pH and Logarithms
The pH Scale
The acidity or alkalinity of a solution is measured by its pH, which is
given by the following formula:
 
pH  log H
 

where H measures the concentration of hydrogen ions in moles per
liter. The pH scale ranges from 0 to 14. The pH of pure water is 7
which is considered neutral. A solution is considered acidic if the pH is
below 7 and alkaline if its pH is above 7.
Example: The pH of watermelon is 5.5, and the pH of some varieties of
honey is 4.0. Which is more acidic? How many times more acidic?
Compare the [H+] values.
Watermelon:
pH  log H
 
5.5  logH 
 5.5  logH 
10  H 


 5 .5

Honey:
pH  logH 
4  logH 
 4  logH 
 
104  H
10 4  10 5.5
104
 101.5  31.6227766
To see how much, we divide
5.5
10
So lemons are about 32 times as acidic as watermelons.
Example: The pH of yogurt is 4.5, while the pH of lemon juice is 4.0.
Find the concentration of hydrogen ions in each food and use it to tell
how many times more acidic lemon juice is than yogurt? Remember
that the units of [H+] are moles per liter, M. Show all your work.
Yogurt
pH = -log[H+]
4.5 = -log[H+]
-4.5 = log[H+]
10-4.5 = [H+]
Lemon juice
pH = -log[H+]
2.0 = -log[H+]
-2.0 = log[H+]
10-2.0 = [H+]
Since 10-2.0 > 10-4.5, divide 10-2.0 by 10-4.5.
102.0
 2.0   4.5 

10
104.5
 102.5
 316.2...
Thus, lemon juice is about three hundred and sixteen times as acid as
yogurt.
Practice Problems
1. The pH of ibuprofen is 5.3, while the pH of Tylenol is 4.0. Which
medication is more acidic? How many times more acidic is it?
Remember that the units of [H+] are moles per liter, M. Show all your
work.
2. The pH of tofu is 7.2, while the pH of grapefruit juice is 3.0. Find the
concentration of hydrogen ions in each food and use it to tell how many
times more acidic grapefruit is than tofu? Remember that the units of
[H+] are moles per liter, M. Show all your work.