Buffering and Henderson-Hasselbalch equation

Definitions & Key takeaways

The Henderson-Hasselbalch equation is a mathematical expression that is used to predict how much of a given acid or base is required to produce a desired pH in a given solution. The equation is named after British chemists Louis Hodgkin and Frederick Gowland Hopkins, who developed it in 1898, and German chemist Wilhelm Hasselbalch, who published it in 1909. The Henderson-Hasselbalch equation can be expressed as follows:

pH = pKa + log [base]/[acid] The pH is the desired pH of the solution, pKa is the dissociation constant of the acid, [base] is the concentration of the base, and [acid] is the concentration of the acid.

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Every single moment, there are trillions of biochemical reactions occurring throughout the human body that are mediated by enzymes.
Enzymes are types of proteins, and they’re generally sensitive to even slight changes in the environment - in particular things like the hydrogen ion concentration.
For this reason, the blood pH which corresponds to the hydrogen ion concentration needs to stay in a very narrow range---between 7.37 and 7.42.
If the blood pH rises or falls by more than a few tenths of a unit, it can lead to death. Now, acids and bases are generated by cells all the time.
So, the body has a few mechanisms to deal with these molecules and keep blood pH within normal range. The first scientist who studied one of these mechanisms was Robert Pitts.
Pitts injected 150 mEq of hydrochloric acid HCl into his dog. He calculated this his dog’s body contained a total 11.4 liters of water, so separately, Pitts put 150mEq of hydrochloric acid HCl in a volume of 11.4 liters of water.
The dog’s blood pH dropped from 7.44 to 7.14, which is very low, but not fatal. In the water, the pH dropped from 7 to 1.84, and that would have killed the dog instantly.
Based on this, Pitts concluded that his dog had a buffer contained in its body fluids, and the dog concluded that he could no longer trust Pitts to take care of him.
Physiologic buffers shield the pH from rising or falling too quickly. The reason the body needs buffers is that acids - molecules that readily give up their hydrogen ion - are being generated by the body all the time.
So the body needs a way to handle the extra hydrogen ions that are released without having a major shift in the overall pH.
To accomplish this, buffers are usually a weak acid with its conjugate base form, or a weak base with its conjugate acid form.
The weak acid could be symbolized as HA, where A represents molecules like fluorine or acetate. And the fact that it’s weak means that it has a “weak” effect on pH, because it doesn’t fully dissociate in water.
For example, if we were to add 100 HA molecules in 1 ml of water, only a tiny fraction, let’s say 5 of the 100 HA molecules would dissociate or break down into hydrogen H+ and their conjugate base A-: 100 HA ⇄ 95 HA + 5 H+ + 5 A-.
They like to maintain this balance. So if we remove some hydrogen ions, HA will dissociate and release a hydrogen ion and A-, maintaining that equilibrium.
And if we add hydrogen ions, the A- will bind to a hydrogen ion to form HA. Since it maintains this equilibrium, we call it an equilibrium reaction, and HA ⇄ H+ + A-.
By definition, this equilibrium reaction can move forward or backward depending on the concentrations of the molecules, and this is known as the Le Chatelier’s principle.
So, let’s imagine you’ve got this tank of water, which at any one time has some hydrogen ions floating around as well as some hydroxide ions that are in equilibrium with the water.
Imagine that we add a strong base like sodium hydroxide NaOH to water. Since it’s a strong base, the sodium hydroxide would dissociate almost completely into sodium Na+ ions and hydroxide OH- ions, and the hydroxide ions would bind to any available hydrogen H+ ions, and this rapid loss of hydrogen increases the pH really fast.
Now, if there was a weak acid around, then as the hydrogen H+ ions are consumed, the weak acid would dissociate and more hydrogen H+ ions would enter the solution, preventing the pH from rising so quickly!
Now, weak bases can also «act as buffers. In water, weak bases grab some hydrogen H+ ions from the surrounding water H2O, giving its conjugate acid BH and leaving hydroxide OH- ions to jump off, and again, just like with the weak acid, this is in equilibrium according to their concentrations.
Now again taking the water tank example but this time if there’s a strong acid, like hydrogen chloride HCl, then it will initially dissociate into hydrogen H+ ions and chloride Cl- anions, and the hydrogen H+ will react with hydroxides OH- forming water H2O.
This will result in more hydrogen ions relative to hydroxide ions, which decreases the pH and makes it get acidic really fast!
When the buffer is around, more B- will turn into BH and replace OH- ions, preventing the pH from falling too quickly and staying relatively neutral.
Now, thinking back to the weak acid buffer, there’s a rate of the forward reaction, where HA dissociates into H+ and A- , and a rate of the reverse reaction, where H+ and A- join to form HA.
Equilibrium is reached when these two rates are exactly equal, and the concentrations of the reactants are stable. For every buffer, there’s an equilibrium constant K, which is the ratio of the concentration of H+ multiplied by the concentration of A- , divided by the concentration of HA.
which you’ll notice is essentially products over reactants. So if the value of K is high, that means that at equilibrium, more of the acid is dissociated and that means that there are more products, or hydrogen ions and that means that there’ll be a lower pH.
If we rearrange this equation, we can solve for the hydrogen concentration [H+]. We can then take the negative log10 of both sides, which is actually equal to: .
And, since the negative log of the concentration is equal to the pH, the equation becomes: Which is the Henderson-Hasselbalch equation we have all come to know and love.
This equation allows us to calculate the pH of a buffered solution by knowing the pK of the buffer, the concentration of the base form of the buffer ([A−]), and the concentration of the acid form of the buffer ([HA]).
Also, if [A−] equals [HA], then we get the log of 1 which equals 0. So that means that when [A−] equals [HA], the pH equals the pK of the buffer.
From that point, if we add more hydrogen H+ to the solution, then the [HA] goes up and we have the log of a fraction which is a negative number, so the pH goes down a bit, so it’s lower than the pK.
On the other hand, if we take away hydrogen H+ from the solution, then the [HA] goes down and we have the log of a number greater than 1 which is a positive number, so the pH goes up a bit, so it’s higher than the pK.
All right, as a quick recap, buffers are pairs of a weak acid and a conjugate base form, which releases hydrogen ions when the pH starts to rise, or a weak base and a conjugate acid form which binds hydrogen ions when the pH starts to drop, so both resist pH changes of body fluids.
The pH of the buffered solution can be calculated with the Henderson- Hasselbach equation: