Bases Henderson-Hasselbalch

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. 

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. 

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. 

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. 

What about amine bases In what form do they exist at the physiological pH inside cells—as the amine (A- = RNH2), or as the ammonium ion (HA = RNH3+) Let s take a 0.0010 Vf solution of methylamine at pH = 7.3, for example. According to Table 24.1, the pKa of methvlammonium ion is 10.64, so from the Henderson-Hasselbalch equation, we have... 

The values of [HA] and [A ] in this expression are the equilibrium concentrations of acid and base in the solution, not the concentrations added initially. However, a weak acid HA typically loses only a tiny fraction of its protons, and so [HA] is negligibly different from the concentration of the acid used to prepare the buffer, [HA]initia. Likewise, only a tiny fraction of the weakly basic anions A- accept protons, and so [A-] is negligibly different from the initial concentration of the base used to prepare the buffer. With the approximations A ] [base]initia and [HA] [acid]initia, we obtain the Henderson-Hasselbalch equation ... 

A note on good practice Keep in mind the approximations required for the use of the Henderson-Hasselbalch equation (that the concentrations of both the weak acid and its conjugate base are much greater than the hydronium ion concentration). Because the equation uses molar concentration instead of activities, it also ignores the interactions between ions. 

In practice, the Henderson-Hasselbalch equation is used to make rapid estimates of the pH of a mixed solution intended to be used as a buffer, and then the pH is adjusted to the precise value required by adding more acid or base and monitoring the solution with a pH meter. 

Step 5 Use an equilibrium table to find the H.O concentration in a weak acid or the OH concentration in a weak base. Alternatively, if the concentrations of conjugate acid and base calculated in step 4 are both large relative to the concentration of hydronium ions, use them in the expression for /<, or the Henderson—Hasselbalch equation to determine the pH. In each case, if the pH is less than 6 or greater than 8, assume that the autoprotolysis of water does not significantly affect the pH. If necessary, convert between Ka and Kh by using Kw = KA X Kb. 

Heisenberg uncertainty principle If the location of a particle is known to within an uncertainty Ax, then the linear momentum parallel to the x-axis can he known only to within an uncertainty Ap, where ApAx > till. Henderson-Hasselbalch equation An approximate equation for estimating the pH of a solution containing a conjugate acid and base. See also Section 11.2. Henry s constant The constant kH that appears in Henry s law. 

The last part of Eq. (1) is derived from the pH dependence of permeability, given a pH gradient between the two sides of the intestinal barrier, based on the well known Henderson-Hasselbalch equation. Direct measurement of in situ intestinal perfusion absorption rates confirmed this pH dependence [14]. 

Figure 3.2(a) shows a plot of log S versus pH for naproxen, based on re-analysis (unpublished) of the shake-flask [49, 77] and microtiter plate [20] data reported in the literature. The dashed curves in Fig. 3.2 were calculated with the simple Henderson-Hasselbalch equations. For pH pKa, the function reduces to the horizontal line log S = log Sq. For pH pXi, log S is a straight line as a function of pH, exhibiting a slope of 1 (and an intercept of log So-pKj). Where the slope is 0.5, the pH equals to the pKj. 

Fig. 3.2 Solubility profiles log S-pH. The dashed curves, representing uncharged precipitate in equilibrium with solution of the drugs, were calculated by Henderson-Hasselbalch equations. The dotted horizontal lines are estimates of the solubility of the charged form of the drugs, using either actual data (naproxen) or estimates based on the sdiff 3-4 approximation (atenolol and...

Fig. 3.3 Solubility profiles of sparingly soluble drugs, based on data taken from Avdeef et al. [20]. The solutions consisted of robotically adjusted universal buffers, based on a mixture of Good buffers (see text), and contained 0.2 M KCl. The dashed lines were calculated by the Henderson-Hasselbalch equation and, as can be seen, did not accurately describe the solubility profiles. The solid curves were...

Listed after the reactions are the corresponding equilibrium quotients. The law of mass action sets the concentration relations of the reactants and products in a reversible chemical reaction. The negative log (logarithm, base 10) of the quotients in Eqs. (3.1)—(3.4) yields the familiar Henderson-Hasselbalch equations, where p represents the operator -log ... 

The case of a buffer consisting of a weak base and its acidic form (for example, NH3 and NH4) is treated in an analogous way. Equations of the type of (1.4.26) are sometimes called the Henderson-Hasselbalch equations. 

Dissociation of the neutral acid in water necessitates modifications for air-sea exchange in the model, which is based on Henry s law. Other possible pathways, e.g. sea spray, are neglected. Henry s law is restricted to concentrations of physically solved, non dissociated substances. Since only the non-dissociated acid is volatile, it is important to correct the air-water partition coefficient as to reflect the relative proportions of volatile and non-volatile components. The corrected parameter is the effective Henry s law coefficient, which is related to the Henry s law coefficient as a function of pH (modified Henderson-Hasselbalch equation) ... 

There are two ways of dealing with the bicarbonate buffer system. The first uses the Henderson-Hasselbalch equation and an effective pKa of 6.1. If there is more base (HCO 3) than acid (C02), the pH will always be bigger than the pKa. This is usually the case physiologically (pH = 7.4 pKa = 6.1) so that on a molar basis there is always more than 10-fold more HCO 3 than C02. 

Words that can be used as topics in essays 5% rale buffer common ion effect equilibrium expression equivalence point Henderson-Hasselbalch equation heterogeneous equilibria homogeneous equilibria indicator ion product, P Ka Kb Kc Keq KP Ksp Kw law of mass action Le Chatelier s principle limiting reactant method of successive approximation net ionic equation percent dissociation pH P Ka P Kb pOH reaction quotient, Q reciprocal rule rule of multiple equilibria solubility spectator ions strong acid strong base van t Hoff equation weak acid weak base... 

Consider how a weak electrolyte is distributed across the gastric mucosa between plasma (pH 7.4) and gastric fluid (pH 1.0). In each compartment, the Henderson-Hasselbalch equation gives the ratio of acid-base concentrations. The negative logarithm of the acid dissociation constant is designated here by the symbol pAa rather than the more precisely correct pK1. 

Buffers are solutions that resist a change in pH when we add an acid or base. A buffer contains both a weak acid (HA) and its conjugate base (A-). The acid part will neutralize any base added and the base part of the buffer will neutralize any acid added to the solution. We may calculate the hydronium ion concentration of a buffer by rearranging the Ka expression to yield the Henderson-Hasselbalch equation, which we can use to calculate the pH of a buffer ... 

The common-ion effect is an application of Le Chatelicr s principle to equilibrium systems of slightly soluble salts. A buffer is a solution that resists a change in pH if we add an acid or base. We can calculate the pH of a buffer using the Henderson-Hasselbalch equation. We use titrations to determine the concentration of an acid or base solution. We can represent solubility equilibria by the solubility product constant expression, Ksp. We can use the concepts associated with weak acids and bases to calculate the pH at any point during a titration. 

Thus, for a weak acid with a given Ka (or pKJ and a given ratio of conjugate base concentration to acid concentration, the pH may be calculated. Or, given the desired pH and IQ (pKa), the ratio of salt concentration to acid concentration can be calculated and the buffer subsequently prepared. Equations (5.26) to (5.30) are each a form of the Henderson-Hasselbalch equation for dealing with buffer solutions. 

The Henderson-Hasselbalch equation is an equation expressing the relationship between pH, pK l, and the log of the ratio of the concentrations of the base to its conjugate acid or an acid to its conjugate base. It is derived from the K l or Kb expression. See Equations (5.26) to (5.30) in the text. They are each a form of this equation. 

Using the Henderson-Hasselbalch equation, we can easily calculate the amount of ionized form of an acid or base present at a given pH, provided we know the pK,. 

Addition of an acid such as HCl to the buffer solution provides H" ", which combines with the acetate ion to give acetic acid. This has a twofold effect it reduces the amount of acetate ion present and, by so doing, also increases the amount of undissociated acetic acid. Provided the amount of acid added is small relative to the original concentration of base in the buffer, the alteration in base acid ratio in the Henderson-Hasselbalch equation is relatively small and has Mttle effect on the pH value. 

The amino acid histidine contains an imidazole ring. We have just seen that unsubstituted imidazole as a base has p/Ca 7.0. From the Henderson-Hasselbalch equation... 

The imidazole side-chain of histidine has a value of 6.0, making it a weaker base than the unsubstituted imidazole. This reflects the electron-withdrawing inductive effect of the amino group, or, more correctly the ammonium ion, since amino acids at pH values around neutrality exist as doubly charged zwitterionic forms (see Box 4.7). Using the Henderson-Hasselbalch equation, this translates to approximately 9% ionization of the heterocyclic side-chain of histidine at pH 7 (see Box 4.7). In proteins, plCa values for histidine side-chains are estimated to be in range 6-7, so that the level of ionization will, therefore, be somewhere between 9 and 50%, depending upon the protein. 

The second pair of equations relate pH to pATa for weak acids and weak bases, though they are actually variants of the Henderson-Hasselbalch equation ... 

It follows that we use the Henderson-Hasselbalch equation when both acid and base concentrations are applicable. 

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