Table of Contents
- Introduction
- Designing a buffer
- Considerations in designing a buffer for a particular experiment
- Designing a Buffer; a worked example
- In general
Introduction
A buffer is a mixture of dissolved substances which tends to keep the pH of a solution constant when modest additions of acid and base are made to that solution.
Buffers work by reacting with any added acid or base to control the pH. For example, consider the action of a buffer composed of the weak base ammonia, NH3, and its conjugate acid, NH4+. When HCl (strong acid) is added to that buffer, the NH3 “soaks up” the acid’s proton to become NH4+. Because that proton is locked up in the ammonium ion, it does not serve to significantly increase the pH of the solution. When NaOH is added to the same buffer, the ammonium ion donates a proton to the base to become ammonia and water; hence the buffer also serves to neutralize the base.
As the above example shows, a buffer works by replacing a strong acid or base with a weak one. The strong acid’s proton is replaced by ammonium ion, a weak acid. The strong base OH– is replaced by the weak base ammonia. These replacements of strong acids and bases for weaker ones give buffers their extraordinary ability to moderate pH.
Buffers must be chosen for the appropriate pH range that they are called on to control. The pH range of a buffered solution is given by the Henderson-Hasselbalch equation. For the purpose of the derivation, we will imagine a buffer composed of an acid, HA, and its conjugate base, A–. We know that the dissociation constant pKa of the acid is given by this expression:
The equation can be rearranged as follows:
Taking the -log of this expression and rearranging the terms to make each one positive gives the Henderson-Hasselbalch equation:
The most convenient form of this Henderson-Hasselbalch equation, is:
The sample species HA and A- in expression 4 above are generalized to the terms acid and base, respectively. To use the equation, the concentration of the acidic buffer species is placed where the equation says “acid” while the concentration of the basic buffer species is placed where the equation calls for “base”. It is essential that you use the pKa of the acidic species and not the pKb of the basic species when working with basic buffers.
Taking a close look at Henderson-Hasselbalch equation, we notice that:
- When the acid and conjugate base are equal (where the acid is one half dissociated), the pH of the solution is the pKa of the weak acid. Substituting in the Henderson-Hasselbalch Equation:
pH = pKa + log 10(1)
Therefore pH = pKa + 0
Therefore pH = pKa
Equation (5)
One way of thinking about this is to say that the pKa of a weak acid solution is the pH where the acid and the conjugate base are at equal concentrations. - When more acid than conjugate base is present, the pH of the solution is less than the pKa, since the [A-]/[HA] result would yield a number less than 1, the logarithm of which is negative. The opposite is true; if more conjugate base is present: the resulting fraction would be greater than one, the log would be positive, and the pH would be greater than the pKa.
- There is a logarithmic relationship between the ratio of acid and conjugate base and the pH. Therefore, when 10 times more acid than conjugate base is present, the pH will be 1 unit lower than the pKa. If there were 100 times more conjugate base than acid, then the pH would be 2 units higher than the pKa. A buffer is therefore only effective when the ratio between the weak acid and conjugate base is less than tenfold; in other words, weak acids and their conjugate bases make good buffers only in the pH range within one unit of their pKa. This can be seen on the titration curve below; the flat region only subs about ±1 pH unit away from the pKa.
By using pKa values, we are able to express the strength of an acid (i.e. its tendency to dissociate) with reference to the pH scale. If Ka, the dissociation constant, is large, then pKa will have a low numerical value. A strong acid is one which is largely, perhaps completely, dissociated, and which therefore has a high Ka value. A weak acid is one that is only slightly dissociated in solution, and has a low Ka value. In other words, acids with the lowest pKa values are able to dissociate in solutions of low pH, i.e. even where the hydrogen ion concentration is high, while acids with higher pKa values dissociate only in solutions of high (more alkaline) pH.
| Acid | Ka | pKa | |
|---|---|---|---|
| Trichloroacetic | 2 x10-1 | =10 -0.7 | 0.7 |
| Dichloroacetic | 5 x10-2 | =10 -1.3 | 1.3 |
| Monochloroacetic | 1.6 x10-3 | =10 -2.8 | 2.8 |
| Formic | 2.1 x10-4 | =10 -3.7 | 3.7 |
| Benzoic | 7.8 x10-5 | =10 -4.1 | 4.1 |
| Acetic | 1.9 x10-5 | =10 -4.7 | 4.7 |
| H2CO3 | 2.9 x10-7 | =10 -6.5 | 6.5 |
| H2S | 5.8 x10-8 | =10 -7.2 | 7.2 |
| HCN | 1.3 x10-9 | =10 -8.9 | 8.9 |
The table above gives some examples of Ka and pKa values for a number of acids, which are listed in order of decreasing strength.
Designing a buffer
The desired buffer pH determines what compounds are used to make buffer. To make a buffer with acidic pH, (pH less than 7), the solution is made using a weak acid and a soluble salt of its anion. Typically the range for an acid buffer is centered around the value of the dissociation constant for the weak acid. The pH is adjusted by controlling the ratio of the moles of weak acid and the moles of soluble salt.
To make a buffer solution with acidic pH, (pH is more than 7), the solution is typically made using a weak base and a soluble salt of its cation.
In general, buffers have at least two major limitations:
- The natural pH range that matches the properties of the solute acid or base. This depends on the dissociation constant for the weak acid or base.
- The capacity of the buffer. This comes from the limited solubility of the acids, bases or their salts.
Considerations in designing a buffer for a particular experiment
- What is the desired pH of the buffer?
The desired buffer pH limits the possible choices for conjugate weak/acid base pair. As already discussed, a good buffer can be made for any pH within ±1 pH units of the weak acid’s pKa. The pH range of the buffer is
If for example the buffer needs a pH of 7.00, then the weak acid must have a pKa between 6.00 and 8.00. For a weak acid with pKa of 8.00, buffers with pH levels between 7.00 and 9.00 are possible.
For example, with a pH of 9.87 needed, which one of the following conjugate weak acid/weak base pairs can be used?
Answer: Given a target pH of 9.87, the conjugate weak acid’s pKa must be between 8.87 and 10.87. The pKa values for the possible conjugate weak acids are:
| Acid | pKa |
|---|---|
| CH3COOH | 4.757 |
| H2CO3 | 6.35 |
| H2CO3 | 6.35 |
| HCO3– | 10.33 |
| H3PO4 | 2.15 |
| H2PO4– | 7.20 |
| HPO42- | 12.38 |
The only conjugate weak acid in this list with a suitable pKa is HCO3–; thus the buffer must be one using HCO3– and CO32-
- Does the buffer need to be better in neutralizing against the addition of acid or base?
In cases where a conjugate acid/weak, then we need not worry about this question. But if the buffer is used in a system where it is necessary to protect the addition of acid or base, but not both; then, then we need to consider this question.
Basically, if you want to protect against the addition of strong acid, choose a buffer whose pKa is less than desired pH. (From Henderson-Hasselbalch equation, it can be seen that, the concentration of conjugate weak base is greater than the conjugate weak acid will have a pH > pKa).
If you want to protect against the addition of strong base, choose a buffer whose pKa is greater than desired pH.
Example: Using the same list of possible buffers in 1 above, what is the best choice if you need a buffer with a pH of 6.85 that must be able to protect against the addition of a strong base?
With the target pH of 6.85, the weak acid must have a pKa between 5.85 and 7.20. Both H2CO3 and H2PO42- meet this condition. To protect against the addition of strong base, we want the buffer to have more of its conjugate weak acid than its conjugate weak base. We need therefore, to use a weak acid whose pKa is greater than the desired pH. Of the two choices, only H2PO4– meets this condition. A H2PO4–/HPO42- buffer is therefore the best choice for this case.
- What is the desired buffer capacity?
Given that a buffer’s purpose is to maintain a solution’s pH against the addition of strong acid or strong base; a useful buffer therefore must be able to neutralize whatever quantities of acid or base that are reasonably expect to enter the system. The amount of strong acid or strong base that can be neutralized is called buffer’s capacity. Buffer’s capacity is determined by the concentration of the conjugate weak acid and conjugate weak base used to prepare the buffer. A higher concentration of these buffering reagents leads to an improved buffering capacity.
Designing a Buffer; a worked example
Let us imagine that we have isolated a new protein in our research, and have determined that it is most active and stable at pH 7.2. The task is to design a buffer to store and handle our protein in a 100 mM concentration. We are then required to make 1 L of this buffer, giving the molar amounts of each compound used in our preparation. How do we go about making this buffer?
Step 1 : Determine the correct buffering agent to use.
We know that for our buffer to be effective, the pKa of the weak acid has to be within 1 unit of the desired pH, and the closer the better. From the chart given earlier or the one below, H2PO4– seems to be the best choice.
| Buffer acid | pKa |
|---|---|
| H3PO4 | 1.27 |
| Glycine | 2.35 |
| Acetic acid | 4.76 |
| H2CO3 | 6.35 |
| H2PO4– | 6.82 |
| Tris(hydroxymethyl)aminomehane (Tris) | 8.08 |
| Glycine | 9.78 |
| HCO3– | 10.33 |
| HPO42- | 12.38 |
Since phosphate anions don’t come in bottles on the shelf, so what need to use is the phosphate salt, such as sodium phosphate (NaH2PO4), for the weak acid, and the disodium salt Na2HPO4 for the conjugate base. In solution, these would dissociate into H2PO4– and HPO42-, respectively.
Step 2: Determine the ratio of each of the salts to use in the buffer.
For this, we use the Henderson-Hasselbalch equation
Placing in the pKa for our weak acid and the desired pH of our solution in the equation:
7.2 = 6.82 + log [HPO42-]/[H2PO4–]
log [HPO42-]/[H2PO4–] = 0.38
Take the inverse log:
[HPO42-]/[H2PO4–] = 10 0.38
[HPO42-]/[H2PO4–] = 2.4
So we need 2.4 times as much conjugate base as acid.
Step 3 : Determine the exact molar amounts for the weak acid and conjugate base in the final solution.
We need 1l of a 100 mM buffer solution:
[HPO42-] + [H2PO4–] = 100 mM
We also know from above:
[HPO42-]/[H2PO4–] = 2.4
We need 2.4 times as much conjugate base as acid, hence
[HPO42-] = 2.4[H2PO4–]
Substituting to get rid of one unknown variable (two equations, two unknowns):
2.4[H2PO4–] + [H2PO4–] = 100 mM
3.4[H2PO4–] = 100 mM
[H2PO4–] = 29.4 mM
[HPO42-] = 100 mM – 29.4 mM
[HPO42-] = 70.6 mM
So for 1l, we would add 29.6 mmoles of monobasic sodium phosphate acid and 70.6 mmoles of dibasic sodium phosphate conjugate base, then fill that solution up with water to 1l. To get the weight of each salt in milligrams to add, multiply number of moles by the molecular weight. (See the Molarity section for detail)
In general
When the salts to be used in making a particular buffer are already known, below is the formula for determining the amount of salts required
Weight required = Molarity * Molecular weight * Required volume (L)
For example,
Making 100 ml of 0.1 M KH2PO4; How much of the powder is required?
0.1M * 136.09 * 0.1L = 1.309 g
Now you know!!!!