4.8×10−2 which begins to freeze at −9.84×10−2

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Issue 36, From the journal: Physical Chemistry Chemical Physics. Satya P. Joshi , a Timo T. Pekkanen , a Prasenjit Seal , a Raimo S. Timonen a and Arkke J. This article is Open Access. Please wait while we load your content Something went wrong. The titration curve has two equivalence points, one at In sketching the curve, we plot two points before the first equivalence point using the p K a1 of 3 for H 2 A. This is, of course, absurd; as we add NaOH the pH cannot decrease.

The results is a reasonable approximation of the exact titration curve. The difference between these two terms is important and deserves repeating. An equivalence point, which occurs when we react stoichiometrically equal amounts of the analyte and the titrant, is a theoretical not an experimental value.

Earlier we learned how to calculate the pH at the equivalence point for the titration of a strong acid with a strong base, and for the titration of a weak acid with a strong base.

We also learned how to sketch a titration curve with only a minimum of calculations. Can we also locate the equivalence point without performing any calculations. The answer, as you might guess, often is yes! The red arrows in Figure 9. An inflection point actually precedes its corresponding equivalence point by a small amount, with the error approaching 0.

Acta , 29 , —]. The principal limitation of an inflection point is that it must be present and easy to identify. For some titrations the inflection point is missing or difficult to find. An inflection point is visible, even if barely so, for acid dissociation constants larger than 10 —9 , but is missing when K a is 10 — An inflection point also may be missing or difficult to see if the analyte is a multiprotic weak acid or weak base with successive dissociation constants that are similar in magnitude.

During the titration the following two reactions occur. Malonic acid, on the other hand, has acid dissociation constants that differ by a factor of approximately The same holds true for mixtures of weak acids or mixtures of weak bases.

To detect separate inflection points when titrating a mixture of weak acids, their p K a values must differ by at least a factor of One interesting group of weak acids and weak bases are organic dyes. Because an organic dye has at least one highly colored conjugate acid—base species, its titration results in a change in both its pH and its color.

Unfortunately, we rarely know the exact pH at the equivalence point. As shown in Figure 9. The properties of several common acid—base indicators are listed in Table 9.

The explanation is simple. For some indicators only the weak acid or the weak base is colored. For other indicators both the weak acid and the weak base are colored, but one form is easier to see. For example, in Figure 9. Bromothymol blue, on the other hand, is an inappropriate indicator because its change in color begins well before the initial sharp rise in pH, and, as a result, spans a relatively large range of volumes.

The early change in color increases the probability of obtaining an inaccurate result, and the range of possible end point volumes increases the probability of obtaining imprecise results. Suggest a suitable indicator for the titration of You constructed a titration curve for this titration in Exercise 9.

The pH at the equivalence point is 5. Of the indicators in Table 9. The result is a plot of the entire titration curve, which we can use to locate the end point with a minimal error. A pH electrode is the obvious sensor for monitoring an acid—base titration and the result is a potentiometric titration curve. For example, Figure 9. This is also the least accurate method, particularly if the titration curve has a shallow slope at the equivalence point. See Chapter 11 for more details about pH electrodes.

Another method for locating the end point is to plot the first derivative of the titration curve, which gives its slope at each point along the x -axis. Examine Figure 9. Because the slope reaches its maximum value at the inflection point, the first derivative shows a spike at the equivalence point Figure 9. The second derivative of a titration curve can be more useful than the first derivative because the equivalence point intersects the volume axis. Using the first two points, the first derivative is.

For the second and third points, the first derivative is 0. Using the two points from our calculation of the first derivative, the second derivative is. Note that calculating the first derivative comes at the expense of losing one piece of information three points become two points , and calculating the second derivative comes at the expense of losing two pieces of information.

Derivative methods are particularly useful when titrating a sample that contains more than one analyte. If we rely on indicators to locate the end points, then we usually must complete separate titrations for each analyte so that we can see the change in color for each end point. If we record the titration curve, however, then a single titration is sufficient. The precision with which we can locate the end point also makes derivative methods attractive for an analyte that has a poorly defined normal titration curve.

Derivative methods work well only if we record sufficient data during the rapid increase in pH near the equivalence point. This usually is not a problem if we use an automatic titrator, such as the one seen earlier in Figure 9. Because the pH changes so rapidly near the equivalence point—a change of several pH units over a span of several drops of titrant is not unusual—a manual titration does not provide enough data for a useful derivative titration curve.

A manual titration does contain an abundance of data during the more gently rising portions of the titration curve before and after the equivalence point. Substituting these equations into the K a expression and rearranging leaves us with. This method of data analysis, which converts a portion of a titration curve into a straight-line, is a Gran plot. Values of K a determined by this method may have a substantial error if the effect of activity is ignored.

See Chapter 6. The reaction between an acid and a base is exothermic. Heat generated by the reaction is absorbed by the titrand, which increases its temperature. This part of a thermometric titration curve is called the titration branch. The temperature continues to rise with each addition of titrant until we reach the equivalence point. Ideally, the equivalence point is a distinct intersection of the titration branch and the excess titrant branch. The latter problem is minimized by using a titrant that is 10— times more concentrated than the analyte, although this results in a very small end point volume and a larger relative error.

If necessary, the end point is found by extrapolation. Although not a common method for monitoring an acid—base titration, a thermometric titration has one distinct advantage over the direct or indirect monitoring of pH.

As discussed earlier, the use of an indicator or the monitoring of pH is limited by the magnitude of the relevant equilibrium constants. Thus far we have assumed that the titrant and the titrand are aqueous solutions. You should recognize that K w is just specific form of K s when the solvent is water. The most important limitation imposed by K s is the change in pH during a titration.

Before the equivalence point, the pH is determined by the untitrated strong acid. However, the pH after adding Here, too, the solvent plays an important role. The strength of an acid or a base is a relative measure of how easy it is to transfer a proton from the acid to the solvent or from the solvent to the base. If we place acetic acid in a solvent that is a stronger base than water, such as ammonia, then the reaction.

All other things being equal, the strength of a weak acid increases if we place it in a solvent that is more basic than water, and the strength of a weak base increases if we place it in a solvent that is more acidic than water.

In some cases, however, the opposite effect is observed. For example, the p K b for NH 3 is 4. In contradiction to our expectations, NH 3 is a weaker base in the more acidic solvent. You should be aware, however, that a titration that is not feasible in water may be feasible in a different solvent.

The best way to appreciate the theoretical and the practical details discussed in this section is to carefully examine a typical acid—base titrimetric method. Although each method is unique, the following description of the determination of protein in bread provides an instructive example of a typical procedure. The description here is based on Method The amount of unreacted HCl is determined by a back titration using a standard strong base titrant.

Because different cereal proteins contain similar amounts of nitrogen—on average there are 5. Transfer a 2. Bring the solution to a boil. Continue boiling until the solution turns clear and then boil for at least an additional 30 minutes.

Add a few Zn granules to serve as boiling stones and 25 g of NaOH. Quickly connect the flask to a distillation apparatus and distill the NH 3 into a collecting flask that contains a known amount of standardized HCl.

The tip of the condenser must be placed below the surface of the strong acid. After the distillation is complete, titrate the excess strong acid with a standard solution of NaOH using methyl red as an indicator Figure 9. There are two reasons for not directly titrating the ammonium ion. Second, even if we can determine the end point with acceptable accuracy and precision, the solution also contains a substantial concentration of unreacted H 2 SO 4.

The presence of two acids that differ greatly in concentration makes for a difficult analysis. Ammonia is a volatile compound as evidenced by the strong smell of even dilute solutions. This volatility is a potential source of determinate error. Is this determinate error negative or positive? Any loss of NH 3 is loss of nitrogen and, therefore, a loss of protein. The result is a negative determinate error. Identify the steps in this procedure that minimize the determinate error from the possible loss of NH 3.

Although many quantitative applications of acid—base titrimetry have been replaced by other analytical methods, a few important applications continue to find use. In this section we review the general application of acid—base titrimetry to the analysis of inorganic and organic compounds, with an emphasis on applications in environmental and clinical analysis. First, however, we discuss the selection and standardization of acidic and basic titrants.

Solutions of these titrants usually are prepared by diluting a commercially available concentrated stock solution. The nominal concentrations of the concentrated stock solutions are The reaction in this case is. Any solution in contact with the atmosphere contains a small amount of CO 2 aq from the equilibrium. This is not a problem if the end point pH is less than 6. Under these conditions the presence of CO 2 does not affect the quantity of OH — used in the titration and is not a source of determinate error.

Under these conditions some OH — is consumed in neutralizing CO 2 , which results in a determinate error. We can avoid the determinate error if we use the same end point pH for both the standardization of NaOH and the analysis of our analyte, although this is not always practical.

Solid NaOH is always contaminated with carbonate due to its contact with the atmosphere, and we cannot use it to prepare a carbonate-free solution of NaOH. Briefly boiling the water expels CO 2 ; after it cools, the water is used to prepare carbonate-free solutions of NaOH. A solution of carbonate-free NaOH is relatively stable if we limit its contact with the atmosphere. Standard solutions of sodium hydroxide are not stored in glass bottles as NaOH reacts with glass to form silicate; instead, store such solutions in polyethylene bottles.

Acid—base titrimetry is a standard method for the quantitative analysis of many inorganic acids and bases. If an inorganic acid or base that is too weak to be analyzed by an aqueous acid—base titration, it may be possible to complete the analysis by adjusting the solvent or by an indirect analysis. We can analyze a neutral inorganic analyte if we can first convert it into an acid or a base. The NH 3 is removed by distillation and titrated with HCl.

Acid—base titrimetry continues to be listed as a standard method for the determination of alkalinity, acidity, and free CO 2 in waters and wastewaters.

Total alkalinity is determined by titrating to a fixed end point pH of 4. Reporting the total alkalinity as if CaCO 3 is the only source provides a means for comparing the acid-neutralizing capacities of different samples.

For a solution that contains OH — alkalinity only, the volume of strong acid needed to reach each of the two end points is identical Figure 9. The volume of strong acid to titrate OH — is the same whether we titrate to a pH of 8. Consequently, when we titrate a mixture of these two ions, the volume of strong acid needed to reach a pH of 4.

Problem 15 in the end-of-chapter problems asks you to explain why this is true. In addition, weak acid acidity may include a contribution from organic acids.

Acidity is determined by titrating with a standard solution of NaOH to a fixed pH of 3. Titrating to a pH of 3. Weak acid acidity is the difference between the total acidity and the strong acid acidity. An alternative approach for determining strong acid and weak acid acidity is to obtain a potentiometric titration curve and use a Gran plot to determine the two equivalence points. This approach has been used, for example, to determine the forms of acidity in atmospheric aerosols [Ferek, R.

The concentration of free CO 2 is determined by titrating with a standard solution of NaOH to the phenolphthalein end point, or to a pH of 8. This analysis essentially is the same as that for the determination of total acidity and is used only for water samples that do not contain strong acid acidity. Acid—base titrimetry continues to have a small, but important role for the analysis of organic compounds in pharmaceutical, biochemical, agricultur- al, and environmental laboratories.

Perhaps the most widely employed acid—base titration is the Kjeldahl analysis for organic nitrogen. Examples of analytes determined by a Kjeldahl analysis include caffeine and saccharin in pharmaceutical products, proteins in foods, and the analysis of nitrogen in fertilizers, sludges, and sediments. Because some aromatic heterocyclic compounds, such as pyridine, are difficult to oxidize, a catalyst is used to ensure a quantitative oxidation.

Nitrogen in other oxidation states, such as nitro and azo nitrogens, are oxidized to N 2 , which results in a negative determinate error. Including a reducing agent, such as salicylic acid, converts this nitrogen to a —3 oxidation state, eliminating this source of error. Several organic functional groups are weak acids or weak bases. Sodium hydroxide is the titrant of choice for aqueous solutions. Nonaqueous titrations often are carried out in a basic solvent, such as ethylenediamine, using tetrabutylammonium hydroxide, C 4 H 9 4 NOH, as the titrant.

Aliphatic and aromatic amines are weak bases that are titrated using HCl in aqueous solutions, or HClO 4 in glacial acetic acid. Other functional groups are analyzed indirectly following a reaction that produces or consumes an acid or base.

Typical examples are shown in Table 9. After reaction [1] is complete, water is added to covert any unreacted acetic anhydride to acetic acid reaction [2].

Many pharmaceutical compounds are weak acids or weak bases that are analyzed by an aqueous or a nonaqueous acid—base titration; examples include salicylic acid, phenobarbital, caffeine, and sulfanilamide. Amino acids and proteins are analyzed in glacial acetic acid using HClO 4 as the titrant.

Acta , , —; b Barbosa, J. Acta , , —]. If the titrand is polyprotic, then we must know to which equivalence point we are titrating. Because citric acid is a triprotic weak acid, we first must determine if the phenolphthalein end point corresponds to the first, second, or third equivalence point. Based on this ladder diagram, the first equivalence point is between a pH of 3. To reach the equivalence point, each mole of citric acid consumes three moles of NaOH; thus.

Because this is the amount of citric acid in a The complete titration curve is shown in Figure 9. Your company recently received a shipment of salicylic acid, C 7 H 6 O 3 , for use in the production of acetylsalicylic acid aspirin. Salicylic acid is a diprotic weak acid with p K a values of 2.

Because salicylic acid is a diprotic weak acid, we must first determine to which equivalence point it is being titrated. From Table 9. The titration, therefore, is to the first equivalence point for which the moles of NaOH equal the moles of salicylic acid; thus.

In an indirect analysis the analyte participates in one or more preliminary reactions, one of which produces or consumes acid or base. Despite the additional complexity, the calculations are straightforward. The acid is titrated to the bromothymol blue end point using a standard solution of NaOH. Calculate the purity of the preparation given that a 0. The bromothymol blue end point has a pH range of 6. Sulfuric acid is a diprotic acid, with a p K a2 of 1. The titration, therefore, proceeds to the second equivalence point and the titration reaction is.

Because all the sulfur in H 2 SO 4 comes from the sulfanilamide, we can use a conservation of mass to determine the amount of sulfanilamide in the sample. A conservation of mass on nitrogen requires that each mole of NO 2 produces one mole of HNO 3 ; thus, the mass of NO 2 in the sample is. For a back titration we must consider two acid—base reactions.

Again, the calculations are straightforward. The amount of protein in a sample of cheese is determined by a Kjeldahl analysis for nitrogen. After digesting a 0. The excess HCl is back titrated with 0. Because all the nitrogen in NH 3 comes from the sample of cheese, we use a conservation of mass to determine the grams of nitrogen in the sample. Limestone consists mainly of CaCO 3 , with traces of iron oxides and other metal oxides.

To determine the purity of a limestone, a 0. After heating to expel CO 2 , the excess HCl was titrated to the phenolphthalein end point, requiring Earlier we noted that we can use an acid—base titration to analyze a mixture of acids or bases by titrating to more than one equivalence point.

The concentration of each analyte is determined by accounting for its contribution to each equivalence point. Titrating a A second Identify the sources of alkalinity and their concentrations in milligrams per liter.

Because the volume of titrant to reach a pH of 4. Titrating to a pH of 8. Titrating to a pH of 4. This leaves The sample contains Of the two analytes, 2-methylanilinium is the stronger acid and is the first to react with the titrant.

Titrating to the bromocresol purple end point, therefore, provides information about the amount of 2-methylanilinium in the sample. Titrating from the bromocresol purple end point to the phenolphthalein end point, a total of The amount of 3-nitrophenol in the sample, therefore, is.

Example 9. We can extend this approach to other systems. As outlined in Table 9. Note that mixtures containing three or more these species are not possible.