Calculating pH
Sörenson defined pH as the negative logarithm of the hydrogen ion concentration.
pH = - log [H+]
Remember that sometimes H3O+ is written, so
pH = - log [H3O+]
means the same thing.
So let's try a simple problem: The [H+] in a solution is measured to be 0.010 M. What is the pH?
The solution is pretty straightforward. Plug the [H+] into the pH definition:
pH = - log 0.010
An alternate way to write this is:
pH = - log 10¯2
Since the log of 10¯2 is -2, we have:
pH = - (- 2)
Which, of course, is 2.
Another sample problem: Calculate the pH of a solution in which the [H3O+] is 1.20 x 10¯3 M.
For the solution, we have:
pH = - log 1.20 x 10¯3
This problem can be done very easily using your calculator. So you enter 1.20 x 10¯3 into the calculator, press the "log" button (NOT "ln") and then the sign change button (usually labeled with a "+/-").
The answer is: 2.921.
Sörenson also just mentions the reverse direction. That is, suppose you know the pH and you want to get to the hydrogen ion concentration ([H+])?
Here is the equation for that:
[H+] = 10¯pH
That's right, ten to the minus pH gets you back to the [H+] (called the hydrogen ion concentration).
This is actually pretty easy to do with the calculator. Here's the sample problem: calculate the [H+] from a pH of 2.45.
The calculator technique depends on which type of button you have. Let's assume you have the standard key. It's labed EITHER xy or yx.
1) Enter the number "10" into the calculator.
2) Press the xy (or the other, depending on what you have)
3) Enter 2.45 and make it negative.
4) Press the equals button and the calculator will do its thing.
Some people have a calculator with a key labeled "10x." In that case, enter the 2.45, make it negative, then press the "10x" key. An answer appears!! Just remember to round it to the proper number of significant figures and you're on your way.