The chemical acidity of a solution is measured in units of pH: , where is the hydrogen ion concentration in the solution. If a sample of rain has a pH of 3.3, how many times higher is its than pure water's, which has a pH of 7?

Question

The chemical acidity of a solution is measured in units of pH:  , where  is the hydrogen ion concentration in the solution. If a sample of rain has a pH of 3.3, how many times higher is its  than pure water's, which has a pH of 7?

Quizplus · Accepted Answer

The pH scale is logarithmic, meaning that each increase or decrease of one pH unit corresponds to a ten-fold increase or decrease in hydrogen ion concentration. 
Therefore, to calculate the difference in hydrogen ion concentration between a solution with pH 3.3 and pure water with pH 7:

11eb80b1_b021_2188_a291_c7a0f55192aa_TB8633_11 of pH 3.3 = 10^(-3.3) 
11eb80b1_b021_2188_a291_c7a0f55192aa_TB8633_11 of pH 7 = 10^(-7)

Dividing these two expressions:

(10^(-3.3))/(10^(-7)) = 10^(-3.3+7) = 10^3.7

Therefore, the hydrogen ion concentration of the solution with pH 3.3 is approximately 10^(3.7) times higher than that of pure water, which has a pH of 7. 
Round off to four significant figures gives D as the answer: 
11eb80b1_b021_6fac_a291_1f062ed14e59_TB8633_11

The Chemical Acidity of a Solution Is Measured in Units