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pH  and pOH

pH:  What is it?  

One of the ways that people show where the water equilibrium lies is by stating the pH of the water solution.  pH is a shorthand description of the hydrogen ions concentration.  It is defined as:

pH = - log [H+]

in which 
pH= power of hydrogen
log = logarithm (math function)
[H+] = concentration of H+ expressed in Molarity (moles/liter)

Some of you might never have seen a log function before, or so you think.  Let's begin by reviewing a few math facts that should show you that you have indeed accomplished log problems before.

You have looked at exponential math like this...   If 10 is raised to this power it equals

102 = x
x = 100

10-4 = y
y= 0.0001
And if you need to find the exponent... The power that 10 is raised to get this number is...

10z = 100000
z= 5

10a = 0.001
a = -3
Notice that if one expresses the number as a power of ten, this problem becomes an even easier problem.

10w = 105
w = 5

10a=10-3
a=-3
The power that 10 is raised to in  obtaining 105 (100000) is 5. The power that 10 is raised to in obtaining 10-3 (0.001) is -3.
Well another way once can present these problems is like this....
log10100000 = log 105 = w log100.001 = log 10-3 = a

So this means log 1000 = log 103 = 3 or that log 0.0000001 = log 10-7= 7

Log problems are just exponent problems involving powers of 10.

So this means that some pH problems, the ones that are powers of 10 are vey easy. Let's look at some of these.

[H+]

pH calculation

pH

10-1

pH = -log[H+] = - log 10-1 = - -1 =

1

10-2

pH = -log[H+] = - log 10-2 = --2 =

2

10-3

pH = -log [H+] = -log 10-3 = --3 =

3

10-4

pH = -log [H+] = -log 10-4 = --4 =

4

10-5

pH = -log [H+] = -log10-5 = --5 =

5

10-6

pH = -log [H+] = -log10-6= --6 =

6

10-7

pH = -log [H+] = -log10-7 = --7 =

7

And so on..

Making a simplified chart.

[H+]

pH

0.1 = 10-1

1

0.01 = 10-2

2

0.001 = 10-3

3

0.0001 = 10-4

4

0.00001 = 10-5

5

0.000001 = 10-6

6

0.0000001 = 10-7

7

0.00000001 = 10-8

8

0.000000001 = 10-9

9

0.0000000001 = 10-10

10

0.00000000001 = 10-11

11

0.000000000001 = 10-12

12

0.0000000000001 = 10-13

13

0.00000000000001 = 10-14

14

This means that a pH of 3 has a [H+] ten times greater than a pH of 4.  A pH of 5 has 100 times as many hydrogen ions as a pH of 7.  It also means that pH stand for the hydrogen ions concentration's power of 10.

If the hydrogen concentration is not a power of ten, then a calculator comes in handy but we can still make a pretty good guess.  Be certain to convert it to a number in scientific notation if it isn't one already when you see see it.  By having a number in scientific notation, you can immediately interpret the power of 10, an approximate pH.

[H+] = 0.0000576 = 5.76 x 10-5M
If you realize that 10-4 > 5.76 x 10-5 > 10-5

And you know that the pH for a [H+] = 10-4 M = 4 and the pH for a [H+ ] = 10 -5 M = 5, we can reason that he pH of a [H+] = 5.76 x 10-5 must be between 4 and 5.  

Actually calculating it...
pH = - log [5.76 x 10-5] = - log 5.76 + - log10-5 = - log 5.76 +--5 = -0.76 + 5 = 4.76
(You can use a calculator or a log table to find the log of non-power of tens.)

Using a calculator to find the pH: 
Recognize that there are many different types of calculators.  If you have a question as to how to use your calculator, consult your calculator's manual.  Or ask your instructor for help.

Given [H+] (or [OH-]) to find pH (or pOH)
TI-83 Graphing calculators TI - 30 Series, Casio 260 Series
1.  Use (-) key 1.  Input [H+] 
2, Touch log key 2.  Depress log key
3.  Input [H+] 3.  Change sign (-)

To do just the opposite, given the pH to find the [H+], if it is a whole number pH, it is another very easy problem.  pH = 4 means the [H+]= 10-4M for instance.  Remember p stands for the power.  Just put a negative sign in front of the exponent.

[H+] = 10-pH

Given pH (or pOH) to find [H+] (or [OH-])
TI-83 Graphing calculators TI - 30 Series, Casio 260 Series
1.  Touch 2nd 10x Key 1.  Input pH 
2, Change sign (-) 2.  Change sign (-)
3.  Input pH 3. Touch Inv log (or 10x) key  

pOH

p_ is just a short hand way of describing large concentration differences that exists for many other particles.  pAg describes the concentration of silver ions.  pCl describes the concentration of Cl ions.  pOH descries the concentration of hydroxide ions.  pOH is calculated in exactly the same way that pH is calculated.  

pOH = - log [OH-]

Meaning that...Making a simplified chart....

[OH-]

pOH

0.1 = 10-1

1

0.01 = 10-2

2

0.001 = 10-3

3

0.0001 = 10-4

4

0.00001 = 10-5

5

0.000001 = 10-6

6

0.0000001 = 10-7

7

0.00000001 = 10-8

8

0.000000001 = 10-9

9

0.0000000001 = 10-10

10

0.00000000001 = 10-11

11

0.000000000001 = 10-12

12

0.0000000000001 = 10-13

13

0.00000000000001 = 10-14

14

To find the pOH of a solutions that does not have a [OH-1] that is a power of 10, you can use a calculator and do the following.  

[OH-] = 0.00000000845 M     Convert this first to a number in scientific notation.

[OH-] = 8.45 x 10 -9 M        (immediately you can see that the pOH should be close to 8 or 9)

pOH =  - log (8.45 x 10 -9) = --8.07 = 8.07

See the calculator notes to see how you might use your calculator to solve pOH problems.  

To do just the opposite, given the pOH, to find the [OH-].... as before...

[OH-] = 10-pOH

 

 
D.C. Everest Senior High
6500 Alderson Street
Weston, WI 54476

Bill Heeren, Teacher
November 16, 2013

Phone (715) 359-6561
Extension 4204
Fax (715) 355-7220