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The pH Scale and pH Calculations

SECTION 14 - Acids and Bases

Water is an Amphoteric Substance

Amphoteric  =  it can act as either an acid or a base.

Besides H2O, ammonia (NH3) is also an amphoteric substance.  Let's take a look at the autoionization of water...

Autoionization of water

Water is capable of ionizing itself, as shown below:

ex:    H2O  +  H2O  ⇌  H3O+  +  OH-

Autoionization of Water
From above, we have:

2H2O (l)   ⇌   H3O+ (aq)   +   OH- (aq)

so,  the Dissociation Constant for Water is:
       Kw  =  [H3O+] [OH-]

or,  Kw  =  [H+] [OH-]  =  1.0 x 10-14  (at 25°C)

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In pure water, or a neutral solution at 25°C,

[H+]  =  [OH-]  =  1.0 x 10-7 M

➞  in an acidic solution,  [H+]  >  [OH-]
      but  Kw  =  1.0 x 10-14  still.

➞  in a basic solution,  [OH-]  >  [H+]
      but  Kw  =  1.0 x 10-14  still.

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ex:  Calculate the [H+] and [OH-] concentrations.

  a.  1.0 x 10-5 M OH-

    ➞  Kw  =  [H+] [OH-]  =  1.0 x 10-14

    ➞  Kw  =  [H+] (1.0 x 10-5)  =  1.0 x 10-14

    ➞  [H+]  =  1.0 x 10-8 M  ➞  [OH-]  >  [H+]
          so the solution is basic.

    
   b.  10.0 M OH-

    ➞  Kw  =  [H+] [OH-]  =  1.0 x 10-14

    ➞  Kw  =  (10.0) [OH-]  =  1.0 x 10-14

    ➞  [OH-]  =  1.0 x 10-15 M  ➞  [H+]  >>  [OH-]
          so the solution is very acidic.

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The pH Scale

The pH scale is a convenient way to represent a solution's acidity.  The pH equation is shown below, and the scale goes from 0.00 to 14.00.

The pH Equation and pH Scale

pH Equation and pH ScaleAs you can see in the image above, pH values less than 7.00 are acidic, while pH values above 7.00 are basic.  A pH value equal to 7.00 would be neutral.

ex:  Calculate the pH of the following solutions. 

  a.  1.0 x 10-3 M  H+

    ➞  pH  =  - log [H+]  =  - log (1.0 x 10-3)

    ➞  pH  =  3.00

 

  b.  1.0 x 10-5 M  H+

    ➞  pH  =  - log [H+]  =  - log (1.0 x 10-5)

    ➞  pH  =  5.00

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shortcut:  when you're asked to find the pH of a solution having a concentration of 1.0 x 10-z, the pH = "z"

ex:  1 x 10-9 M  H+  ➞  pH = 9.00
ex:  1.0 x 10-8 M  H+  ➞  pH = 8.00
ex:  2.3 x 10-7 M  H+  ➞  no shortcut

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The pOH Scale

If you know the equation for pH, then you can probably guess the pOH equation.  Below you can see how pH, pOH, and pKw are all related...

pOH Scale

ex Calculate the pH and pOH of a 2.6 x 10-12 M OH- solution.
_________
answer:

"2.6" is the base number, so we can't do the shortcut calculation.  Since we're given the [OH-], we should calculate the pOH first:

    ➞  pOH  =  - log [OH-]
          pOH  =  - log (2.6 x 10-12)
          pOH  =  11.58

Now, use the pOH value of 11.58 to solve for pH...

    ➞  pH  +  pOH  =  14.00
          pH  +  11.58  =  14.00
          pH  =  2.42

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ex:  The pH of blood is 7.41.  Find the pOH, [H+], and [OH-]

_________
answer:

It's easiest to solve for pOH first.  Not because they ask for it first in the question, but because it's so easy to solve.

Then we can solve for [H+], and [OH-], as shown in the image below.

pH Calculations

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Next up in SECTION 14 - Acids and Bases,

We'll focus on ICE Tables, and how to find the pH of both strong and weak acid solutions.