The pH and pOH Scale

While it is great to understand and be able to predict why an acid is weak or strong, we also need to be able to quantify the acidity or basicity of a solution.

Since we expect a strong acid to produce far more H⁺ ions than an identical amount of weak acid scientists designed a scale centered on measuring the H⁺ concentration present in a solution. We would predict that a more acidic solution would have a greater concentration of H⁺ ions while a basic solution would have far less.

Instead of displaying the actual concentration of H⁺ ions in a solution, scientists came up with the pH scale since the small concentration of H⁺ ions in even profoundly acidic solutions makes it impractical to use the concentrations themselves. Here the p is a special type of scale and means the -log of whatever is listed. Here are a couple of examples:

[latexpage]
\[pH=-log[H^+]
\]
\[pOH=-log[OH^-]
\]
\[pKa=-logKa
\]
\[pKb=-logKb
\]

So if an acid produces an H⁺ concentration of 1×10^-3 M it would have a pH of 3 and if a base adjusted the H⁺ concentration of a solution to 1×10^-12 the solution would have a pH of 12. Here we can see that the lower the pH the more acidic the solution and the higher the pH the more basic the solution.

We can apply this same concept to the pOH which is nearly identical to pH except here we are focused on the hydroxide concentration. So a solution with an OH^– concentration of 1×10^-3 M would have a pOH of 3 and a solution with 1×10^-12 M hydroxide concentration a pOH of 12. We expect strong bases to produce more hydroxide so strong bases will have low pOH values while weak bases will have higher pOH values.

[latexpage]
\[pH = -log([H^+])\]
\[pOH = -log([OH^-])\]

Water Matters Too

Before we get ahead of ourselves we have to remember that these reactions are all taking place in water. This is important because water is an amphoteric species and is an integral part of the acid-base reactions taking place.

Under standard conditions (0 °C and 1 atm) pure water exists at a pH = 7 which we define as neutral. This means that water has an H⁺ concentration of 1×10^-7. If we also measured the OH^– concentration in solution it would be 1×10^-7 as well yielding a pOH of 7 too.

From this information, we can determine the water’s equilibrium constant (K_w). Since all K values are the products over the reactants and H₂O is omitted:

[latexpage]
\[K_w=[H^+][OH^-]\]
\[K_w=[1\times10^{-7}][1\times10^{-7}]\]
\[K_w=1\times10^{-14}\]

This means that our acidic solution from the previous section had an H⁺ concentration of 1×10^-3 and an OH^– concentration of 1×10^-11.

[Latexpage]
\[K_w=[H^+][OH^-]
\]
\[1\times10^{-14}=[1\times10^{-3}][x]
\]
\[[x]=\frac{10^{-14}}{10^{-3}}\]
\[[x]= 1\times10^{-11}\]

No matter what solution we are dealing with the concentration of the H⁺ and the OH^– will always be equal to 1×10^-14 with one caveat the temperature must be at 0 °C or 298 K. Concentration, pressure, or volume have absolutely no effect on this so while we might continue to add more and more H⁺ ions into a solution K_w will remain the same.

This also leads us to another important conclusion that the pH and pOH of a solution must always equal 14. If we take the Kw equilibrium equation and put it on the p-scale we can see why this is the case. While you don’t need to know this bit of math for the MCAT it is important to note that the log of multiplication results in addition as seen below.

[latexpage]
\[K_w=[H^+][OH^-]\]
\[10^{-14}=[H^+][OH^-]\]
\[14=pH + pOH\]

Litmus Paper

It’s great if we already know the exact concentration of hydroxide or hydrogen ions in solution, but we rarely do. Do you know the H⁺ concentration of the lemon in your fridge? I certainly don’t.

Nonetheless, we can quickly determine if the lemon juice is acidic or basic with a simple test. The test involves a special piece of paper called litmus paper that changes color depending on the solution it is in. There are actually two types of litmus paper that are defined by their color: red litmus paper and blue litmus paper.

Red litmus paper changes its color to blue in the presence of basic solutions while blue litmus paper changes its color from blue to red in the presence of acidic solutions. So if we juiced our lemon and dipped the red litmus paper into the juice nothing would happen. The paper would still be red however if we dipped the blue paper into the lemon juice the paper would turn red. From both tests, we would know that our lemon is acidic.

The exact opposite would occur if we dipped our paper into a basic solution. In this case, the blue litmus paper wouldn’t change color, but the red one would. Here it would turn blue indicating the presence of a base.