Acid-base titrations calculating from

Any titration involves the progressive change of the activities (or concentrations) of the titrated and titrating species and, in principle, can be done potentiometrically. However, for an accurate determination it is necessary that there is a fairly rapid variation in equilibrium potential in the region of the equivalence point. Useful applications are redox, complexation, precipitation, acid-base titrations, etc. From the titration curve it is possible to calculate values of the formal potentials of the titrated and titrating species, as explained below. 

In Example 14-1, we generated an acid/base titration curve from the reaction stoichiometry. We can show that all points on the curve can also be calculated from the charge-balance equation. 

When an acid in solution is exactly neutralized with a base the resulting solution corresponds to a solution of the salt of the acid-base pair. This is a situation which frequently arises in analytical procedures and the calculation of the exact pH of such a solution may be of considerable importance. The neutralization point or end point in an acid-base titration is a particular example (Chapter 5). Salts may in all cases be regarded as strong electrolytes so that a salt AB derived from acid AH and base B will dissociate completely in solution. If the acid and base are strong, no further reaction is likely and the solution pH remains unaffected by the salt. However if either or both acid and base are weak a more complex situation will develop. It is convenient to consider three separate cases, (a) weak acid-strong base, (b) strong acid-weak base and (c) weak acid-weak base. 

Common chemical titrations include acid-base, oxidation-reduction, precipitation, and complexometric analysis. The basic concepts underlying all titration are illustrated by classic acid-base titrations. A known amount of acid is placed in a flask and an indicator added. The indicator is a compound whose color depends on the pH of its environment. A solution of base of precisely known concentration (referred to as the titrant) is then added to the acid until all of the acid has just been reacted, causing the pH of the solution to increase and the color of the indicator to change. The volume of the base required to get to this point in the titration is known as the end point of the titration. The concentration of the acid present in the original solution can be calculated from the volume of base needed to reach the end point and the known concentration of the base. 

This is the basis for a common method for the determination of ammonia in soil.1 Soil is suspended in water and placed in a Kjeldahl flask. The suspension is made basic by the addition of a strong (5-50%) sodium hydroxide solution, and the flask is immediately attached to a steam distillation setup. Steam distillation of the suspension carries the released ammonia to an Erlenmeyer flask, catching the distillate in a standardized acid solution that is subsequently back titrated via acid-base titration. The amount of ammonia in soil can be calculated from the end point of the titration. This procedure is similar to a standard Kjeldahl determination and can be carried out using the same equipment, although no digestion is needed. 

In an acid-base titration, you carefully measure the volumes of acid and base that react. Then, knowing the concentration of either the acid or the base, and the stoichiometric relationship between them, you calculate the concentration of the other reactant. The equivalence point in the titration occurs when just enough acid and base have been mixed for a complete reaction to occur, with no excess of either reactant. As you learned in Chapter 8, you can find the equivalence point from a graph that shows pH versus volume of one solution added to the other solution. To determine the equivalence point experimentally, you need to measure the pH. Because pH meters are expensive, and the glass electrodes are fragile, titrations are often performed using an acid-base indicator. 

An acid-base titration is a procedure that is used where a base of known concentration is added to an acid of unknown concentration (or vice-versa) in order to determine the concentration of the unknown. In addition, it is possible to determine the Ka of the acid being titrated (or Kb of the base) as well as an appropriate indicator. Acid-base titrations are often the topic of AP test questions and are frequently used in the laboratory questions. You should know about titrations from a conceptual level, be able to perform calculations for titrations, and know how to properly perform one in the laboratory. We ll begin with the conceptual explanation of titrations. 

The normality of a solution of an acid or base is the number of equivalents of acid or base per liter a 1 solution contains 1 equivalent per liter of solution. By determining, with use of an indicator, such as litmus, the relative volumes of acidic and alkaline solutions which are equivalent the normality of one solution can be calculated from the known value of the other. This process of acid-base titration (the determination of the titer or strength of an unknown solution), with use of special apparatus such as graduated burets and pipets, is an important method of volumetric quantitative analysis. 

It is important to know the dissociation constant of an indicator in order to use it properly in acid-base titrations. Spectrophotometry can be used to measure the concentration of these intensely colored species in acidic versus basic solutions, and from these data the equilibrium between the acidic and basic forms can be calculated. In one such study on the indicator wj-nitrophenol, a 6.36 X 10 M solution was examined by spectrophotometry at 390 nm and 25°C in the following experiments. In highly acidic solution, where essentially all the indicator was in the form HIn, the absorbance was 0.142. In highly basic solution, where essentially all of the indicator was in the form In , the absorbance was 0.943. In a further series of experiments, the pH was adjusted using a buffer solution of ionic strength I, and absorbance was measured at each pH value. The following results were obtained ... 

Nevskaya, E.Yu., et al.. Calculations of acid-base equilibrium constants from the pH dependence of the electrokinetic potential and potentiometric titration data on aluminum oxides and hydroxides, Russ.. 1. Phys. Chem., Ti, 1421, 1999. 

Evaluate the importance of a buffer in controlling pH. Design strategies for doing acid-base titrations, and calculate results from titration data. 

Despite the possibility of the simultaneous realization of these processes, the potentiometric curves of acid-base titration of Mo03 have no distinctive features as compared with the conventional ones [145]. However, the reverse titration curve differs appreciably from the direct titration results. Using the latter data the equilibrium constant of the formation of dimolybdate in the molten KCl-NaCl eutectic was calculated in Ref. [145] as... 

An acid-base titration, (a) An exact volume of a standard solution (in this example, a base) is added to a solution of unknown concentration (in this example, an acid), (b) From the volume (read from the buret) and concentration of the standard solution, coupled with the mass or volume of the unknown, the concentration of the unknown may be calculated. 

We should note that the pH calculated from the relatively simple equations presented here break down near the equivalence point for weak acids and bases because the assumptions used in deriving them no longer apply. Even for strong acid-base titrations, we reach a point very near the equivalence point where the ionization of water becomes appreciable compared to the acid or excess base concentration, and the calculations are in error. You can satisfy yourself of these limitations by inserting in the spreadsheet examples titrant values that are, say, 99.99% or 99.999% and see where the calculated pH falls off the otherwise smooth titration curve. 

The titration vessel was purged with nitrogen to eliminate CO 2. From the volume and molarity of added base and the mass of titrated DOC, the content of acidic functional groups can be calculated. Carboxylic acid content was calculated from the amount of base added until the end-point was reached. Phenolic acid content was calculated as twice the difference in titrant required to change the pH of the titrate from 8 to 10, since it was assumed that at pH 10 only half the phenolic groups were dissociated. A solution of a concentration of 20 mgL" as DOC NOM were titrated. The error due to the salt content of NOM is likely to be high. 

Functionality. The number of carboxyl equivalents was determined from the potentlometrlc acid-base titration. The number molecular weight iii of the CTPnBA was determined by the Vapor Pressure Osmometer measurement. The product of the number of acid equivalents by the molecular weight divided by the weight of the titrated PnBA sample is the calculated average number of carboxyl groups per chain of the poly n-butyl acrylate. 

When titrating a rain vrater sample according to an acid/base-titration, one sometimes finds that the sample consumes more alkali than should be expected on the basis of the acid concentration calculated from the pH. The surplus of alkali consumption is caused, however, by the simultaneous titration of the components Al3+, Fe, Mn and NHt[, the so-called Bronsted acids, sometimes contained in precipitation, and the titration of (if present) weak acids whose contribution to the free acidity can be neglected. 

In Lewis acid/base titrations, the concentration variable comparable to [H1 is the ligand concentration, but the volume of ligand or the titration fraction is plotted against pM or [Mx], depending on whether the titration is being plotted logarithmically or linearly. This is no cause for concern since we will be able to calculate this quantity, like all the others we need, from the ligand concentration. 

Lewis-Russ [26] reviewed methods for determining pzc values, and Table 1 contains values for different aluminas from the literature. It can be seen that the pzc values vary by about 5 units, and thus they cannot be used to replace direct methods of obtaining equilibrium constants. The pzc values, if obtained by acid-base titration, reflect uncertainties even for the corresponding adsorption constants. Therefore constants should be determined with the same material and under the same experimental conditions if the values are to be used in model calculations for... 

Figure 12.21 A typical acid—base titration curve for measurement of a OH -containing chemistry. The left ordinate is the automated pH reading from a pH electrode the right ordinate is the first derivative of the pH curve. Volume (mL) of titrant (acid) is shown on the abscissa. The endpoint shown is calculated with the first derivative method—the maximum of the pink curve. Used with permission from the author.

For the evaluation, By, Uxand Ft are calculated from their constant relationship to the salinity (Bj = 0.00042 S/35 Swr = 0.02824 S/35 and Ft = 0.000073 5/35 all in mol/(kg-seawater)) and the stability constants for the protonation of the bases are calculated from their salinity dependence. Omission of 5/t from the equations has very little effect on the result for At, because the dominant portion of the silicate is present in the acidic form at the seawater pH. Omission of Ft has even less effect on the At estimate. It however, Cr is also to be evaluated from the titration, omissian of Ft in the evaluation equation introduces an overestimate of Cr, which is about equal to Ft Johansson and Wedborg, 1982). 

Chapter 14, Acids and Bases, discusses acids and bases and their strengths, conjugate acid-base pairs, the dissociation of weak acids and bases and water, pH and pOH, and buffers. Acid-base titration uses the neutralization reactions between acids and bases to calculate quantities of acid in a sample. Section 14.9, Acid-Base Properties of Salt Solutions, has been deleted. Combining Ideas from Chapters 11,12,13, and 14 follows as an interchapter problem set. 

---