Titration Henderson-Hasselbalch

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.

Henderson-Hasselbalch Equation Titration Curves p/—Isoelectric Point The Bicarbonate Buffer Imbalance in Blood pH Acidosis and Alkalosis... 

To determine pH during this titration, we divide the region into five equal portions of 5.5 mL and use the Henderson-Hasselbalch equation. 

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. 

Figure I-I. Weak acids act as buffers in a pH range near their pK s. According to the Henderson-Hasselbalch equation, when the ratio of conjugate base to conjugate acid, [A ]/[HA] is plotted versus pH, a titration curve is generated that indicates a region of good buffering at pH = pK I pH unit.

The pKa value may be checked after addition of each 0.5 ml since the concentrations of acid and salt are known at each point on the titration curve. The slight increase in volume due to addition of the 0.1 M KOH may be ignored. For a base, the Henderson-Hasselbalch equation is written as given in Chapter 2, page 20. 

Application of the Henderson-Hasselbalch equation The dissociation constant of the carboxyl group of an amino acid is called K1f rather than Ka, because the molecule contains a second titrat-able group. The Henderson-Hasselbalch equation can be used to analyze the dissociation of the carboxyl group of alanine in the same way as described for acetic acid. 

Titration curve of alanine By applying the Henderson-Hasselbalch equation to each dissociable acidic group, it is possi ble to calculate the complete titration curve of a weak acid. Figure 1.11 shows the change in pH that occurs during the addition of base to the fully protonated form of alanine (I) to produce the completely deprotonated form (III). Note the following ... 

Equations 16-9 and 16-10 are analogous to the Henderson-Hasselbalch equation of acid-base buffers. Prior to the equivalence point, the redox titration is buffered to a potential near E+ = formal potential for Fc 1 Fe2+ by the presence of Fe 1 and Fe2+. After the equivalence point, the reaction is buffered to a potential near E+ = formal potential for Ce4+ Ce3+. [R. de Levie Redox Buffer Strength, J. Chem. Ed. 1999, 76, 574.]... 

Because HC1 is a strong acid and dissociates completely, adding 30 mL of 1.0 m HC1 adds 30 meq of H+ to the solution. These 30 meq titrate 30 meq of the conjugate base, so the [base]/[acid] ratio is 1. Solving the Henderson-Hasselbalch equation for pH ... 

Thus, 0.0075 mol — 0.005 mol = 0.0025 mol of NaOH is available to titrate the other group, and, using the Henderson-Hasselbalch equation,... 

FIGURE 2.4 Exact and Henderson-Hasselbalch pH as a function of base volume during titration of 100 mL of 0.01 M weak acid. Solid lines without symbols represent the exact pH symbols represent the Henderson-Hasselbalch pH. [Graph reconstructed from data by Po and Senozon, J. Chem. Ed, 78, 1499 (2001).]... 

The OH" in Equation 1.27 reacts completely with HA to convert it to A-. The data in Table 1.19 represent titration of 0.1 M HA with a pKa of 5. Nearly every point in between the starting and end points have HA and A- present so the Henderson-Hasselbalch equation can be used ... 

This reaction shows that Eh is related to the standard potential ( ° - 0.77 V) and the proportionality of Fe3+ to Fe2+ in the solution phase. A number of J5° values representing various reactions in soils are given in Tables 5.2 and 5.3. Note that Equation 5.16 is analogous to the Henderson-Hasselbalch equation. A plot of Eh versus (Fe3+/Fe3+ + Fe2+) would produce a sigmoidal line with midpoint ° (Fig. 5.2) (recall that the Henderson-Hasselbalch equation gives the pKa at the titration midpoint see Chapter 1). To the left of ° (midpoint in the jc axis E° = 0.77 V) the reduced species (e.g., Fe2+) predominates, whereas to the right of ° (midpoint in the x axis), the oxidized species (e.g., Fe3+) predominates. 

Using the Henderson-Hasselbalch equation, calculate the pAa value for each ionizable group titrated. 

Note that this expression is the reciprocal of the ratio for the titration of an acid. Substituting this ratio into the Henderson-Hasselbalch equation gives... 

Potentlometrlc titration has also been widely applied to polyelectrol des and proteins conductometric titration to a lesser extent. For colloids with a variety of different groups (proteins), application of the Henderson-Hasselbalch equation (3.6.52 or 531 or Its semi-emplrlcal variant [3.6.54] Is viable only when the pK s of the various groups are sufficiently far apart. 

In other words, if A" is 10% ionized (to HA-f-OH"), then the Henderson-Hasselbalch equation cannot be used to estimate the pH of a solution of HA that has been 99% titrated. 

An expression for instantaneous buffer capacity, jS, can be derived using calculus. Essentially, /S is the reciprocal of the slope of the titration curve at any point. Starting with the Henderson-Hasselbalch equation ... 

When constructing Table 1-3, we assumed that at the first equivalence point the a-carboxyl is completely ionized and that the /S-carboxyl is completely un-ionized. These assumptions, of course, are not entirely true the actual degree to which the a- and /S-carboxyls are ionized can be calculated using the Henderson-Hasselbalch equation. If we carry out the calculation, we find that the proportion of a-carboxyl that is still in the COOH form exactly equals the proportion of /3-carboxyl in the COO form. (At pH 2.98, we are just as far above the p/ a, for the a-carboxyl as we are below the for the /S-carboxyl.) Thus, to determine the net charge on the molecule, we are justified in tallying only the predominant ionic forms at each key point along the titration curve. 

Warning You cannot typically use the Henderson-Hasselbalch equation to find the pH at the equivalence point. Instead, you must use the Kh of the conjugate base. You can find the Kb from the K and the K.te. The concentration of the conjugate base at the equivalence point is equal to the number of moles of acid divided by the volume of add plus the volume of base used to titrate. Don t forget to consider the volume of base used to titrate. Unless the base has no volume, the concentration of the conjugate at the equivalence point will not be equal to the original concentration of the acid. The pH at the equivalence point involves much more calculation than the pH at the half equivalence point. For this reason, it is more likely that the MCAT will ask about the pH at the half equivalence point. 

Unusual features of the titration curves for charged groups, such as deviation from the expected Henderson-Hasselbalch pattern, indicating mutual interaction or the failure of a residue, e.g., histidine or tyrosine to titrate with the expected p/C, which can be taken to reflect local interactions. 

The titration behavior can be described by the Henderson-Hasselbalch equation... 

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