TITRATION CURVES OF ACIDS AND BASES

Acid-base titrations are reactions by which we can determine the amount of acid or base present in a solution. This is done by reacting the solution with a base or acid (of known concentration), and by measuring the volume of the known acid or base used up in the process. The reaction data is usually plotted with the volume of the substance (concentration known) in the x-axis, and the pH of the solution in the y-axis. The graph is called a titration curve. 

Vj is the volume of unknown acid or base, and V, is the volume of the known base or acid. 

An indicator is usually used to detect the equivalence point in an acid-base reaction or titration. The most common indicators used are weak organic acids or bases that change color in response to a change from acidic to basic medium or vice versa. The pH at which the color change occurs is characteristic of each indicator. For an acid-base reaction, the indicator is chosen based on the pH at which the equivalence point is expected to occur. Consider the hypothetical dissociation reaction of an indicator represented by HIn. 

Let s consider a scenario in vsiiich the indicator is in an acidic solution. Acidic solution means there is exeess ff. So the equilibrium will shift to the left (LeChatelier s principle), and the predominant species will be HIn making the indicator show yellow color. On the other hand, in a basic solution, the equilibrium will 

Indicator Approx. pH Range of Color Chaise Color Change 

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By analogy to pH titration curves of acids and bases, it is customary in precipitation titrations to plot the quantity pM (defined by either — log [M " ] or — log a m ) against titration volume. For certain metals that form reversible electrodes with their ions, the measured electrode potential is a linear function of the logarithm of ion activity, so the titration curve can be realized experimentally in a potentiometric titration. In any case, the curve gives a useful indication of the sharpness of an endpoint break. 

Calculation of Titration Curves for Acid and Base Determination... 

Niels Bjerrum (1879-1958) was a Danish physical chemist who made fundamental contributions to inorganic coordination chemistry and is responsible for much of our understanding of acids and bases and titration curves.5... 

Why study titration curves The shape of a pH titration curve makes it possible to identify the equivalence point in a titration, the point at which stoichiomet-rically equivalent quantities of acid and base have been mixed together. Knowing the shape of the titration curve is also useful in selecting a suitable indicator to signal the equivalence point. We ll explore both of these points later. 

When the progression of an acid-base titration is graphed as a function of pH vs the volume of acid or base added, the curve will appear as shown below. If we recall, from general chemistry coursework, that the steepest point on the curve represents the equivalence point of the titration (the point where the amount of acid and base are equal), we can locate the point on the curve that represents the midpoint of the titration. This point is found at half the concentration of base added to acid (or acid added to base) to reach the equivalence point. Once we have done this, we recall the Henderson-Hesselbach equation (Fig. 2.8)—specifically, the term dealing with the concentrations of the ionic and the neutral species. Realizing that at the midpoint of the titration, these concentrations are equal, the logarithmic term in the Henderson-Hesselbach equation reduces to log(l), which is equal to zero. Therefore, the equation reduces to pA a = pH at the midpoint of the titration. 

When a weak acid is titrated with a weak base, the titration curve shows a continuously and gradually changing pH with the addition of base. No region with a sharp shift in pH is obtained for small additions of titrant. If a sharp shift occurs, it is still less than 2 pH units and not detectable by indicators. On both sides of the equivalence point, buffers are present, and at the equivalence point, the pH depends on the relative strengths of acid and base. 

For an acid titrated halfway to its equivalent point, pH = pKa. For mixtures of acids and bases, and hence for carbons having functional groups of different acid or basic strength, this holds true as well. For weak acid and base groups, the effect of water dissociation is significant around pH = 7. Therefore, a simple potentiometric titration can give information about the dissociation constants and neutralization equivalence of the carbon. In several cases these indications can be sufficient to determine the nature of the functional groups and provide a comprehensive description of the behavior of carbon in terms of acidity and basicity. A differential plot of the titration curve can be considered in the same way as a conventional absorption spectrum of the sample. Acidity or basicity constants are then calculated at half-titration, as pH = pKw — pKb for a base and pH = pKa for an acid. 

Figure 19-3 (a) The titration curve for 100. mL of 0.100 M HCl with 0.100 M NaOH. Note that the vertical section of the curve is quite long. The titration curves for other strong acids and bases are identical with this one if the same concentrations of acid and bases are used and if both are monoprotic. (b) The titration curve for 100. mL of 0.100 M NaOH with 0.100 M HCl. This curve is similar to that in part (a), but inverted. 

Aqueous titrations of amines are amply discussed elsewhere d. Nonaqueous titrations. Three main purposes may be served by carrying out titrations in nonaqueous solvents increased solubility, change of the pH scale, and resolution of mixtures. The prediction of a potentiometric titration curve in an arbitrary solvent is a difficult task, in which many factors intervene, such as dielectric constant, definition of acid and base in relation to the solvent, electrodes, actual structure of conjugate acids and bases, etc. Acetic acid, sulphuric acid, acetonitrile, and alcohol-water mixtures have been extensively studied and were reviewed elsewhere Some solvents will be treated here briefly ... 

The units that chemists and engineering specialists most frequently use to quantify the concentration of acids and bases in a solution are molar, molal, and normality. The concentration unit that plant engineers commonly use is weight or mass fraction. However, since what is shown on process flow sheets and the specifications for control valves are reagent and influent flows, it is desirable to be able to convert from any of these concentration units to flow units. It will be shown in the remainder of the text how valuable it will be for control valve sizing and pH system analysis to have the ratio of reagent to influent flow as the abscissa of the titration curv e. 

The shape and position of the titration curve (figure P.7) depends on the strengths of acid and base. The curve for the titration of a strong acid with a strong base (I-II) is readily calculated since c(H ) = concentration of unneutralised acid up to the equivalence point (B). At this point the solution is identical with one containing the neutral salt, and c(H ) = 10" mol dm . Further addition of base results in the solution containing free base, and the pH can be readily calculated. 

Whereas titration curves with large, sharp, marked end point jumps are usually desired, with this technique one tries to attain the most linear relationship between EMF and volume (or concentration at constant volume) of titrant possible. Leithe [222] used a mixture of weak bases with overlapping pK values to linearize the titration curves of strong acids. The linearization represents nothing else but the superposition of the not very sharp titration curves of the individual bases (see Fig. 46). The advantage of this... 

The approach that we have worked out for the titration of a monoprotic weak acid with a strong base can be extended to reactions involving multiprotic acids or bases and mixtures of acids or bases. As the complexity of the titration increases, however, the necessary calculations become more time-consuming. Not surprisingly, a variety of algebraic and computer spreadsheet approaches have been described to aid in constructing titration curves. 

This approach can be used to sketch titration curves for other acid-base titrations including those involving polyprotic weak acids and bases or mixtures of weak acids and bases (Figure 9.8). Figure 9.8a, for example, shows the titration curve when titrating a diprotic weak acid, H2A, with a strong base. Since the analyte is... 

Locate the equivalence point for each of the titration curves in problem 1. What is the stoichiometric relationship between the moles of acid and moles of base at each of these equivalence points ... 

The shapes of the titration curves of weak electrolytes are identical, as Figure 2.13 reveals. Note, however, that the midpoints of the different curves vary in a way that characterizes the particular electrolytes. The pV, for acetic acid is 4.76, the pV, for imidazole is 6.99, and that for ammonium is 9.25. These pV, values are directly related to the dissociation constants of these substances, or, viewed the other way, to the relative affinities of the conjugate bases for protons. NH3 has a high affinity for protons compared to Ac NH4 is a poor acid compared to HAc. 

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