Answer Key: Understanding pH
What is a log?
Log 10 = 1
Log 1 = 0
Log 100,000,000 = 8
Log 0.001 = -3
Log 1.0 x 10-8 = -8
Explain why the following problem is more complicated than the previous ones.
Log 650 = not a whole-number power of ten
The number 650 is between 100 and 1000, so the answer must be between _2_ and _3__.
Using your Calculator
Log 650 = 2.812913357
Directions on how to enter this into my calculator: Log button followed by 650 = (no need to use end
parentheses).
Calculating pH
pH = - log [H+], where brackets mean concentration in M
Find pH when [H+] = 2.6 x 10-6 M pH = 5.585026652 (for now, just report to lots of significant figures)
Find pH when [H+] = 1.8 x 10-6 M pH = 5.744727495
Find pH when [H+] = 3.9 x 10-4 M pH = 3.408935393
Notice that it is easier to compare pH values since concentration values are so small.
The ___lower___ the [H+], the ____higher___ the pH. (or vice versa)
Note that pH values do not have units.
Acidic or Basic?
When [H+] > [OH-], the solution is acidic
When [H+] < [OH-], the solution is basic
When [H+] = [OH-], the solution is neutral
Find [H+] in a neutral solution using the equation for Kw:
Kw = [H+][OH-] let x = [H+], since [H+]=[OH-], Kw = x2 = 1.0 x 10-14 M2 x = 1.0 x 10-7 M = [H+]
What is the pH of this neutral solution?
pH = 7
Therefore, when pH < _7__, the solution is ___acidic___
When pH > ___7___, the solution is ____basic____
When pH = ___7____, the solution is ____neutral___
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A note on Sig Figs
For pH: Since the number to the left of the decimal point is simply an exponent, it does not count as a
significant figure. Therefore, only numbers to the right of the decimal point count.
For [H+] or any other concentration: Regular significant figure rules apply because it is a measured
value.
6.8  _1_ sf
12.672 _3__ sf
[H+] = 1.00 x 10-2, find pH _2.000____  pH has __3__ sf, even though there are __4_ digits
Antilog
10-pH = [H+] which is the inverse of log
Use antilog when you have the pH and are trying to find [H+].
If you ever get confused, remember that log 1 = 0, so antilog of 0 is 1, or 10 0 = 1
Find [H+] of a solution if pH = 4.97. 1.1 x 10-5 M (rounded to 2 sig figs since pH had 2 decimal places.)
Directions on how to enter this into my calculator:
2nd log (-) pH value =
Post-Quiz
Your teacher will reveal a set of numbers on the board. Your goal is to write the numbers
down in numerical order (smallest to largest) as fast as you can. Raise your hand when
finished.
Compare your time for the pre-quiz with that of the post-quiz. If they differed, why do
you think that was the case? It’s easier to organize numbers of intermediate magnitude
(not super small or large).
Propose a reason for the negative sign in the calculation of pH. Without the negative sign,
all pH values would themselves be negative. It’s easier to order positive values because
we have more experience with it.
Practice Problems
Use the following relationships to solve the problems below.
Kw = [H3O+] [OH-] = 1.0 x 10-14 M2 @ 25oC
pH = - log [H+] (or, solving for [H+] = 10-pH)
pOH = - log [OH-] (or, solving for [OH-] = 10-pOH)
pH + pOH = 14
1. pH = 1.34, find pOH = 12.66
2. [H3O+] = 8.20 x 10-9 M, find [OH-] = 1.22 x 10-6 M
3. [H3O+] = 8.20 x 10-9 M, find pH = 8.086
4. [OH-] = 6.4 x 10-12 M, find pOH = 11.19
5. [H3O+] = 3.65 x 10-2 M, find pOH = 12.562
6. The pH of black coffee is 5.66, find [H3O+] = 2.2 x 10-6 M
7. Some battery acid has pOH = 13.06, find [H3O+] = 1.1 x 10-1 M
8. Circle the acidic solutions in the above problems. #1, 5, 6, 7 are acidic
9. Coca-Cola has a pH value of 2.53, while Barq’s Root Beer has a pH of 4.61.
a. Find [H3O+] of each soft drink. 3.0 x 10-3 M; 2.5 x 10-5 M
b. Which drink is more acidic? Coca-Cola
c. How many times more acidic is the drink you chose in Part b? 120 x more acidic
10. Briefly research the Richter scale, used to describe the magnitude of earthquakes. Explain its
significance to today’s topic. It is also a logarithmic scale.
American Association of Chemistry Teachers
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