# Acid – Base Chemistry

by James R. Barrante, Ph.D.

There have been a lot of articles and blogs online covering the so-called “acidification of the oceans.”  (See OAI, OAII on this website).  Much of the information found in many of these articles and blogs, while very well written, is scientifically incorrect.  The primary reason is a complete misunderstanding of acid-base physical chemistry.  So this post hopefully will address some of these errors.

There are a number of ways to define an acid and a base.  In this post we will use what is referred to as the Arrhenius definition.  An aqueous solution is acidic if (H+) > (OH) and basic (alkaline) if (OH) < (H+), where () refers to molar concentration.  There is a notion out there that these are the only two states available, and the system is “dipolar,” like electrical charge.  That is, if a system is less basic, it must be more acidic.  This is not the case, because there is a third state that is neither acidic nor basic and this is the neutral state, (H+) = (OH).

Because hydrogen ion and hydroxide ion concentration can vary over a wide range of values (many powers of ten), a logarithmic scale, known as pH and pOH, has been designed to make concentrations more manageable.  The definition of pH and pOH are:

pH  = – log aH+     and     pH  = – log aOH-,

where aH+ and aOH- are the activities (effective concentrations) of the ions, respectively.  For example, the assumption is made that if the pH of an alkaline solution drops, it is becoming more acidic.  The problem with this idea has to do with the neutral state.  You see, you can lower the pH of an alkaline solution simply by adding water, a neutral substance.  The solution is simply becoming less basic approaching neutrality.  To be acidic, it would have to cross the pH 7 boundary, and it will never do that, no matter how much water you add.  It is akin to asking what is the pH of a 10-8 M HCl solution?  I know you want to say 8.  The pH of an acid solution can never be greater than 7.  It’s a problem we give our students in Analytical Chemistry to figure out.

So, having said all this, it is clear that with a pH around 8, our oceans are alkaline and dropping the pH toward 7 doesn’t make them more acidic, it simply makes them less basic.  A solution that is not acidic in the first place cannot become more acidic.  And it is scientifically dishonest to suggest that it could.  The question now centers around what happens to an aqueous solution when CO2 gas is bubbled through it.  We know that CO2 gas reacts with water to form carbonic acid H2CO3.  But carbonic acid is a very weak acid and that is important.  (By the way, the term weak and strong, when referring to acids and bases, has nothing to do with concentration.)  The acid dissociates according to the equation (we will consider only the first dissociation at this point):

The double arrow here means that the reaction is reversible.  At some the concentrations of these substances will reach thermodynamic equilibrium, at which point

where () designates molar concentration and K1 is the apparent equilibrium constant.  A true thermodynamic equilibrium constant would require the use of activities (effective concentrations) of the substances rather than the concentrations themselves.  In this case we will take K1  = 4.45 x 10-7.  Obviously, the excess of hydrogen ion in solution makes the solution acidic.  But look at the equilibrium constant.  It is telling us that most of the dissolved carbon dioxide is H2CO3.  We know that at a temperature of 298.2K, when the pressure of CO2(g) is 400 ppm (0.0004 atm), the concentration of dissolved CO2 is about 1.35 x 10-5  M.  Using Eq (1), we can find that the concentrations of H+ and HCO3  are both equal to 2.47 x 10-6 M,  giving a pH = 5.61, which is mildly acidic.

Wouldn’t it be nice if nature was so simple.  Unfortunately, bicarbonate ion also is a weak acid.  That is, it dissociates according to the equation

where K2 is the second dissociation constant of carbonic acid equal to 4.69 x 10-11 .  From the size of K2 you can see that very little hydrogen ion is produced by the dissociation of bicarbonate.  In fact, the pH of a saturated solution of sodium bicarbonate can be found by the equation

pH  =  1/2 (pK1 + pK2)

where pK1 = – log K1  and pK2 = – log K2.

pH  =  1/2 (6.35 + 10.33)  =  8.34

considerably alkaline.  Of course, this explains why bicarbonate of soda is a good antacid.  Moreover, it turns out that the solution of sodium bicarbonate does not have to be saturated.  Since a solution of NaHCO3 is the first equivalence point in the titration of carbonic acid, any solution of  NaHCO3 in water will have a pH of 8.34.

So let’s see what would happen to ocean water if we added a little Na2CO3 to it.  Not too much, just enough to make it equal the carbonic acid concentration.  Combining the two equilibrium constant expressions gives

Since  (CO3-2)  =  (H2CO3) ,  (H+)2  =  K1K2  and pH  =  ½ (pK1  +  pK2)  =  8.34.  Adding a small amount of carbonate ion to the system drastically increases the pH to make the system alkaline.  You will find that at this point also, it is very difficult to change the pH of the solution.  The solution here is said to be “buffered.”  In fact, our oceans are gigantic buffered systems.  It is important to note that since we are using concentrations here, we should not expect to get very good answers.  This is because seawater has a high ionic strength and as the ionic strength goes up, the difference between activities and concentrations increases.  Either we use activities here or we correct equilibrium constants for salinity.

Of all the gases, CO2 gas is one of the most soluble.  But that being said, gases in general are not very soluble in water.  Even at the low temperature 280K, the solubility of CO2 in water at a pressure of 4000 ppm or 0.004 atm, is only about 2.4 x 10-4 M.  The point is that it is not enough to simply look at the production of hydrogen ions to decide on the acidity or alkalinity of a solution.  When the source of the hydrogen ions is a weak acid, the presence of other ions will drastically effect the pH of the solution.