Equivalence point

Equivalence point or stoichiometric point occurs during a chemical titration when the amount of titrant added is equivalent, or equal, to the amount of analyte present in the sample. In some cases there are multiple equivalence points which are multiples of the first equivalent point, such as in the titration of a diprotic acid. A graph of the titration curve exhibits an inflection point at the equivalence point. A striking fact about equivalence is that in a reaction the equivalence of the reactants as well as products is conserved.

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Acid-base titration example

Equivalence point occurs during an acid-base titration when equal amounts of acid and base have been reacted. A graph of pH against concentration becomes almost vertical at the equivalence point. The equivalence point of a titration does not mean that the solution has reached pH 7; merely that all the initial reactants have been reacted. The actual pH of the solution at equivalence point is determined by considering the acidity or basicity of the aqueous product of the reaction, most commonly by the Brønsted-Lowry Theory of acids and bases.

When performing a manual titration, it may be difficult or impossible to detect when the equivalence point is reached. Often a pH indicator is added to the reaction vessel with an endpoint that is very close to the equivalence point. This causes a visible color change at the equivalence point and therefore at the point that no more titrant should be added.

Acid-base titrations are commonly taught in school and are the most familiar form of titration, however, it is only one of numerous forms of titration. See titration for more detail.

Methods to determine the endpoint

Different methods to determine the endpoint include:

pH indicator

This is a substance that changes colour in response to a chemical change. An acid-base indicator (e.g., phenolphthalein) changes colour depending on the pH. Redox indicators are also frequently used. A drop of indicator solution is added to the titration at the start; when the colour changes the endpoint has been reached.

Potentiometer

A potentiometer can also be used. This is an instrument which measures the electrode potential of the solution. These are used for titrations based on a redox reaction; the potential of the working electrode will suddenly change as the endpoint is reached.

pH meter

This is a potentiometer which uses an electrode whose potential depends on the amount of H+ ion present in the solution. (This is an example of an ion selective electrode. This allows the pH of the solution to be measured throughout the titration. At the end point there will be a sudden change in the measured pH. It can be more accurate than the indicator method, and is very easily automated.

Conductance

The conductivity of a solution depends on the ions that are present in it. During many titrations, the conductivity changes significantly. (For instance, during an acid-base titration, the H+ and OH- ions react to form neutral H₂O. This changes the conductivity of the solution.) The total conductance of the solution depends also on the other ions present in the solution (such as counter ions). Not all ions contribute equally to the conductivity; this also depends on the mobility of each ion and on the total concentration of ions (ionic strength). Thus, predicting the change in conductivity is harder than measuring it.

Colour change

In some reactions, the solution changes colour without any added indicator. This is often seen in redox titrations, for instance, when the different oxidation states of the product and reactant produce different colours.

Precipitation

If the reaction forms a solid, then a precipitate will form during the titration. A classic example is the reaction between Ag+ and Cl- to form the very insoluble salt AgCl. Surprisingly, this usually makes it difficult to determine the endpoint precisely. As a result, precipitation titrations often have to be done as "back" titrations (see below).

Isothermal titration calorimeter

An isothermal titration calorimeter uses the heat produced or consumed by the reaction to determine the endpoint. This is important in biochemical titrations, such as the determination of how substrates bind to enzymes.

Thermometric titrimetry

Thermometric titrimetry is an extraordinarily versatile technique. This is differentiated from calorimetric titrimetry by the fact that the heat of the reaction (as indicated by temperature rise or fall) is not used to determine the amount of analyte in the sample solution. Instead, the endpoint is determined by the rate of temperature change. Because thermometric titrimetry is a relative technique, it is not necessary to conduct the titration under isothermal conditions, and titrations can be conducted in plastic or even glass vessels, although these vessels are generally enclosed to prevent stray draughts from causing "noise" and disturbing the endpoint. Because thermometric titrations can be conducted under ambient conditions, they are especially well-suited to routine process and quality control in industry. Depending on whether the reaction between the titrant and analyte is exothermic or endothermic, the temperature will either rise or fall during the titration. When all analyte has been consumed by reaction with the titrant, a change in the rate of temperature increase or decrease reveals the endpoint and an inflection in the temperature curve can be observed. The endpoint can be located precisely by employing the second derivative of the temperature curve. The software used in modern automated thermometric titration systems employ sophisticated digital smoothing algorithms so that "noise" resulting from the highly sensitive temperature probes does not interfere with the generation of a smooth, symmetrical second derivative "peak" which defines the endpoint. The technique is capable of very high precision, and coefficients of variance (CV's) of less than 0.1 are common. Modern thermometric titration temperature probes consist of a thermistor which forms one arm of a Wheatstone bridge. Coupled to high resolution electronics, the best thermometric titration systems can resolve temperatures to 10^-5K. Sharp endpoints have been obtained in titrations where the temperature change during the titration has been as little as 0.001K. The technique can be applied to essentially any chemical reaction in a fluid where there is an enthalpy change, although reaction kinetics can play a role in determining the sharpness of the endpoint. Thermometric titrimetry has been successfully applied to acid-base, redox, EDTA, and precipitation titrations. Examples of successful precipitation titrations are sulfate by titration with barium ions, phosphate by titration with magnesium in ammoniacal solution, chloride by titration with silver nitrate, nickel by titration with dimethylglyoxime and fluoride by titration with aluminium (as K₂NaAlF₆) Because the temperature probe does not need to be electrically connected to the solution (as in potentiometric titrations), non-aqueous titrations can be carried out as easily as aqueous titrations. Solutions which are highly colored or turbid can be analyzed by thermometric without further sample treatment. The probe is essentially maintenance-free. Using modern, high precision stepper motor driven burettes, automated thermometric titrations are usually complete in a few minutes, making the technique an ideal choice where high laboratory productivity is required.

Spectroscopy

Spectroscopy can be used to measure the absorption of light by the solution during the titration, if the spectrum of the reactant, titrant or product is known. The relative amounts of the product and reactant can be used to determine the endpoint. Alternately, the presence of free titrant (indicating that the reaction is complete) can be detected at very low levels.

Amperometry

Amperometry can be used as a detection technique (amperometric titration). The current due to the oxidation or reduction of either the reactants or products at a working electrode will depend on the concentration of that species in solution. The endpoint can then be detected as a change in the current. This method is most useful when the excess titrant can be reduced, as in the titration of halides with Ag+. (This is handy also in that it ignores precipitates.)