 
Calculating pH and pOH
Next let's look at values for pH and pOH. pOH is simply the power
of hydroxide ion concentration and is figured the same way as pH but using the
concentration of hydroxide ion instead.) For your notes, expand the table in exercise 24a
by making columns for pH and pOH.)
Let's start by working with the concentrations that are 1.0 x 10^{(raised
to some power)}. These pH and pOH values can be figured very simply. When [H_{3}O^{+}]
is 10^{7} M, the pH is 7. Also the [OH^{}] is 10^{7} M
and the pOH is 7. Note that the pH and pOH add up to 14. 
pH 
[H_{3}O^{+}] 
[OH^{}] 
pOH 
7 
1.0 x 10^{7} M 
1.0 x 10^{7} M 
7 

Now look at the acidic solutions. When the [H_{3}O^{+}] is
10^{6} M, the pH is 6. Also, the [OH^{}] is 10^{8} M
and the pOH is 8. Again, the pH and the pOH add up to 14. When the [H_{3}O^{+}]
is 10^{5} M, pH is 5, [OH^{}] is 10^{9} M, and
pOH is 9. pH + pOH = 14. 
6
5 
1.0 x 10^{6} M
1.0 x 10^{5} M 
1.0 x 10^{8} M
1.0 x 10^{9} M 
8
9 

Next, the basic solutions. When [OH^{}] is 10^{6} M,
the pOH is 6. Since [H_{3}O^{+}] 10^{8} M, the pH is 8.
When [OH^{}] is 10^{5} M, and [H_{3}O^{+}] is 10^{9}
M, the pOH is 5 and pH is 9. Again in both cases the sum of pH and pOH is 14. 
8
9 
1.0 x 10^{8} M
1.0 x 10^{9} M 
1.0 x 10^{6} M
1.0 x 10^{5} M 
6
5 

However, the hydrogen ion concentration is not always going to be equal to
exactly 1 x 10 raised to a negative number. For example, we skipped over the value of 2.0
x 10^{7}. This is more complicated. However, if you use a calculator that will
handle logarithms, it is a very simple calculation. First you enter the hydronium ion
concentration. You can use decimal format or scientific notation. Next push the log
button. Then change the sign by pushing the +/ button. In this case we get 6.70 for the
pH. The other values can be obtained in the same way. 
6.70
7.30 
2.0 x 10^{7} M
0.5 x 10^{7} M 
0.5 x 10^{7} M
2.0 x 10^{7} M 
7.30
6.70 

Significant Digits in pH
Now a word about significant digits and log
values like pH's. Let's compare the parts of the pH value to the parts of the
value in the scientific notation from which it was derived. The value of 2.0 x 10^{7}
shows both precision (two significant digits in 2.0) and size or magnitude (shown in the
exponent ^{7}). In the pH value, the size or magnitude is shown in the number in
front of the decimal point. The two significant digits are shown after the decimal point.
The size match is a little easier to see if the the concentration is written in nonstandard
scientific notation. 
[H_{3}O^{+}] = 2.0
x 10^{7}
precision (two significant digits)
size 
pH = 6.70
precision (two significant digits)
size 
[H_{3}O^{+}] = 0.20
x 10^{6}
precision (two significant digits)
size 

Practice  pH
I'd like you to practice calculating pH values by figuring values for the two empty
columns in this table (exercise 26 in your workbook). Write the hydronium ion
concentrations in scientific notation and also calculate the pH value for each. Check your
answers below, then continue with the lesson.
[H_{3}O^{+}] 
scientific notation 
pH 
0.1 


0.01 


0.001 


0.0007 


0.0001 


0.000001 


0.0000003 


0.0000001 


0.0000000001 


0.00000000002 


Answers
Your answers should be as follows:
[H_{3}O^{+}] 
scientific notation 
pH 
0.1 
1 x 10^{1} 
1.0 
0.01 
1 x 10^{2 } 
2.0 
0.001 
1 x 10^{3} 
3.0 
0.0007 
7 x 10^{4} 
3.2 
0.0001 
1 x 10^{4} 
4.0 
0.000001 
1 x 10^{6} 
6.0 
0.0000003 
3 x 10^{7} 
6.5 
0.0000001 
1 x 10^{7} 
7.0 
0.0000000001 
1 x 10^{10} 
10.0 
0.00000000002 
2 x 10^{11} 
10.7 
Note that each pH value has one digit to the right of the decimal point because each
concentration value had one significant digit.
If your answers are not correct, get some help from the instructor.
Hydronium Ion Concentration from pH
It is also possible to run the calculations in the other direction as well. If you know
the pH, you can calculate the hydrogen ion concentration. Here is how you do it. Let's say
the pH is 4.3. Enter the pH value and make it negative using the +/ button.
Then press the 10^{x} button. It will probably be the 2nd
function or inverse of the log button. I get
0.00005 or 5 x 10^{5} M. If you don't get this value when you try it with
your calculator, or if you cannot find the right buttons, check with the instructor in the
lab.
Practice  pH and pOH
Once you have that calculation under control, try your hand at filling in the blank
spots in this table (exercise 27 in your workbook). Check your answers below then continue
with the lesson.
pH 
[H_{3}O^{+}] 
pOH 
[OH^{}] 
3.2 



8.2 





6.4 


0.0050 





0.0050 



2.3 x 10^{5} 


7.8 x 10^{4} 

Answers
All concentrations are expressed in molarity.
pH 
[H_{3}O^{+}] 
pOH 
[OH^{}] 
3.2 
0.0006 or
6 x 10^{4} 
10.8 
1.6 x 10^{11} or
2 x 10^{11} 
8.2 
0.000000006 or
6 x 10^{9} 
5.8 
1.6 x 10^{6} or
2 x 10^{6} 
7.60 
2.5 x 10^{8} 
6.40 
4.0 x 10^{7} 
2.30 
0.0050 
11.70 
2.0 x 10^{12} 
11.70 
2.0 x 10^{12} 
2.30 
0.0050 
9.36 
4.3 x 10^{10}
(from the K_{w} equation) or 4.4 x 10^{10} (if going from
pH to conc.) 
4.64 
2.3 x 10^{5} 
3.11 
7.8 x 10^{4} 
10.89 
1.3 x 10^{11} 
If you had trouble with any of these, first double check your calculations to make sure
you entered the values and functions correctly on your calculator. Then check with your
instructor.
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Email instructor:
Eden Francis
Clackamas Community College
©1998, 2002 Clackamas Community College, Hal Bender
