What is pKa? Relationship with pH

The pK _a measures the “strength” of a Bronsted acid, that is, of a substance that donates an H+ ion (proton) to form a conjugate base. An H+ proton is a strong Lewis acid that attracts electron pairs very efficiently, so efficiently that it is almost always bound to an electron donor. A strong Bronsted acid is a compound that gives up its proton very easily. For its part, a weak Bronsted acid is a compound that gives up its proton with more difficulty. In an extreme case, a compound from which it is very, very difficult to remove a proton is not considered an acid at all.

When a compound donates a proton, it retains the pair of electrons it previously shared with that proton, thus becoming a conjugate base. From another point of view, a strong Bronsted acid easily donates a proton and becomes a weak Bronsted base. The Bronsted base does not easily form a bond with the proton and is not good at giving its electron pair to a proton. Therefore, it does so weakly.

Similarly, if a compound gives up a proton and becomes a strong base, the base will easily regain the proton. In fact, the strong base competes so much with the proton that the compound remains protonated. Here, the compound is still a Bronsted acid instead of ionizing to become the strong conjugate base, making it a weak Bronsted acid.

Thus, you must take into account that:

• A low pKa means that the proton does not hold steady.
• Sometimes the pKa can be so low that it is a negative number.
• A high pKa means that the proton is strongly held.

The Henderson–Hasselbalch equation

The Henderson-Hasselbalch equation was developed independently by the American biological chemist LJ Henderson and the Swedish physiologist KA Hasselbalch, to relate pH to the bicarbonate buffer system of the blood. In its general form, the Henderson-Hasselbalch equation is a useful expression for calculating caps. It can be derived from the expression of the equilibrium constant for a general weak acid (HA) dissociation reaction in the equation:

where K _a is the equilibrium constant at a given temperature. For a defined set of experimental conditions, this equilibrium constant is denoted K _a and is called the apparent dissociation constant. The higher the value of K _a , the greater the number of H+ ions released per mole of acid in the solution, and therefore the stronger the acid. K _a is therefore a measure of the strength of an acid. Rearranging the equation and solving for the concentration of hydrogen ions we obtain:

Since log [H+] = pH and log (Ka) = pK _a and by applying logarithms to the above equations we obtain:

either

Where:

[A ^– ] is the concentration of the conjugate base,

[HA] is the concentration of the (undissociated) acid,

pK _a is the negative logarithm of the K _{a value}

and K _a is the dissociation constant of the acid.

Discussion of pH and pKa values

The Henderson-Hasselbalch equation is often used to determine the ratio of conjugate base [A-] to conjugate acid [HA] that must be used to achieve a given pH value of a buffer. To do this, we need to know the pKa value of the conjugate acid that you are going to use. However, the above equation has additional information that we must understand.

While the concept of pK _a is explained above, the functional definition of pK _a is often misunderstood. The thing to remember from this topic is that when the pH equals the pKa of an acid, the concentration of the conjugate base and the conjugate acid are equal, which means there is a 50% ratio of conjugate base to a 50% ratio of 50% conjugate acid.

Thus, if we plug the concentrations of the conjugate base and the conjugate acid into the Henderson-Hasselbach equation (it doesn’t matter what the concentration is) and they are the same, their ratio will be 1:1, which means that the logarithm of this proportion is zero (0). Regardless of which acid (represented as a proton donor [H+]) is observed, the above relationship holds.

For example, since acetic acid has a pK a value _of approximately 4.7, when the pH equals that pKa, the ratio of acetate to acetic acid would be 1:1. For another acid, such as hydrofluoric (HF), which has a pKa value of about 4.0, when the pH equals 4.0, the ratio of fluoride ion to hydrofluoric acid would be 1:1.

Buffer solutions

Buffer solutions are aqueous solutions consisting of a mixture of a weak acid and its conjugate base or a weak base and its conjugate acid. An important property of buffer solutions is their ability to maintain a relatively constant pH value in response to the addition of a small amount of acid or base. Furthermore, the pH of the buffer solutions remains relatively stable even during dilution.

For this reason, buffers are used in a wide range of chemical applications, primarily as reagents to maintain a constant pH value. For example, in the production of dyes, in fermentation processes, as well as for adjusting the pH of food, cosmetics and medicines. The pH of the buffer depends on the pK _a of the acid (or the pK _b of the base) and the ratio of the concentrations of the acid (base) and its conjugate base (acid). This dependency is described by the Henderson-Hasselbalch equation presented above.

Sources

• Garritz, M. (2005). Acid-base balances .
• Pardo, J. and Matus, D. (2014). The use of the Henderson-Hasselbalch equation for the calculation of blood pH.
• Vásquez, E. and Rojas, G. (2016). pH : theory and 132 problems.