Equivalence point
Encyclopedia
The equivalence point, or stoichiometric
Stoichiometry
Stoichiometry is a branch of chemistry that deals with the relative quantities of reactants and products in chemical reactions. In a balanced chemical reaction, the relations among quantities of reactants and products typically form a ratio of whole numbers...

 point
, of a chemical reaction when a titrant is added and is stoichiometrically equal to the amount of moles of substance (known as analyte) present in the sample: the smallest amount of titrant that is sufficient to fully neutralize or react with the analyte. 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
Diprotic acid
A diprotic acid is an acid such as H2SO4 that contains within its molecular structure two hydrogen atoms per molecule capable of dissociating in water. The complete dissociation of diprotic acids is of the same form as sulfuric acid:The dissociation does not happen all at once due to the two...

.

A graph of the titration curve
Titration curve
Titrations are often recorded on titration curves, whose compositions are generally identical: the independent variable is the volume of the titrant, while the dependent variable is the pH of the solution...

 exhibits an inflection point
Inflection point
In differential calculus, an inflection point, point of inflection, or inflection is a point on a curve at which the curvature or concavity changes sign. The curve changes from being concave upwards to concave downwards , or vice versa...

 at the equivalence point—where the graph is steepest. A striking fact about equivalence is that in a reaction the equivalence of the reactants as well as products is conserved.

The endpoint (similar, but not the same as the equivalence point) refers to the point at which the indicator changes color in a colorimetric titration.

Methods to determine the equivalence point

Different methods to determine the equivalence point include:
pH indicator
PH indicator
A pH indicator is a halochromic chemical compound that is added in small amounts to a solution so that the pH of the solution can be determined visually. Hence a pH indicator is a chemical detector for hydronium ions or hydrogen ions in the Arrhenius model. Normally, the indicator causes the...

: This is a substance that changes color in response to a chemical change. An acid-base indicator (e.g., phenolphthalein
Phenolphthalein
Phenolphthalein is a chemical compound with the formula C20H14O4 and is often written as "HIn" or "phph" in shorthand notation. Often used in titrations, it turns colorless in acidic solutions and pink in basic solutions...

) changes color depending on the pH
PH
In chemistry, pH is a measure of the acidity or basicity of an aqueous solution. Pure water is said to be neutral, with a pH close to 7.0 at . Solutions with a pH less than 7 are said to be acidic and solutions with a pH greater than 7 are basic or alkaline...

. Redox indicator
Redox indicator
A redox indicator is an indicator that undergoes a definite color change at a specific electrode potential....

s are also frequently used. A drop of indicator solution is added to the titration at the start; when the color changes the endpoint has been reached, this is an approximation of the equivalence point.
Potentiometer: A potentiometer
Potentiometer
A potentiometer , informally, a pot, is a three-terminal resistor with a sliding contact that forms an adjustable voltage divider. If only two terminals are used , it acts as a variable resistor or rheostat. Potentiometers are commonly used to control electrical devices such as volume controls on...

 can also be used. This is an instrument which measures the electrode potential
Electrode potential
Electrode potential, E, in electrochemistry, according to an IUPAC definition, is the electromotive force of a cell built of two electrodes:* on the left-hand side is the standard hydrogen electrode, and...

 of the solution. These are used for titrations based on a redox reaction; the potential of the working electrode will suddenly change as the equivalence point is reached.
pH meter
PH meter
A pH meter is an electronic instrument used for measuring the pH of a liquid...

: This is a potentiometer which uses an electrode whose potential depends on the amount of H3O+ present in the solution. This is an example of an ion selective electrode
Ion selective electrode
An ion-selective electrode , also known as a specific ion electrode , is a transducer that converts the activity of a specific ion dissolved in a solution into an electrical potential, which can be measured by a voltmeter or pH meter. The voltage is theoretically dependent on the logarithm of the...

. This allows the pH of the solution to be measured throughout the titration. At the equivalence 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
Conductivity (electrolytic)
The conductivity of an electrolyte solution is a measure of its ability to conduct electricity. The SI unit of conductivity is siemens per meter ....

 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 H3O+ 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
Ionic strength
The ionic strength of a solution is a measure of the concentration of ions in that solution. Ionic compounds, when dissolved in water, dissociate into ions. The total electrolyte concentration in solution will affect important properties such as the dissociation or the solubility of different salts...

). Thus, predicting the change in conductivity is harder than measuring it.
Color 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.
Isothermal titration calorimeter: An isothermal titration calorimeter uses the heat produced or consumed by the reaction to determine the equivalence point. This is important in biochemical
Biochemistry
Biochemistry, sometimes called biological chemistry, is the study of chemical processes in living organisms, including, but not limited to, living matter. Biochemistry governs all living organisms and living processes...

 titrations, such as the determination of how substrate
Substrate (biochemistry)
In biochemistry, a substrate is a molecule upon which an enzyme acts. Enzymes catalyze chemical reactions involving the substrate. In the case of a single substrate, the substrate binds with the enzyme active site, and an enzyme-substrate complex is formed. The substrate is transformed into one or...

s bind to enzyme
Enzyme
Enzymes are proteins that catalyze chemical reactions. In enzymatic reactions, the molecules at the beginning of the process, called substrates, are converted into different molecules, called products. Almost all chemical reactions in a biological cell need enzymes in order to occur at rates...

s.
Thermometric titrimetry
Thermometric titration
Thermometric titration is one of a number of instrumental titration techniques where endpoints can be located accurately and precisely without a subjective interpretation on the part of the analyst as to their location...

: 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 equivalence point 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
Plastic
A plastic material is any of a wide range of synthetic or semi-synthetic organic solids used in the manufacture of industrial products. Plastics are typically polymers of high molecular mass, and may contain other substances to improve performance and/or reduce production costs...

 or even glass
Glass
Glass is an amorphous solid material. Glasses are typically brittle and optically transparent.The most familiar type of glass, used for centuries in windows and drinking vessels, is soda-lime glass, composed of about 75% silica plus Na2O, CaO, and several minor additives...

 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
Exothermic
In thermodynamics, the term exothermic describes a process or reaction that releases energy from the system, usually in the form of heat, but also in the form of light , electricity , or sound...

 or endothermic
Endothermic
In thermodynamics, the word endothermic describes a process or reaction in which the system absorbs energy from the surroundings in the form of heat. Its etymology stems from the prefix endo- and the Greek word thermasi,...

, 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 equivalence point and an inflection in the temperature curve can be observed. The equivalence point can be located precisely by employing the second derivative
Derivative
In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...

 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
Thermistor
A thermistor is a type of resistor whose resistance varies significantly with temperature, more so than in standard resistors. The word is a portmanteau of thermal and resistor...

 which forms one arm of a Wheatstone bridge
Wheatstone bridge
A Wheatstone bridge is an electrical circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component. Its operation is similar to the original potentiometer. It was invented by Samuel Hunter Christie in 1833 and...

. Coupled to high resolution electronics, the best thermometric titration systems can resolve temperatures to 10−5K. Sharp equivalence points 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
Silver nitrate
Silver nitrate is an inorganic compound with chemical formula . This compound is a versatile precursor to many other silver compounds, such as those used in photography. It is far less sensitive to light than the halides...

, 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
Spectroscopy
Spectroscopy is the study of the interaction between matter and radiated energy. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, e.g., by a prism. Later the concept was expanded greatly to comprise any interaction with radiative...

 can be used to measure the absorption of light by the solution during the titration, if the spectrum
Spectrum
A spectrum is a condition that is not limited to a specific set of values but can vary infinitely within a continuum. The word saw its first scientific use within the field of optics to describe the rainbow of colors in visible light when separated using a prism; it has since been applied by...

 of the reactant, titrant or product is known. The relative amounts of the product and reactant can be used to determine the equivalence point. Alternatively, the presence of free titrant (indicating that the reaction is complete) can be detected at very low levels.
Amperometry: Amperometry
Amperometry
Amperometry in chemistry and biochemistry is detection of ions in a solution based on electric current or changes in electric current.Amperometry is used in electrophysiology to study vesicle release events using a carbon fiber electrode...

 can be used as a detection technique (amperometric titration
Amperometric titration
Amperometric titration refers to a class of titrations in which the equivalence point is determined through measurement of the electric current produced by the titration reaction. It is a form of quantitative analysis.-Background:...

). 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 equivalence point 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.)

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