1. 6.4 – The pH Scale
Unit 6 – Acids and Bases

2. What is pH?
pH is just another way to express [H+], the hydrogen ion concentration of an acidic or basic solution.
Hydrogen acid concentrations are often small numbers, such as 1.3 × pH is a method of transforming this number into something that is a little easier to work with.
In math class you may have learned about logarithms - log for short. We'll leave the definitions of logs to math and just work with how to find them here.
Get your calculators out. Different calculators work in slightly different ways, and it will be VERY IMPORTANT for you to know how to use yours when working with logs.

3. Logs – Using your Calculator
Example: Find the log of 1.0 ×105
Enter the number 1.0 ×105 (don't forget to use the calculator's scientific notation feature!), then press the LOG key. Try that. You should get an answer of "5".
If you get a different answer, or an error, try pressing the LOG key before you enter the number 1 ×105.
Be sure you get the correct answer of 5 before continuing on.
Try the examples shown on the right. Again, be sure you are getting the correct answers - if not, try changing the order than you enter items into your calculator.
Number
Log
1 ×10-3 -3
2.5 ×1012 12
3.5×10-9
-8.5

4. Logs & pH
pH is defined as the negative log of hydrogen ion concentration.
pH = -log[H+]
Because hydrogen ion concentration is generally less than one (for example, 1.3 x 10-3), the log of the number will be a negative number.
To make pH even easier to work with, pH is defined as the negative log of [H+], which will give a positive value for pH.

5. pH & Your Calculator - Practice
Try the examples shown on the right.
Find the pH, given [H+].
Answers are shown, but be sure you are able to arrive at that answer with your calculator!
Notice the last example.
1.0 ×10-7 is the [H+] in pure water.
Pure water therefore has a pH of 7.
[H+] pH
1 ×10-3 3
2.5 ×10-11 11
4.7 ×10-9
8.3
5.8 ×10-4
3.2
1.0×10-7
7.0

6. What do pH Values Mean?
By looking at the [H+] values in the table above, can you determine which solutions would be acidic, and which would be bases?
Number 1 and 4 are acids. In those, [H+] is greater than 1.0×10-7
Numbers 2 and 3 are bases. In those solutions, [H+] is less than 1.0×10-7.
Working with negative powers of 10 is not easy for many of us, so some of you may be confused by trying to identify acids and bases based on [H+].
But if we use pH values instead we find it much easier to identify acids and bases.

7. What do pH Values Mean? Acids Bases Neutral solutions pH < 7
The lower the pH, the stronger the acid
Bases
pH > 7
The higher the pH, the stronger the base
Neutral solutions
pH = 7

8. Examples of Calculating pH
1. Calculate the pH of a 0.01M HNO3 solution.
2. Find the pH of a 0.01 M solution of ammonia.

9. pOH
There is a way to simplify the last parts of this operation. In addition to pH, we can also define pOH:
pOH = - log [OH-]
For bases, once we find [OH-] for a base, we can quickly determine pOH:
For example:
[OH-] =4.2 × 10-4
pOH = -log [OH-]
= -log (4.2×10-4)
pOH= 3.4 answer

10. pH & pOH
Next we make use of the following easy-to- memorize relationship:
pH + pOH = 14
Does the number 14 ring a bell?
Remember Kw = 1.0 ×
The negative log of 1.0 × = 14
Once we find pOH, it is a simple matter to find pH:
pH = 14 - pOH =
pH = 10.6

11. Finding [H+] when you know pH
Sometimes you need to work "backwards" - you know the pH of a solution and need to find [H+], or even the concentration of the acid solution. How do you do that?
To convert pH into [H+] involves taking the antilog of the negative value of pH .
[H+] = antilog (-pH)
As mentioned above, different calculators work slightly differently - make sure you can do the following calculations using your calculator. Practice as we go along . . .

12. Finding [H+] when you know pH
Example 3. We have a solution with a pH = What is [H+]?
With some calculators you will do things in the following order:
Enter 8.3 as a negative number (use the key with both the +/- signs, not the subtraction key)
Use your calculator's 2nd or Shift or INV (inverse) key to type in the symbol found above the LOG key. The shifted function should be 10x.
You should get the answer 5.0 × 10-9

13. Finding [H+] when you know pH
Example 3. We have a solution with a pH = What is [H+]?
Other calculators require you to enter keys in the order they appear in the equation.
Use the Shift or second function to key in the 10x function.
Use the +/- key to type in a negative number, then type in 8.3
You should get the answer 5.0 × 10-9
If neither of these methods work, try rearranging the order in which you type in the keys. Don't give up - you must master your calculator!

14. Example 4.
Find the hydronium ion concentration in a solution with a pH of Is this solution an acid or a base? How do you know?

15. Example 5.
A 0.24M solution of the weak acid, H2CO3, has a pH of Determine Ka for H2CO3 (carbonic acid). *Assume only the first (or one) H+ ionizes.