CHE 341 Lab 1 Lesson

Background Part 3: Working with Buffers and Presenting Results

Suggested Reading

• Lehninger 2.2-2.3

Temperature affects the pKa of a weak acid

In addition to the background from Lehninger, it is important to note that buffers are at their best when the pH is adjusted correctly at the temperature at which they will be used. For all weak acids, the pKa is function of temperature, some are more sensitive than others.² Table 1 shows the change in pKa with temperature for some buffers. What this means is that if you calculate the change in pKa with temperature, the pH of the buffer will change the same amount because changing the temperature will not change the ratio of the basic form to acid form. Pay attention to the sign on the number. For example, raising the temperature of HEPES by 1.0 °C lowers both the pKa and pH by 0.014.

Table 1. Common biological buffers and their properties.

 

Ionic strength affects the pKa of a weak acid

Buffers are at their best when the pH is adjusted at the working concentration. However, most researchers make up concentrated solutions to save time and space. The solutions are then diluted to the appropriate concentrations before use. For example, you may see a bottle labeled 20x TAE. This means that the solution is TAE buffer (TRIS, Acetate, EDTA) that must be diluted 20 to 1 before use. The concentrated stock solution was prepared such that the buffer will have the correct pH only after 20 fold dilution. The pH of the stock solution will be different because total ion concentration in a solution affects pKa.

The reason for this is that equilibria of ionic species deviate from ideal behavior. Compared to uncharged solutes, the behavior of ions in solution is modified by an interaction energy such that a term called activity (represented as a) replaces concentration in calculations. Activity a is defined as concentration c times the activity coefficient γ. Activity coefficients change with ionic strength, the concentration of ions in solution, according to Debye–Hückel theory. Examples are illustrated in Table 2. Behavior of a solute is ideal when the activity coefficient is 1. As both charge and concentration of an ionic solute increase, so does the deviation from ideal behavior.

Table 2. Activity Coefficients (γ) at Different Concentrations.

In many equilibria, the quotient of the activity coefficients is assumed to be approximately constant and thus concentration may be used in calculations. In contrast, activity has significant impact on acid-base ionization and cannot be ignored. Since the activity coefficient γ changes with ionic strength, the Ka (and pKa) will change with concentration even though the ratio of species appears to stay the same.

What all this means to the pH of a buffer is rather complicated. Some buffers will show a pH increase with dilution, whereas others will show a pH decrease. The zwitterionic buffers, such as HEPES, do not have as pronounced an effect compared to phosphoric acid or citric acid. An approximation of this behavior derived from Debye–Hückel theory is described by Equation 1.³

(Equation 1)

In this equation, z is the charge on the conjugate base, A is a temperature-dependent constant (e.g. A is 0.509 and 0.526 at 23 and 37 °C respectively), and I is the molar ionic strength of the entire solution. Ionic strength I is defined according to Equation 2 as one-half the sum of the concentration of each species c_i times its electrical charge z_i squared.

I = 0.5 Σ c_i z_i² (Equation 2)

Ionic strength is calculated from the concentrations of all ions present in a solution. Thus, it is one-half because we are including both cations and anions whose charges are always paired. Note that ionic strength includes all ions in solution, including acids, bases, and salts (e.g. NaCl). Equation 1 does not calculate activity explicitly. It is simplified to claculate pKa directly as a function of total ionic strength I and charge z of the conjugate base of interest.

Since we now see that pKa is dependent on both temperature and ionic strength of the solution, you should always make sure that you know the conditions of a reported pKa value before using it in calculations. For simplicity, most reported pKa values are extrapolated to infinite dilution based on a series of measurements at different concentrations. This is called the thermodynamic pKa.² Equation 1 only works with the thermodynamic pKa. Whenever you find differing values for pKa of the same compound in the literature, it is likely that one of these values is not the thermodynamic pKa. Using the pKa_(apparent) at a given ionic strength and temperature allows you to use concentrations rather than activities in buffer calculations.

In this lab, you will dilute a buffer to one tenth of its ionic strength. This will change the pKa and thus the pH. By calculating the the initial and diluted ionic strength using Equation 2, you will be able to calculate the amount of NaCl required to shift the pH of the diluted buffer back to that of the undiluted.

Good's Buffers

If you are unfamiliar with some of the buffers in Table 1, all of the ones with names that are acronyms (e.g. CHES, TRIS, etc.) are Good's buffers.⁴ Biologist Norman Good brought these and many other buffers to the attention of the research community for their important properties: they buffer between pH 6 and 8, are non-toxic to organisms, they do not permeate the interior of cells (thus altering internal pH), and are not metabolized by cells or organisms. Before Good's work, pH control in experiments with live cells always required numerous controls to verify that the buffer was not altering cellular metabolism and that the pH was stable.

Lecture Videos

How To Prepare a Buffer

We don't have to add both HA and A - to make a buffer. The easier way to do it is to titrate the HA with a strong base or the A^- with a strong acid. If we start with a weak acid, such as acetic acid, and we add a strong base, such as NaOH, we will quantitatively force the production of A^-:

HAc + NaOH → H₂O + Ac^- + Na⁺

This is not like a weak acid situation where we have to use the weak acid equation to figure out the extent of the reaction. Strong bases will always win the tug-of-war against a weak acid. For every molecule of NaOH that's put into the solution, one molecule of HAc will be converted to Ac^-.

Using the Henderson-Hasselbalch equation to determine how much weak acid and salt to add to make a buffer is appropriate if we don't have a pH meter available. Normally, one is available making a buffer of known pH and concentration much easier. Once you have the correct ratio of HA to A^- , it doesn't really matter how you arrived at that state.

By convention, a buffer concentration is the total concentration of both weak acid and conjugate base. To make a phosphate buffer with a concentration of 0.1 M and a pH of 6.0, rather than calculating the ratios of H₂PO₄^- and HPO₄^2- that should be added, just start out with an amount of H₂PO_4^- and add NaOH until the pH is 6.0. Then, by definition, this will give a buffer at the correct pH. The only trick is getting the concentration correct. In this example, if we want to end up with 100 ml of buffer, we need 0.01 mol of buffer (0.1 M × 0.1 L = 0.01 mol). Thus, we dissolve 0.01 moles of NaH₂PO₄ in about 60-80 ml of water, add NaOH until the pH is correct, and then add water until the volume is 100 mL. We then have the 0.1 M buffer that we need, and the pH is 6.0. The small dilution made after adjusting the pH is assumed to have a negligible effect on the final pH.