Acids and bases

For now we've been studying interactions between water molecules and other molecules with water. A whole set of phenomena take place in water due to the ability of polar molecules to dissociate, as well as the ability of water to self-dissociate. This explains many of the properties of water not fully represented simply by uncharged water molecules. In this lecture we will start analyzing the dissociation of molecules in water, particularly how acids and bases behave in aqueous solution.

We first refresh the definition of acids and bases of Bronsted and Lowry: An acid is a compound that can give up a proton. Similarly, a base can accept a proton. We say that the acid dissociates when it gives up the proton. The molecule that is 'left behind' after the proton leaves can recombine with a proton (i.e. the dissociation is reversible), and so it must be a base. It is the conjugate base of the acid.

A brief review of equilibrium will be helpful also. Any reversible equation has a parameter associated with the concentrations of reactants and products called the equilibrium constant:

The equilibrium constant is directly proportional to the concentration (activities) of products and inversely proportional to the concentration (activities) of reactants. This constant is always the same for a particular reaction under the same conditions. Using it we can calculate concentrations of different species if other concentrations are given. As with every equilibrium, the free energy (DG) associated with the reaction is related to K_eq by:

These basic principles apply to every equilibrium: Acid/base reactions, the reaction between two small molecules, the binding of a small molecule to a protein receptor, and the binding between DNA and the protein complex that unwinds it for DNA replication. As we see from the equation, K_eq depends on T (DG^o is fixed).

Water self-dissociation

The most common acid - base reaction is simply the self-dissociation of water. Since water is polar and every one molecule is interacting with every other molecule, a water molecule may lose a hydrogen (proton) to other water molecule:

The H₃O⁺ molecule is called an hydronium ion, and it is basically an hydrated proton. Remeber that ionic species get stabilized by the solvation shell formed around them, which is good in terms of enthalpy. Although a proton on its own has no physical meaning whatsoever, we usually simplify things a bit, because the concentration of hydronium is equal to the hypothetical concentration of protons, and the concentration of water is constant:

In this reaction (or in the one above, actually), water is the acid, and water is also the base. The hydronium ion is the conjugate acid of the water acting as base, and the hydroxyl ion the conjugate base of the water acting as acid. Since this is an equilibrium, we can write out the expression for K_eq:

Now, [H₂O] is always the same in aqueous solution, and equal to 55.5 M (1 L of H₂O has 1000g / 18 g/mol moles, 55.5 moles). We define a new constant, K_w, as K_eq * 55.5, which is called the ion product of water, and holds true in any aqueous solution. Then:

K_eq for water is 1.8 x 10^-16. Then K_w is 1 x 10^-14. In pure water, the concentrations of protons and hydroxyl ions are the same, so we can calculate either one:

When we have pure water, we have a neutral solution. Therefore, a neutral solution means a concetration of protons (or hydroxyls) of 1 x 10^-7. This is an indication of the acid/base power of water. When the proton concentration goes below 1 x 10-7 we have a basic soultion, and when it goes above, an acidic solution.

Strong acids and bases

Now, what will happens if we add 1 mol of HCl (hydrochloric acid) to a liter of water? The reaction here would be:

Here the acid is HCl, and the conjugated base the Cl^- ion. Since HCl is an ionic compound, it will dissociate completely in water, so [H⁺] = [HCl] = 1 mol/L. The K_eq is huge for HCl and other so called mineral acids: HNO₃, HBr, H₂SO₄, etc. Now, we are doing all this in water, so the equilibrium of water is still mantained. We can calculate [OH^-] from Kw:

We can see clearly that the solution is acidic, and that the concentration of hydroxyl (the base) drops considerably. Water is the only source of hydroxyl,  and they are consumed by the protons from the dissociation of HCl. The same thing, but reversed, goes for strong bases, such as NaOH, KOH, etc. They liberate completely their hydroxyl ions in aqueous solution, consuming protons given up by water. Form all this, a couple of things:

a) In water, there cannot be a base stronger than OH^-, or an acid stronger than H⁺ (actually, H₃O⁺).

b) The conjugated base of a strong acid (Cl^- in this case) is a very weak base, and viceversa.

c) Working with [H⁺] concentrations to indicate acidity or basicity of a solution sucks - We have a huge variation, from 1 x 10^-7 to 1 (7 orders of magnitude!) just by making a 1 molar solution of HCl. We therefore use a logarithmic scale, the pH scale.

So, for neutral water, [H⁺] = 1 x 10^-7, then pH = 7. For 1 molar HCl, [H⁺] = 1, then pH = 0. As you probably know or figured out already, acidic solutions will have pH < 7, neutral solutions pH = 7, and basic solutions pH > 7.

Weak acids and bases

In biological systems, not considering our stomach, we are not so lucky as to have things that dissociate fully. Most of the biological acids and bases are part of amino acids (R-COOH and R-NH₂), and if you remember, even if these compounds are highly polar, they won't dissociate fully in water - They are weak acids and bases. That is, we have an equilibrium that depends on the concentrations of the different species in solution. If we disolve some acetic acid (CH₃COOH) in water, some of the protons liberated by it will react with water (acting here as a base) forming CH₃COO^-, but we will still have some considerable ammount of protonated acid (CH₃COOH):

For this case, the acetate ion (CH₃COO^-) is the conjugate base. The equilibrium constant can be written as:

Note that we used K_a instead of K_eq. This is to denote that we are talking about the acids dissociation equilibrium constant. Remember also that K_a will have the [H₂O] included, because it stays constant. If we now think of a general case, we can re-write this as follows:

Again, AH is the acid donating a proton to water, and A^- is its conjugate base. The equilibrium constant is basically telling us how easy it will be to pull a proton from a particular acid. If the molecule has low tendency to lose a proton, then [AH] will be large and [A^-] small. The equilibrium constant will be small. The stronger the acid (that is, the higher its tendency to lose a proton to water), the larger the K_a.

Now, why make things simple if we can make them complicated? Lets work out our neurons trying to figure out the reactions if we think of the reverse reaction, that is, the conjugated base pulling an electron from water:

Again, we have the the water concentration hanging around. Since [H₂O] = 55.5 M, we do as ee did with acids, and define the equilibrium constant for the base as:

For the the conjugated acid (AH), we had:

If we combine them we can see how both constants are related by the solvent:

Enough of this. As was the case for proton concentration [H⁺], the values of K_a and K_b are all over the place, spreding over several orders of magnitude. We do the same thing we did for acidity, and use the 'p' operator. We then express the dissociation constants of weak acids/bases as their pK value. It works the same way the pH scale works: For a weak acid, the smaller the pK_a, the stronger the acid (the more acidic its solutions).

Here are some dissociation constants and pK_a values for weak acids in water:
 

Acid	Ka	pKa
Acetic acid	1.74 x 10-5	4.76
Ammonium	5.62 x 10-10	9.25
Ascorbic acid	7.94 x 10-5 (1st)	4.10
Citric acid	7.24 x 10-4 (1st)	3.14
Glycine	4.47 x 10-3 (1st)	2.35

Titration and buffers

For strong acids and bases, the only equilibrium we have to worry about is the self-dissociation of water: Strong acids and bases dissociate fully in aqueous, and react between each other to form water and salts. For HCl and NaOH:

Combining both we get:

Both the conjugated acid (Na⁺) and conjugated base (Cl^-) are extremely weak, so they won't re-associate with water. This means that we only have to worry about K_w. Since the acid has a high tendency to give away a proton and the base is more than willing to to take it, we have no 'compromises' between them - Everything goes to water and salts.

In the titration of a strong acid with a strong base, the pH will be determined by the excess concentration of the acid while we are below the equivalency point (where we have the same number of equivalents of acid and base). The pH will be 7 at this point (here we have to remember that the only equilibrium is self-dissociation of water). Above that, we simply calculate [H⁺] and the pH from the [OH^-] and K_w. We can also calculate the pOH, and use:

A plot of pH versus equivalents of base in the titration of a strong acid will look like this:

Now, the story changes with a weak acid or a weak base: The reason is that now the conjugated base (or acid) will tend to react with water. In this case, we also have the equilibrium of the weak acid to worry about. For acetic acid:

Lets think of what happens when we start titrating a solution of CH₃COOH. First, hydroxide ions will pull protons from the acid to form water and acetate, CH₃COO^-. Oposite to what happened in strong acids, acetate is a base, so after the hydroxyde we aded reacted, it will react with water to try to re-establish all the equilibria. The concentration of [H⁺] or [OH^-] is not simply determined by the difference between the [H⁺] and [OH^-] concentrations and the K_w, but by K_a also.

Put in another way: not all the CH₃COOH dissociates in water, and we have a 'reserve' of non-dissociated CH₃COOH. As we add more hydroxyl, more CH₃COOH will dissociate, because we are removing free H⁺ form the system (they are reacting with OH^-). Additionally, the formed CH₃COO^- ions will capture H⁺ from water and make CH₃COOH. The net effect of all this is that for a relatively large range of OH^- additions, the pH of the solution will not change very dramatically, and will stay within a a range of 2 pH units from the pK_a of acetic acid:

These type of systems are called buffer systems, and they are crucial to all biological systems: A small change in the pH of blood or the cytosol can make an enzyme shut down completely, pretty much killing you. In blood, the normal pH is approximately 7.4. If the pH drops to 6.8 (which corresponds to a [H⁺] concentration change from 4 x 10^-8 to 1.6 x 10^-7, a 4-fold change in concentration), you would be pushing up the daysies. Fortunately, we have the bicarbonate buffer system working (among other buffers) for us:

The pK_a of the system is 3.77. Although we are far from the pH we have to maintain, [H₂CO₃] depends on two more equilibrium processes: One is the formation of carbonic acid from CO₂ dissolved in water (d) and H₂O, and the other is the equilibrium of gaseous CO₂ (in the lungs) to that of disolved CO₂ in blood:

When combined, these make a buffer system that keeps the pH of blood were it has to be. In the cell cytosol, we have the phospahte buffer:

The pK_a of this buffer system is 6.9, which maintains the cells in a pH range from 6.4 to 7.4. Next time we will talk more about buffer systems, how we can design a buffer system, how we calculate pHs of buffer systems in different conditions, and we will add numbers to all these concepts that will clarify them (or render them completely uncomprehensible...).

Prepared by Guillermo Moyna, 1999.