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LOGARITHMS, ANTI-LOGARITHMS, AND pH
Practice Problems
Point 1: The common log (logarithm) of a number is the power to which 10 must be
raised to give that number:
100 = 102
The log of 100 is 2.
Point 2: An anti-log (antilogarithm) is the number corresponding to a given logarithm:
The antilog of 2 = 100
Because 10 raised to the second power equals 100
Point 3: pH is a method to express the concentration of hydrogen ions in a solution.
This concentration typically varies between 1.0 M and 1 X 10 –14 M.
pH is defined as the negative logarithm of the hydrogen ion concentration.
If a solution has a hydrogen ion concentration of 0.01 M, the pH of
that solution is 2.
Why?
0.01 M = 1 X 10–2 M
The log of 10–2 = -2.
pH = -log[H+]
Therefore, the pH = -(-2) = 2.
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Self-Test:
Please complete the following:
1. What is the pH of a solution with a hydrogen ion concentration of
0.001 M?
2. What is the pH of a solution with a hydrogen ion concentration of
0.003 M?
3. What is the pH of a solution with a hydrogen ion concentration of 2 X
10-1 M?
4. What is the hydrogen ion concentration of a solution with a pH of 2?
5. What is the hydrogen ion concentration of a solution with a pH of 3?
6. What is the hydrogen ion concentration of a solution with a pH of 2.5?
Complete the following:
1. log 3 = ____________
2. log 10 = ___________
3. log 0.1 = ___________
4. antilog 2 = ________
5. antilog 3 = __________
6. antilog 2.5 = ___________
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Without using a calculator, explain how you know that the following is
incorrect.
1. log 50 = 3.2
2. antilog 4.5 = 123,456