This module contains material which is fundamental to a study of Structural Biology at the introductory level. It is essential that you should have a thorough grasp of its contents, and that you should be able to apply the knowledge embodied in the contents. When you have mastered this topic, you will:
- know and be able to apply the Henderson-Hasselbalch equation;
- know how to prepare buffer solutions.
Buffer solutions are solutions which resist changes in pH upon addition of relatively small quantities of acids or bases. They therefore are used whenever a sensitive solute, such as a protein, has to be protected from changes in pH during various extraction and purification processes.
pH = -log[H3O+].
Buffer solutions consist of an acid and its conjugate base, normally in the form of its sodium or potassium salt. This will give a buffer whose buffering action will be manifested at pH values below 7. Alternately, certain buffers are ammonia derivatives, and the free base will be used in conjunction with its protonated, conjugate acid form.
For a weak monoprotic acid HA dissociating in water according to
The acid dissociation constant Ka is given by:
Taking logarithms and rearranging gives:
Bearing in mind the definition of pH, and defining pKa = -log Ka gives the Henderson-Hasselbalch equation:
The Henderson-Hasselbalch equation enables us to calculate the pH of a buffer solution, if we know the relative concentrations of the conjugate acid/base partners and the pKa of the conjugate acid. Note that when the two species are present at the same concentration, that is [A–] = [HA], the log term vanishes and pH = pKa. For practical purposes, a buffer solution is effective in the range of pH = pKa ± 1.
When selecting a buffer system, always bear in mind the possible side effects that the buffer ions could have on your solute. Note also that the pKa of acids is temperature dependent.
Some commonly used buffers:
|4.75 at 25°C
|9.14 at 20°C
|6.27 at 25°C
|6.4 at 25°C (pKa3)
|7.21 at 25°C (pKa2)
|8.30 at 20°C
|6.2 at 20°C
|7.2 at 20°C
The ionic strength of buffers
The ionic strength, I of a solution is defined as I = ½ Scizi2, where ci is the molar concentration of the ith ion, and zi its charge, the summation taking place over all ions in the solution.
It follows that if we know the pH of a buffer solution, the pKa of the conjugate acid, and the overall molarity of the buffering species, we can calculate the ionic strength of that buffer. The following example will make this clear.
From the Henderson-Hasselbalch equation, we can write
from which we get
Since the buffer is 0.2M in total acetate (that is acetate ion PLUS acetic acid), we have
The sodium ions, Na+ and the acetate ion, CH3COO–, are the only ions in the solution in significant concentrations (the others are H3O+ and OH–). Since , the ionic strength, I will be
Units of ionic strength are normally not mentioned.
Preparing Buffer Solutions
The reproducibility of your experimental results, by yourself and others, will depend on the accurate description of the protocols that you used. In particular, if you state that you used a 0.05 M phosphate buffer, pH 7.3, it important to know how this pH value was arrived at, and whether the stated concentration can be trusted… The sort of questions that might arise are:
- Did you assume the pH from calculations based on the Henderson-Hasselbalch equation?
- Did you get a recipe from someone, and trusted it?
- Did you actually measure the pH, and if you did
- was the pH meter calibrated close to the expected pH value of your buffer?
- did you take into account the variations of pH with temperature?
- did you measure the pH while stirring the solution?
- in short, did you use the pH meter correctly?
- Are your calculation correct – for example, if you made a citrate buffer by weighing out citric acid, did you check whether you used anhydrous citric acid (Mr= 192.1) or citric acid monohydrate (Mr= 210.1), and used the correct Mr in your calculations?
- always check your calculations;
- make sure you understand the chemistry behind so-called “recipes”;
- check the pH of your buffer at the temperature that will obtain when you use it.
In other words, if you will use the buffer in the cold room, check its pH at that temperature.
Preparation of a 0.050 M phosphate buffer, pH 7.1 at 25°
A pH of 7.1 is close to the second pKa (pka2= 7.2) of phosphoric acid. Hence the buffering ions will be H2PO4– (the conjugate acid) and HPO42- (the conjugate base). Either the sodium or potassium salts may be used, but be sure that you state which you used!
The ratio of the two phosphate salts may be obtained by rearranging the Henderson-Hasselbalch equation:
From this we get a molar ratio: , and we also know that
Solving for these concentrations, we get and .
So, in order to make the buffer, say, 1 litre, we need 0.022 moles disodium hydrogen phosphate and 0.028 moles sodium dihydrogen phosphate.
These two salts are normally hydrated:
Na2HPO4.7H2O, Mr = 269, and NaH2PO4.H2O, Mr = 138.
Weigh out 5.92 g (0.022 mol) Na2HPO4.7H2O and 3.8 g (0.022 mol) NaH2PO4.H2O and dissolve in about 950 ml distilled water. Equilibrate at 25°C, and then measure its pH at that temperature, having calibrated the pH meter at that temperature. The chances are that the pH will not be quite what you expected! Adjust the pH upwards (with 5 M NaOH) or downwards (with 5 M H3PO4) until correct. Decant into a 1 l volumetric flask, (washing the beaker with a squirt or two of distilled water), make up to the mark, mix well, and transfer to a blue top reagent bottle. Label the bottle with your name, date, and the contents: “0.050 M Na phophate buffer, pH 7.1 at 25°C“.
The above is not the best way to make buffers! In fact, the calculations are tedious and the whole procedure time consuming. Let us prepare the buffer in a different way:
Preparation of a 0.025 M Na phosphate buffer, pH 7.1 at 25°C
Previously prepare stock solutions of Na2HPO4.7H2O and NaH2PO4.H2O, at a concentration of 1.0 M. Dilute aliquots of these 40 times, to give solutions that are exactly 0.025 M, and equilibrate them to 25°C.
Now, take one of these solutions, and place in a beaker fitted with a magnetic stirrer. Immerse the pH-meter electrodes into the solution (the pH-meter is assumed to have been properly calibrated at 25°C). Gradually titrate this solution, while stirring, with the other solution, until the desired pH has been achieved. Allow the solution to come to rest and to equilibrate to the right temperature before making the final adjustments. Store and label as shown above.
Preparation of 0.01 M TRIS HCl buffer, pH 8.0 at 5°C.
Make up a stock 1.0 M solution of TRIS base. Pipette 10.0 ml of this solution into a 2 l beaker, and dilute to about 900 ml. Allow to equilibrate in the cold room to 5°C. while stirring. Ttitrate with (cold!) 2M HCl, until the pH (pH-meter calibrated at 5°C!) is 8.0. Allow the solution to “rest” for a while, and make any final adjustments as required. transfer to a volumetric flask, rinse the beaker, and make up to 1 l. Store and label as shown above.