Henderson—Hasselbalch equation

This is one of the two equations you might have to deal with in introductory biochemistry. Like the other equation (the Michaelis-Menten equation), this one took two people to derive (wonder which one was 

WITHOUT BUFFERING, adding a little bit of a strong acid to water decreases 

TTie key to understanding the behavior of buffers is in the ratio [base]/[acid]. The ratio [base]/[acid] = 1.0 represents a special point (one that s easy to remember). When [base]/[acid] = 1.0, log ([base]/[acid]) = 0 and pH = pA a. If [base]/[acid] 1, then pH must be bigger than the pA a. If [base]/[acid] 1, the pH must be lower than the pA a. You may actually be able to get by without memorizing the equation if you realize the general relationships. 

The Henderson-Hasselbalch equation was developed independently by the Ameriean biological chemist L. J. Henderson and the Swedish physiologist K. A. Hasselbaleh, for relating the pH to the bicarbonate buffer system of the blood (see below). In its general form, the Henderson-Hasselbalch equation is a useful expression for buffer caleulations. It can be derived from the equilibrium constant expression for a dissociation reaction of the general weak acid (HA) in Equation (1.3)  

Taking logarithms of both sides of Equation (1.5) and multiplying throughout by — 1 gives 

This relationship is represented by the Henderson-Hasselbalch equation. 

Since a buffer is intended to give only a small change in pH with added H or OH , the best buffer for a given pH is the one that gives the smallest ehange. As may be 

Percent Unprotonated Species and Ratio ofUnprotonated Forms Relative to the Difference between the pH andpK  

For example when acetic acid (p/fa 4.76) is in solution at pH 4.76. The Henderson Hasselbalch equation can be written as follows  

From this relationship for acetic acid it is possible to determine the degree of ionisation of acetic acid at a given pH. 

Acetic acid is 50% ionised at pH 4.76. In the case of a weak acid it is the protonated form of the acid that is un-ionised and as the pH falls the acid becomes less ionised. 

For a base the Henderson-Hasselbalch equation is written as follows  

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This relationship is one form of the Henderson-Hasselbalch equation It is a useful relationship m chemistry and biochemistry One rarely needs to cal culate the pH of a solution—pH is more often mea sured than calculated It is much more common that one needs to know the degree of ionization of an acid at a particular pH and the Henderson-Hasselbalch equation gives that ratio... 

An alternative form of the Henderson-Hasselbalch equation for acetic acid is... 

Hemiketal (Section 17 8) A hemiacetal derived from a ketone Henderson-Hasselbalch equation (Section 19 4) An equa tion that relates degree of dissociation of an acid at a partic ular pH to its... 

As in Example 6.13, the Henderson-Hasselbalch equation provides a simple way to calculate the pH of a buffer and to determine the change in pH upon adding a strong acid or strong base. 

Substituting the new concentrations into the Henderson-Hasselbalch equation gives a pH of... 

Multiprotic weak acids can be used to prepare buffers at as many different pH s as there are acidic protons. For example, a diprotic weak acid can be used to prepare buffers at two pH s and a triprotic weak acid can be used to prepare three different buffers. The Henderson-Hasselbalch equation applies in each case. Thus, buffers of malonic acid (pKai = 2.85 and = 5.70) can be prepared for which... 

Although this treatment of buffers was based on acid-base chemistry, the idea of a buffer is general and can be extended to equilibria involving complexation or redox reactions. For example, the Nernst equation for a solution containing Fe + and Fe + is similar in form to the Henderson-Hasselbalch equation. 

Suppose you need to prepare a buffer with a pH of 9.36. Using the Henderson-Hasselbalch equation, you calculate the amounts of acetic acid and sodium acetate needed and prepare the buffer. When you measure the pH, however, you find that it is 9.25. If you have been careful in your calculations and measurements, what can account for the difference between the obtained and expected pHs In this section, we will examine an important limitation to our use of equilibrium constants and learn how this limitation can be corrected. 

Any solution containing comparable amounts of a weak acid, HA, and its conjugate weak base, A-, is a buffer. As we learned in Chapter 6, we can calculate the pH of a buffer using the Henderson-Hasselbalch equation. 

The dissociation constant is most accurately estimated from kinetic data when all of the data points are used in the evaluation. There are several ways to do this. The Henderson-Hasselbalch equation... 

This relationship is known as the Henderson-Hasselbalch equation. Thus, the pH of a solution can be calculated, provided and the concentrations of the weak acid HA and its conjugate base A are known. Note particularly that when [HA] = [A ], pH = pAl,. For example, if equal volumes of 0.1 MHAc and 0.1 M sodium acetate are mixed, then... 

The Henderson-Hasselbalch equation provides a general solution to the quantitative treatment of acid-base equilibria in biological systems. Table 2.4 gives the acid dissociation constants and values for some weak electrolytes of biochemical interest. 

If the pfC, value of a given acid and the pH of the medium are knowrn, the percentages of dissociated and undissociated forms can be calculated using what is called the Henderson-Hasselbalch equation. 

As an example of how to use the Henderson-Hasselbalch equation, let s find out what species are present in a 0.0010 M solution of acetic acid at pH = 7.3. According to Table 20.3, the pKa of acetic acid is 4.76. From the Henderson-Hasselbalch equation, we have... 

We saw in Section 20.3 that the extent of dissociation of a carboxylic acid HA in an aqueous solution buffered to a given pH can be calculated with the Henderson-Hasselbalch equation. Furthermore, we concluded that at the physiological... 

Amino Acids, the Henderson-Hasselbalch Equation, and Isoelectric Points... 

To apply the Henderson-Hasselbalch equation to an amino acid, let s find out what species are present in a 1.00 M solution of alanine at pH = 9.00. According to Table 26.1, protonated alanine [ NCHfCH CC H] has p/Cal =2.34, and neutral zwitteTionlc alanine [+ll3NCH(CH3)C02-] has pK52 = 9.69 ... 

Figure 26.1 A titration curve for alanine, plotted using the Henderson-Hasselbalch equation. Each of the two legs is plotted separately. At pH < 1, alanine is entirely protonated at pH = 2.34, alanine is a 50 50 mix of protonated and neutral forms at pH 6.01, alanine is entirely neutral at pH = 9.69, alanine is a 50 50 mix of neutral and deprotonated forms at pH > 11.5, alanine is entirely deprotonated.

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