The Arrhenius definition of an

acid is a substance that when dissolved in water increases the concentration of hydrogen ion, H+(aq).

A base is a substance that when added to water increases the concentration of hydroxide ion, OH-(aq).

Fairly simple definitions in appearance, yet are they? The first word that might give us some pause is 'increase', a word we recognize and use frequently in our own vocabulary, but how is it being used here? What is being increased? The definition says hydrogen ion or H+(aq). If a substance which increases the [H+] in water is an acid, in order for us to use this definition we have to be able to understand increase, how much H+(aq) is found in water before adding any compounds. So before we go any further lets spend sometime talking about water, which will aid us in our understanding of acid/base character.

If we consider pure water, H2O, and measure its electrical conductivity, we see, to the limits of our measuring device, that it is a nonelectrolyte (there are no ions present). Electrical conductivity is a measure of the ability of a solution to carry an electrical current. Solutions of electrolytes conduct an electrical current by the migration of ions under the influence of an electrical field. A solution with a high concentration of ions will have a low resistance to current flow and will have a high conductivity. In fact if we had a device sensitive enough we do measure some conductance. What do we associate with causing the conductance? Ions. What ions? For water I'd like to suggest that the ions that cause the conductance are the following-

 

 

 

Notice I've written the equation, which is referred to as an autoionization equation, as an equilibrium. Doing so suggests that we can write an equilibrium expression for the equation:

Kw = [H+][OH-]

(Remember that water is pure liquid and as such does not appear in our equilibrium expression.) Well, I wonder what the magnitude of Kw is large? Small? Our experiment suggests small, very low concentration of ions, but how low. Well, the agreed upon value of Kw at 25 ºC is 1.0 x 10-14.

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

So how does that help us?

Now we can find the individual concentrations of [H+] and [OH-] in pure water. However much water dissociates will form equal amounts of [H+] and [OH-] so their concentration are equal, if they are equal and their product is 1.0 x 10-14, than

[H+] = [OH-] = 1.0 x 10-7 M

A solution with [H+] or [OH-] of 1.0 x 10-7 M is a neutral solution. An acid is a substance which when added to water increases the concentration of [H+], therefore, an acid must have a [H+] > 1.0 x 10-7 M. A base must have a concentration of [OH-] > 1.0 x 10-7 M.

Chemists usually talk about an acid as a substance whose [H+] is greater than 1.0 x 10-7 M and a base as a substance with [H+] < 1.0 x 10-7 M. Our ability to adjust the definition slightly is imbedded in our equilibrium expression.

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

This expression says that in any aqueous solution the product of [H+][OH-] must always be 1.0 x 10-14. If we know the [H+] or [OH-] we can calculate the other concentration. For example;

The [H+] in a particular solution is 1.0 x 10-4 M, calculate the [-OH] for this solution.

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

1.0 x 10-14 = (1.0 x 10-4)[OH-]

1.0 x 10-10 M = [OH-]

The [OH-] in a particular solution is 1.0 x 10-5 M, calculate the [H+] for this solution.

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

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

1.0 x 10-9 M = [H+]

This solution is basic, as [H+] is less than 1.0 x 10-7 M.

One might think, well who cares about H+ ion concentrations that are so small, certainly they can not be that important. So let me give you an example of how important these concentrations are. Blood in the human body has a H+ ion concentration that ranges from 4.47 x 10-8 M to 3.55 x 10-8 M. Individuals with H+ ion concentrations above 4.47 x 10-8 M experience disorientation, coma and ultimately death. Individuals with H+ ion concentrations below 3.55 x 10-8 M experience weak irregular breathing, muscle cramps and convulsions. Death occurs if the H+ ion concentration falls below 1.6 x 10-8 M or rises above 1.6 x 10-7 M.

 

For coffee it's 5; for tomatoes it's 4;
While household ammonia's 11 or more.
It's 7 for water, if in a pure state
But rainwater's 6, and seawater is 8.
It's basic at 10, quite acidic at 2,
And well above 7 when litmus is blue.
Some find it a puzzlement. Doubtless their fog
Has something to do with that negative log.

In 1909 a Danish biochemist, by the name of Sorenson, suggested reporting the concentration of H+ ion on a logarithmic scale, which he named the pH scale. Because of the magnitude of these concentrations it has become more convenient to give the acidity in terms of the pH, rather than as [H+]. pH is defined as;

pH = -log [H+]

The scale can be adjusted to include pH values at various [H+]. Now an acid can be defined as a substance which when added to water has a pH < 7.00 and base has a pH>7.00.

We can also talk about pOH which is defined as;

pOH = -log [OH-]

And finally that the sum of the pH and pOH must always equal 14. (A restatement of the equilibrium expression).

Sample exercises:

Calculate the pH and pOH of a solution with a [H+] = 3.68 x 10-8 M.

pH = -log [H+]

pH = –log[3.68 x 10-8]

find the log button on your calculator

pH = –(–7.43)

pH = 7.43

pH + pOH = 14

7.43 + pOH = 14

pOH = 14 – 7.43

pOH = 6.57

Calculate the [H+] and [OH-] of a solution with a pH = 4.22.

pH = -log [H+]

4.22 = –log[H+]

–4.22 = log[H+]

find the 10x button on your calculator

10-4.22 = 10log[H+]

6.03 x 10-5 M = [H+]

Kw = [H+][OH-]

1.0 x 10-14 = (6.03 x 10-5)[OH-]

1.0 x 10-14 /(6.03 x 10-5)= [OH-]

1.66 x 10-10 M = [OH-]