^+], where [H^+] is the hydrogen ion concentration in the solution. If the sample of rain has the a pH of 3.9, how many times higher is its [H^+] than pure water's, which has a pH of 7?

Question

The chemical acidity of a solution is in units of pH: pH = -log[H^+], where [H^+] is the hydrogen ion concentration in the solution.  If the sample of rain has the a pH of 3.9, how many times higher is its [H^+] than pure water's, which has a pH of 7?

mathstudent55 · Answer

pH of 3.9
-log x = 3.9
log x = -3.9
x = 10^-3.9

pH of 7
-log y = 7
log y = -7
y = 10^-7

(10^-3.9)/(10^-7) = 1258.9