Equivalence point definition

So, at the equivalence point, mmol of KOH added = 120.0 mmol KOH, by definition... 

The problem the analyst has is to choose indicators that change color close enough to an equivalence point so that the accuracy of the experiment is not diminished, which really means at any point during the inflection point. (Refer to Section 4.2 for the definitions of equivalence point and end point.) It almost seems like an impossible task, since there must be an indicator for each possible acid or base to be titrated. Fortunately, there are a large number of indicators available, and there is at least one available for all acids and bases, with the exception of only the extremely weak acids and bases. Figure 5.5 lists some of these indicators and shows the pH ranges over which they change color. 

Therefore, k+bm and k label the same representation and are said to be equivalent (=). By definition, no two interior points can be equivalent but every point on the surface of the BZ has at least one equivalent point. The k = 0 point at the center of the zone is denoted by T. All other internal high-symmetry points are denoted by capital Greek letters. Surface symmetry points are denoted by capital Roman letters. The elements of the point group which transform a particular k point into itself or into an equivalent point constitute the point group of the wave vector (or little co-group of k) P(k) C P, for that k point. 

In the article of Kaarls and Quinn [34] primary methods are carefully defined as methods for the determination of the amount of substance in pure or simple compound systems, i.e. in samples which do not contain impurities acting as potential interferences. It is explicitly stated that it is a future task of the CCQM to investigate the applicability and robustness of these methods for complex mixtures encountered in practical analytical chemistry. Many other papers (e.g. [36]), however, tend to identify primary methods already as methods of analysis (to be used on complex samples of unknown overall composition). This over-optimistic (and unwarranted) enlargement of the definition implies that all titrimetric methods of analysis would be considered as primary methods putting aside any interference that occurs in complex samples. Considering all possible sources of error that may occur in both the stoichiometry of the reaction and with the determination of the equivalence point of a titration, this cannot be possible. Neither was this the intention of the CCQM. 

Potentiometric titration curves normally are represented by a plot of the indicator-electrode potential as a function of volume of titrant, as indicated in Fig. 4.2. However, there are some advantages if the data are plotted as the first derivative of the indicator potential with respect to volume of titrant (or even as the second derivative). Such titration curves also are indicated in Figure 4.2, and illustrate that a more definite endpoint indication is provided by both differential curves than by the integrated form of the titration curve. Furthermore, titration by repetitive constant-volume increments allows the endpoint to be determined without a plot of the titration curve the endpoint coincides with the condition when the differential potentiometric response per volume increment is a maximum. Likewise, the endpoint can be determined by using the second derivative the latter has distinct advantages in that there is some indication of the approach of the endpoint as the second derivative approaches a positive maximum just prior to the equivalence point before passing through zero. Such a second-derivative response is particularly attractive for automated titration systems that stop at the equivalence point. 

By definition, the equivalence point occurs when all the original NH3 i converted to NH4 +. Thus the major species in solution are... 

The corrected pH-ncutralization curves obtained in this manner are shown by the dotted lines in Fig. 108 the inflexions at the equivalence points are now seen to be sufficiently definite for an accurate estimate of the end-point to be possible. This method has been used for the poten-tiometric titration of amino-acids. ... 

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

This indicator is used for titrations involving iodine. Starch forms a not very reversible complex with I2 that is a very dark-blue color. The color reaction is sensitive to very small amounts of iodine. In titrations of reducing agents with iodine, the solution remains colorless up to the equivalence point. A fraction of a drop of excess titrant turns the solution a definite blue. 

The distinctions established by IUPAC are clear-cut. Thus, the speed of titrant addition is always constant in an automatic titrator, whereas it Is adjusted by a feedback system according to the nearnesa of the equivalence point in an automated titrator. However, some workers [11,12] acknowledge the accuracy of these definitions but consider them too stringent. Very often, the term automatic Is used to refer to systems with and without feedback Indistinctly. In any case, whenever the concept automatic process Is referred to In this book, It will be meant In its widest connotation, namely that Involving partial or complete elimination of human Intervention not related to Instrumentation. 

Equivalence Point Reference Species Proton Condition Definition (Alkalinity and Acidity in eq/liter)... 

In titration of a strong acid, the strong base added removes the acid linearly with respect to the added base. The number of millimoles of strong acid decreases linearly, approaching zero at the equivalence point, and the base increases linearly after the equivalence point. These quantities can be computed from pH readings and plotted to give a V-shaped pair of lines hitting zero at the equivalence point. By definition,... 

In all four cases here, there are two formula units per cell (arbitrarily chosen to make the diagrams of the same size in order to facilitate observation of their differences), but only one equivalent point per cell (by definition, because the space lattice has been chosen to be P) all are monoclinic in these 2D spaces, but a 3D extension of these structures could be designed to change the crystal system. 

The calculation of the titration error is directly connected to the preceding considerations. It is calculated as follows. Let fp be the potential at the final point (when the indicator color changes). The fp value is slightly different from the theoretical one ep (that at the equivalence point). Let (ppf be the fraction titrated at the final point. According to the definition of the titration error, already given when we considered acids and bases, the absolute titration error is %p — 1 since 1 is the fraction titrated at the equivalence point. The general expression of (p — 1, which is valid for any point of the titration curve, is (with i = 2)... 

The absolute titration error (by definition due to the false detection of the equivalence point) depends on the difference in formal potentials AE°. The last expression clearly shows that when AE° is very high, the error tends toward zero since the numerator itself tends toward zero and the denominator simultaneously tends toward unity. For example, when AE° = 0.24 V and when the color redox indicator changes for the potential value Ffp = (Fep — 0.01)V, the relative error expressed in percentages is about —0.67%. When AE° = 0.30 V, with the same difference Ffp — Fep, the error decreases to —0.21%. In the case of the titration of Fe + by Ce, the titration error remains about —0.01 V, even if the indicator color changes for a potential value weaker than that at the equivalence point by a difference as great as 0.20 V. This remarkable result must be attributed to the great difference AE° (AF° = 0.76 V). 

In these conditions, the calculation of aM is immediate since the stability constants intervening in its expression are known. (Let s recall incidentally that the strategy consisting of adding a great excess of reagent to simplify calculations is a method frequently used in analytical chemistry. The closer we are located to the equivalence point, the better the condition [NH3] Cnh3 is since, by the definition of a satisfactory titration, the cation and ammine complexes concentrations must be very weak at diis point.)... 

By definition, once the equivalence point is reached, an excess of silver ions appears. It is detected with potassium chromate K2Cr04, which gives a red precipitate of silver chromate at the equivalence point, according to the reaction... 

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