Half equivalence point

We can just sketch approximate titration curves of pH vs. percent of titration, since we do not have the concentration of the acid or the base, or the volume of solution being titrated. We can, however, precisely determine the pH at the half-equivalence point [mid-way between untitrated and completely titrated for a weak acid (or base)] this is equal to the pof the weak acid (or pOH = pATb of the weak base). Further, if we assume all solutions are 1.00 M, we can determine the pH at each equivalence point. For a weak base, the pH at the equivalence point equals -log >/0.50(ATa). For a weak acid, the pH at the... 

For each of the titrations, the pH at the half-equivalence point equals the pKt of the acid. 

L (a) The two curves cross the point at which half of the total acetate is present as acetic acid and half is present as acetate ion. This is the half equivalence point in a titration, where pH = pK3 = 4.74. 

For the titration of a strong base with a weak acid, the equivalence point is reached when the pH is greater than 7. The half equivalence point is when half of the total amount of base needed to neutralize the acid has been added. It is at this point that the pH = pK of the weak acid. In acid-base titrations, a suitable acid-base indicator is used to detect the endpoint from the change of colour of the indicator used. An acid-base indicator is a weak acid or a weak base. The following table contains the names and the pH range of some commonly used acid-base indicators. 

Point A on the titration curve is half-way to the first equivalence point with 0.5 mol of base added per mole of phosphoric acid. If the pH at this point were between pH > 5 and pH < 9, die concentration of H3P04 and of H2P04 ion could be assumed to be equal. However, because the pH is approximately pH 3, the concentration of H3P04 at this point is less than that of the H2P04 ion by an amount equivalent to about twice the hydronium ion concentration. Thus, the correct expressions at the half-equivalence point for the equilibrium concentrations are... 

At point E on the titration curve, 2.5 of base per mole of phosphoric acid have been added. Again, it is erroneous to assume that the P04- ion concentration equals the HP04- ion concentration at this half-equivalence point because a significant fraction of the base added beyond the second equivalence point (D in Figure 2.4) has not reacted with the HP04- ion. Thus, the proper expression for the third dissociation constant for phosphoric acid is given by the relations... 

Obviously one could measure the pH of a known concentration of a weak acid and obtain a value of its hydronium ion activity, which would permit a direct evaluation of its dissociation constant. However, this would be a one-point evaluation and subject to greater errors than by titrating the acid halfway to the equivalence point. The latter approach uses a well-buffered region where the pH measurement represents the average of a large number of data points. Similar arguments can be made for the evaluation of solubility products and stability constants of complex ions. The appropriate expression for the evaluation of solubility products again is based on the half-equivalence point of the titration curve for the particular precipitation reaction [AgI(OH2)2h represents the titrant] ... 

In the use of potentiometry for the evaluation of stability constants for complex ions, the expressions can become extremely complicated if multiequilibria are present. For a simple one-to-one complex a direct potentiometric titration curve again provides die most satisfactory route to an accurate evaluation of the constant. The curve looks similar to that for an acid-base titration, and the appropriate point to pick is the half-equivalence point. If the complex is extremely stable, then die amount of free metal ion at this point on die dtration curve (ligand titrated with metal ion) is sufficiently low that it can be disregarded. If not, it must be handled in a way similar to the first point on the titration curve for phosphoric acid. Assuming that it is a stable complex, at the first half-equivalence point the concentration of complexed metal ion will be equivalent to that of the free ligand. The potential will give a direct measure of the free metal ion and allow the stability constant for the complex to be evaluated at the half-equivalence point ... 

From a practical standpoint it is often useful to have the observed potential in the medium of measurement for the condition of equal concentrations of the oxidized and reduced species of a half reaction. Such potentials are known as formal potentials, E°, rather than standard potentials, and are not purely thermodynamic quantities. The term formal potential comes from the tradition of having the supporting electrolyte at a one formal concentration. However, other stated solution conditions are also included in many listings. Thus the indicated potential is what one would expect at the half-equivalence point under actual titration conditions. In other words, activity corrections have not been made. Table 2.3 summarizes a number of formal potentials for commonly encountered half-reactions. 

From anon-linear least-squares fit to the data at two concentrations near 21 °C and 0.5m ionic strength, for the first reaction, pKa = 7.74(1), and for the dimerization reaction, Kd = 132(12) m. This singly-bridged dimer is much weaker than the doubly-bridged one in the (en)Pd11 complex above. The maximum concentration of dimer occurs at the half-equivalence point, 0.57 mM for a solution that is 5 mM in total Pd11. This weak dimerization does not affect the results with nucleic bases mentioned below [36],... 

This region of the titration shows clearly the buffering action of a mixture of a weak acid with its conjugate base. At the half-equivalence point V = VJ2, [CH3COOH]o = [CH3COO ]o, which corresponds to an equimolar buffer at this point pH - pK. On either side of this point the pH rises relatively slowly as the NaOH solution is added. 

A volume of 50.00 mL of a weak acid of unknown concentration is titrated with a 0.1000 M solution of NaOH. The equivalence point is reached after 39.30 mL of NaOH solution has been added. At the half-equivalence point (19.65 mL) the pH is 4.85. Calculate the original concentration of the acid and its ionization constant K. ... 

Compute the pH of the titration solution before any acid is added, when the titration is at the half-equivalence point, when the titration is at the equivalence point, and when the titration is 1.00 mL past the equivalence point. 

Notice the half equivalence point. This is probably more likely be tested by the MCAT than the equivalence point. The half equivalence point is the point where exactly one half of the acid has been neutralized, by the base. In other words, the concentration of the acid is equal to the concentration of its conjugate base. Notice that the half equivalence point occurs at the midpoint of the section of the graph that most represents a horizontal line. This is the spot where we could add the largest amount of base or acid with the least amount of change in pH. Such a solution is considered to be buffered. The half equivalence point shows the point in the titration where the solution is the most well buffered. 

Notice also that, at the half equivalence point, the pH of the solution is equal to the pffs of the acid. This is predicted by the Henderson-Hasselbalch equation ... 

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. 

Titrations of polyprotic acids will have more than one equivalence point and more than one half equivalence point. For the MCAT, assume that the first proton completely dissociates before the second proton begins to dissociate. (This assumption is only acceptable if the second proton is a much weaker add than the first, which is usually the case.) Thus we have a titration curve like the one shown below. 

C is correct This is the definition of the half equivalence point. 

Make a rough sketch of the titration curve expected for the titration of a weak monoprotic acid with a strong base. What determines the pH of the solution at the following points (a) No base added (b) half-equivalence point (c) equivalence point (d) excess base added. Compare your curve to Figure 19-4. 

Tanaka H, Tachibana T. Determination of acid/base dissociation constants based on a rapid detection of the half equivalence point by feedback-based flow ratiometry. Anal Sci 2004 Jun 20(6) 979-981. 

Sketch the titration curve of a weak acid versus a strong base like the one shown in Ligure 16.4. On your graph indicate the volume of base used at the equivalence point and also at the half-equivalence point, that is, the point at which half of the acid has been neutralized. Show how you can measure the pH of the solution at the half-equivalence point. Using Equation (16.4), explain how you can determine the pK, of the acid by this procedure. 

The titration curve would look very much like Figure 16.5 of the text, except the 7-axis would be pOH and the x-axis would be volume of strong acid added. The pACb value can be determined at the half-equivalence point of the titration (half the volume of added acid needed to reach the equivalence point). At this point in the titration, the concentrations of the buffer components, [B] and [BH ], are equal, and hence pOH = pATb. 

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