Equivalent weight
Encyclopedia
Equivalent weight is a term which has been used in several contexts in chemistry
. In its most general usage, it is the mass
of one equivalent
, that is the mass of a given substance which will:
Equivalent weight has the dimensions
and units of mass, unlike atomic weight
, which is dimensionless
. Equivalent weights were originally determined by experiment, but (insofar as they are still used) are now derived from molar mass
es. Additionally, the equivalent weight of a compound can be calculated by dividing the molecular weight by the number of positive or negative electrical charges that result from the dissolution of the compound.
s and base
s by Carl Friedrich Wenzel
in 1777. A larger set of tables was prepared, possibly independently, by Jeremias Benjamin Richter
, starting in 1792. However, neither Wenzel nor Richter had a single reference point for their tables, and so had to publish separate tables for each pair of acid and base.
John Dalton's
first table of atomic weights (1808) suggested a reference point, at least for the elements
: taking the equivalent weight of hydrogen
to be one unit of mass. However, Dalton's atomic theory was far from universally accepted in the early 19th century. One of the greatest problems was the reaction of hydrogen with oxygen
to produce water. One gram of hydrogen reacts with eight grams of oxygen to produce nine grams of water, so the equivalent weight of oxygen was defined as eight grams. However, expressing the reaction in terms of gas volumes following Gay-Lussac's law
, two volumes of hydrogen react with one volume of oxygen to produce two volumes of water, suggesting that the atomic weight of oxygen should be sixteen. The work of Charles Frédéric Gerhardt
(1816–56), Henri Victor Regnault
(1810–78) and Stanislao Cannizzaro
(1826–1910) helped to rationalise this and many similar paradoxes, but the problem was still the subject of debate at the Karlsruhe Congress
(1860).
Nevertheless, many chemists found equivalent weights to be a useful tool even if they did not subscribe to atomic theory
. Equivalent weights were a useful generalisation of Joseph Proust's
law of definite proportions
(1794) that enabled chemistry to become a quantitative science. French chemist Jean-Baptiste Dumas
(1800–84) became one of the more influential opponents of atomic theory, after having embraced it earlier in his career, but was a staunch supporter of equivalent weights.
Equivalent weights were not without problems of their own. For a start, the scale based on hydrogen was not particularly practical, as most elements do not react directly with hydrogen to form simple compounds. However, one gram of hydrogen reacts with 8 grams of oxygen to give water or with 35.5 grams of chlorine
to give hydrogen chloride
: hence 8 grams of oxygen and 35.5 grams of chlorine can be taken to be equivalent to one gram of hydrogen for the measurement of equivalent weights. This system can be extended further through different acids and bases.
Much more serious was the problem of elements which form more than one oxide
or series of salts, which have (in today's terminology) different oxidation state
s. Copper
will react with oxygen to form either brick red cuprous oxide (copper(I) oxide
, with 63.5 g of copper for 8 g of oxygen) or black cupric oxide (copper(II) oxide
, with 32.7 g of copper for 8 g of oxygen), and so has two equivalent weights. Supporters of atomic weights could turn to the Dulong–Petit law
(1819), which relates the atomic weight of a solid element to its specific heat capacity, but supporters of equivalent weights had to accept that some elements had multiple "equivalents".
The final death blow for the use of equivalent weights for the elements was the Dmitri Mendeleev's
presentation of his periodic table
in 1869, in which he related the chemical properties of the elements to the approximate order of their atomic weights. However, equivalent weights continued to be used for many compounds for another hundred years, particularly in analytical chemistry
. Equivalent weights of common reagents could be tabulated, simplifying analytical calculations in the days before the widespread availability of electronic calculators: such tables were commonplace in textbooks of analytical chemistry.
es. Equivalent weights may be calculated from molar masses if the chemistry of the substance is well known:
Historically, the equivalent weights of the elements were often determined by studying their reactions with oxygen. For example, 50 g of zinc
will react with oxygen to produce 62.24 g of zinc oxide
, implying that the zinc has reacted with 12.24 g of oxygen (from the Law of conservation of mass): the equivalent weight of zinc is the mass which will react with eight grams of oxygen, hence 50 g × 8 g/12.24 g = 32.7 g.
s in analytical chemistry
, compounds with higher equivalent weights are generally more desirable because weighing errors are reduced. An example is the volumetric standardisation of a solution of sodium hydroxide which has been prepared to approximately 0.1 . It is necessary to calculate the mass of a solid acid which will react with about 20 cm3 of this solution (for a titration using a 25 cm3 burette
): suitable solid acids include oxalic acid dihydrate
, potassium hydrogen phthalate
and potassium hydrogen iodate. The equivalent weights of the three acids 63.04 g, 204.23 g and 389.92 g respectively, and the masses required for the standardisation are 126.1 mg, 408.5 mg and 779.8 mg respectively. Given that the measurement uncertainty
in the mass measured on a standard analytical balance is ±0.1 mg, the relative uncertainty in the mass of oxalic acid dihydrate would be about one part in a thousand, similar to the measurement uncertainty in the volume measurement in the titration. However the measurement uncertainty in the mass of potassium hydrogen iodate would be five times lower, because its equivalent weight is five times higher: such an uncertainty in the measured mass is negligible in comparison to the uncertainty in the volume measured during the titration (see example below).
For sake of example, it shall be assumed that 22.45±0.03 cm3 of the sodium hydroxide solution reacts with 781.4±0.1 mg of potassium hydrogen iodate. As the equivalent weight of potassium hydrogen iodate is 389.92 g, the measured mass is 2.004 milliequivalents. The concentration of the sodium hydroxide solution is therefore 2.004 meq/0.02245 l = 89.3 meq/l. In analytical chemistry, a solution of any substance which contains one equivalent per litre is known as a normal solution (abbreviated N), so the example sodium hydroxide solution would be 0.0893 N. The relative uncertainty
(ur) in the measured concentration can be estimated by assuming a Gaussian distribution of the measurement uncertainties
:
This sodium hydroxide solution can be used to measure the equivalent weight of an unknown acid. For example, if it takes 13.20±0.03 cm3 of the sodium hydroxide solution to neutralise 61.3±0.1 mg of an unknown acid, the equivalent weight of the acid is:
Because each mole of acid can only release an integer number of moles of hydrogen ions, the molar mass of the unknown acid must be an integer multiple of 52.0±0.1 g.
: the it was the mass of precipitate which corresponds to one gram of analyte (the species of interest). The different definitions came from the practice of quoting gravimetric results as mass fractions of the analyte, often expressed as a percentage
. A related term was the equivalence factor, one gram divided by equivalent weight, which was the numerical factor by which the mass of precipitate had to be multiplied to obtain the mass of analyte.
For example, in the gravimetric determination of nickel
, the molar mass of the precipitate bis(dimethylglyoximato
)nickel [Ni(dmgH)2] is 288.915(7) , while the molar mass of nickel is 58.6934(2) : hence 288.915(7)/58.6934(2) = 4.9224(1) grams of [Ni(dmgH)2] precipitate is equivalent to one gram of nickel and the equivalence factor is 0.203151(5). For example, 215.3±0.1 mg of [Ni(dmgH)2] precipitate is equivalent to (215.3±0.1 mg) × 0.203151(5) = 43.74±0.2 mg of nickel: if the original sample size was 5.346±0.001 g, the nickel content in the original sample would be 0.8182±0.0004%.
Gravimetric analysis is one of the most precise of the common methods of chemical analysis, but it is time-consuming and labour-intensive. It has been largely superseded by other techniques such as atomic absorption spectroscopy
, in which the mass of analyte is read off from a calibration curve
.
In polymer chemistry
, the equivalent weight of a reactive polymer is the mass of polymer which has one equivalent of reactivity (often, the mass of polymer which corresponds to one mole of reactive side-chain groups). It is widely used to indicate the reactivity of polyol
, isocyanate
, or epoxy
thermoset resins which would undergo crosslinking reactions through those functional groups.
It is particularly important for ion-exchange polymers (also called ion-exchange resins): one equivalent of an ion-exchange polymer will exchange one mole of singly charged ions, but only half a mole of doubly charged ions.
Nevertheless, given the decline in use of the term "equivalent weight" in the rest of chemistry, it has become more usual to express the reactivity of a polymer as the inverse of the equivalent weight, that is in units of mmol/g or meq/g.
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
. In its most general usage, it is the mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
of one equivalent
Equivalent (chemistry)
The equivalent , sometimes termed the molar equivalent, is a unit of amount of substance used in chemistry and the biological sciences.The equivalent is formally defined as the amount of a substance which will either:...
, that is the mass of a given substance which will:
- supply or react with one moleMole (unit)The mole is a unit of measurement used in chemistry to express amounts of a chemical substance, defined as an amount of a substance that contains as many elementary entities as there are atoms in 12 grams of pure carbon-12 , the isotope of carbon with atomic weight 12. This corresponds to a value...
of hydrogen cations in an acid–base reaction; or - supply or react with one mole of electronElectronThe electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s in a redox reaction.
Equivalent weight has the dimensions
Dimensional analysis
In physics and all science, dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions. The dimension of a physical quantity is the combination of the basic physical dimensions which describe it; for example, speed has the dimension length per...
and units of mass, unlike atomic weight
Atomic weight
Atomic weight is a dimensionless physical quantity, the ratio of the average mass of atoms of an element to 1/12 of the mass of an atom of carbon-12...
, which is dimensionless
Dimensionless quantity
In dimensional analysis, a dimensionless quantity or quantity of dimension one is a quantity without an associated physical dimension. It is thus a "pure" number, and as such always has a dimension of 1. Dimensionless quantities are widely used in mathematics, physics, engineering, economics, and...
. Equivalent weights were originally determined by experiment, but (insofar as they are still used) are now derived from molar mass
Molar mass
Molar mass, symbol M, is a physical property of a given substance , namely its mass per amount of substance. The base SI unit for mass is the kilogram and that for amount of substance is the mole. Thus, the derived unit for molar mass is kg/mol...
es. Additionally, the equivalent weight of a compound can be calculated by dividing the molecular weight by the number of positive or negative electrical charges that result from the dissolution of the compound.
History
The first tables of equivalent weights were published for acidAcid
An acid is a substance which reacts with a base. Commonly, acids can be identified as tasting sour, reacting with metals such as calcium, and bases like sodium carbonate. Aqueous acids have a pH of less than 7, where an acid of lower pH is typically stronger, and turn blue litmus paper red...
s and base
Base (chemistry)
For the term in genetics, see base A base in chemistry is a substance that can accept hydrogen ions or more generally, donate electron pairs. A soluble base is referred to as an alkali if it contains and releases hydroxide ions quantitatively...
s by Carl Friedrich Wenzel
Carl Friedrich Wenzel
Carl Friedrich Wenzel was a German chemist and metallurgist who determined the reaction rates of various chemicals, establishing, for example, that the amount of metal that dissolves in an acid is proportional to the concentration of acid in the solution...
in 1777. A larger set of tables was prepared, possibly independently, by Jeremias Benjamin Richter
Jeremias Benjamin Richter
Jeremias Benjamin Richter was a German chemist. He was born at Hirschberg in Silesia, became a mining official at Breslau in 1794, and in 1800 was appointed assessor to the department of mines and chemist to the royal porcelain factory at Berlin, where he died.-Developer of titration:To him...
, starting in 1792. However, neither Wenzel nor Richter had a single reference point for their tables, and so had to publish separate tables for each pair of acid and base.
John Dalton's
John Dalton
John Dalton FRS was an English chemist, meteorologist and physicist. He is best known for his pioneering work in the development of modern atomic theory, and his research into colour blindness .-Early life:John Dalton was born into a Quaker family at Eaglesfield, near Cockermouth, Cumberland,...
first table of atomic weights (1808) suggested a reference point, at least for the elements
Chemical element
A chemical element is a pure chemical substance consisting of one type of atom distinguished by its atomic number, which is the number of protons in its nucleus. Familiar examples of elements include carbon, oxygen, aluminum, iron, copper, gold, mercury, and lead.As of November 2011, 118 elements...
: taking the equivalent weight of hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...
to be one unit of mass. However, Dalton's atomic theory was far from universally accepted in the early 19th century. One of the greatest problems was the reaction of hydrogen with oxygen
Oxygen
Oxygen is the element with atomic number 8 and represented by the symbol O. Its name derives from the Greek roots ὀξύς and -γενής , because at the time of naming, it was mistakenly thought that all acids required oxygen in their composition...
to produce water. One gram of hydrogen reacts with eight grams of oxygen to produce nine grams of water, so the equivalent weight of oxygen was defined as eight grams. However, expressing the reaction in terms of gas volumes following Gay-Lussac's law
Gay-Lussac's law
The expression Gay-Lussac's law is used for each of the two relationships named after the French chemist Joseph Louis Gay-Lussac and which concern the properties of gases, though it is more usually applied to his law of combining volumes, the first listed here...
, two volumes of hydrogen react with one volume of oxygen to produce two volumes of water, suggesting that the atomic weight of oxygen should be sixteen. The work of Charles Frédéric Gerhardt
Charles Frédéric Gerhardt
Charles Frédéric Gerhardt was a French chemist.-Biography:He was born in Strasbourg, where he attended the gymnasium. He then studied at the Karlsruhe Institute of Technology, where Friedrich Walchner's lectures first attracted his interest to chemistry...
(1816–56), Henri Victor Regnault
Henri Victor Regnault
Henri Victor Regnault was a French chemist and physicist best known for his careful measurements of the thermal properties of gases. He was an early thermodynamicist and was mentor to William Thomson in the late 1840s....
(1810–78) and Stanislao Cannizzaro
Stanislao Cannizzaro
Stanislao Cannizzaro, FRS was an Italian chemist. He is remembered today largely for the Cannizzaro reaction and for his influential role in the atomic-weight deliberations of the Karlsruhe Congress in 1860.-Biography:...
(1826–1910) helped to rationalise this and many similar paradoxes, but the problem was still the subject of debate at the Karlsruhe Congress
Karlsruhe Congress
The Karlsruhe Congress was an international meeting of chemists held in Karlsruhe, Germany from 3 to 5 September, 1860. It was the first international conference of chemistry worldwide.- The meeting :...
(1860).
Nevertheless, many chemists found equivalent weights to be a useful tool even if they did not subscribe to atomic theory
Atomic theory
In chemistry and physics, atomic theory is a theory of the nature of matter, which states that matter is composed of discrete units called atoms, as opposed to the obsolete notion that matter could be divided into any arbitrarily small quantity...
. Equivalent weights were a useful generalisation of Joseph Proust's
Joseph Proust
Joseph Louis Proust was a French chemist.-Life:Joseph L. Proust was born on September 26, 1754 in Angers, France. His father served as an apothecary in Angers. Joseph studied chemistry in his father’s shop and later came to Paris where he gained the appointment of apothecary in chief to the...
law of definite proportions
Law of definite proportions
In chemistry, the law of definite proportions, sometimes called Proust's Law, states that a chemical compound always contains exactly the same proportion of elements by mass. An equivalent statement is the law of constant composition, which states that all samples of a given chemical compound have...
(1794) that enabled chemistry to become a quantitative science. French chemist Jean-Baptiste Dumas
Jean-Baptiste Dumas
Jean Baptiste André Dumas was a French chemist, best known for his works on organic analysis and synthesis, as well as the determination of atomic weights and molecular weights by measuring vapor densities...
(1800–84) became one of the more influential opponents of atomic theory, after having embraced it earlier in his career, but was a staunch supporter of equivalent weights.
Equivalent weights were not without problems of their own. For a start, the scale based on hydrogen was not particularly practical, as most elements do not react directly with hydrogen to form simple compounds. However, one gram of hydrogen reacts with 8 grams of oxygen to give water or with 35.5 grams of chlorine
Chlorine
Chlorine is the chemical element with atomic number 17 and symbol Cl. It is the second lightest halogen, found in the periodic table in group 17. The element forms diatomic molecules under standard conditions, called dichlorine...
to give hydrogen chloride
Hydrogen chloride
The compound hydrogen chloride has the formula HCl. At room temperature, it is a colorless gas, which forms white fumes of hydrochloric acid upon contact with atmospheric humidity. Hydrogen chloride gas and hydrochloric acid are important in technology and industry...
: hence 8 grams of oxygen and 35.5 grams of chlorine can be taken to be equivalent to one gram of hydrogen for the measurement of equivalent weights. This system can be extended further through different acids and bases.
Much more serious was the problem of elements which form more than one oxide
Oxide
An oxide is a chemical compound that contains at least one oxygen atom in its chemical formula. Metal oxides typically contain an anion of oxygen in the oxidation state of −2....
or series of salts, which have (in today's terminology) different oxidation state
Oxidation state
In chemistry, the oxidation state is an indicator of the degree of oxidation of an atom in a chemical compound. The formal oxidation state is the hypothetical charge that an atom would have if all bonds to atoms of different elements were 100% ionic. Oxidation states are typically represented by...
s. Copper
Copper
Copper is a chemical element with the symbol Cu and atomic number 29. It is a ductile metal with very high thermal and electrical conductivity. Pure copper is soft and malleable; an exposed surface has a reddish-orange tarnish...
will react with oxygen to form either brick red cuprous oxide (copper(I) oxide
Copper(I) oxide
Copper oxide or cuprous oxide is the inorganic compound with the formula Cu2O. It is one of the principal oxides of copper. This red-coloured solid is a component of some antifouling paints. The compound can appear either yellow or red, depending on the size of the particles, but both forms...
, with 63.5 g of copper for 8 g of oxygen) or black cupric oxide (copper(II) oxide
Copper(II) oxide
Copper oxide or cupric oxide is the higher oxide of copper. As a mineral, it is known as tenorite.-Chemistry:It is a black solid with an ionic structure which melts above 1200 °C with some loss of oxygen...
, with 32.7 g of copper for 8 g of oxygen), and so has two equivalent weights. Supporters of atomic weights could turn to the Dulong–Petit law
Dulong–Petit law
The Dulong–Petit law, a chemical law proposed in 1819 by French physicists Pierre Louis Dulong and Alexis Thérèse Petit, states the classical expression for the molar specific heat capacity of a crystal...
(1819), which relates the atomic weight of a solid element to its specific heat capacity, but supporters of equivalent weights had to accept that some elements had multiple "equivalents".
The final death blow for the use of equivalent weights for the elements was the Dmitri Mendeleev's
Dmitri Mendeleev
Dmitri Ivanovich Mendeleev , was a Russian chemist and inventor. He is credited as being the creator of the first version of the periodic table of elements...
presentation of his periodic table
Periodic table
The periodic table of the chemical elements is a tabular display of the 118 known chemical elements organized by selected properties of their atomic structures. Elements are presented by increasing atomic number, the number of protons in an atom's atomic nucleus...
in 1869, in which he related the chemical properties of the elements to the approximate order of their atomic weights. However, equivalent weights continued to be used for many compounds for another hundred years, particularly in analytical chemistry
Analytical chemistry
Analytical chemistry is the study of the separation, identification, and quantification of the chemical components of natural and artificial materials. Qualitative analysis gives an indication of the identity of the chemical species in the sample and quantitative analysis determines the amount of...
. Equivalent weights of common reagents could be tabulated, simplifying analytical calculations in the days before the widespread availability of electronic calculators: such tables were commonplace in textbooks of analytical chemistry.
Use in general chemistry
The use of equivalent weights in general chemistry has largely been superseded by the use of molar massMolar mass
Molar mass, symbol M, is a physical property of a given substance , namely its mass per amount of substance. The base SI unit for mass is the kilogram and that for amount of substance is the mole. Thus, the derived unit for molar mass is kg/mol...
es. Equivalent weights may be calculated from molar masses if the chemistry of the substance is well known:
- sulfuric acidSulfuric acidSulfuric acid is a strong mineral acid with the molecular formula . Its historical name is oil of vitriol. Pure sulfuric acid is a highly corrosive, colorless, viscous liquid. The salts of sulfuric acid are called sulfates...
has a molar mass of 98.078(5) , and supplies two moles of hydrogen ions per mole of sulfuric acid, so its equivalent weight is 98.078(5) /2 = 49.039(3) . - potassium permanganatePotassium permanganatePotassium permanganate is an inorganic chemical compound with the formula KMnO4. It is a salt consisting of K+ and MnO4− ions. Formerly known as permanganate of potash or Condy's crystals, it is a strong oxidizing agent. It dissolves in water to give intensely purple solutions, the...
has a molar mass of 158.034(1) , and reacts with five moles of electrons per mole of potassium permanganate, so its equivalent weight is 158.034(1) /5 = 31.6608(3) .
Historically, the equivalent weights of the elements were often determined by studying their reactions with oxygen. For example, 50 g of zinc
Zinc
Zinc , or spelter , is a metallic chemical element; it has the symbol Zn and atomic number 30. It is the first element in group 12 of the periodic table. Zinc is, in some respects, chemically similar to magnesium, because its ion is of similar size and its only common oxidation state is +2...
will react with oxygen to produce 62.24 g of zinc oxide
Zinc oxide
Zinc oxide is an inorganic compound with the formula ZnO. It is a white powder that is insoluble in water. The powder is widely used as an additive into numerous materials and products including plastics, ceramics, glass, cement, rubber , lubricants, paints, ointments, adhesives, sealants,...
, implying that the zinc has reacted with 12.24 g of oxygen (from the Law of conservation of mass): the equivalent weight of zinc is the mass which will react with eight grams of oxygen, hence 50 g × 8 g/12.24 g = 32.7 g.
Use in volumetric analysis
When choosing primary standardPrimary standard
A primary standard in metrology is a standard that is accurate enough that it is not calibrated by or subordinate to other standards. Primary standards are defined via other quantities like length, mass and time. Primary standards are used to calibrate other standards referred to as working...
s in analytical chemistry
Analytical chemistry
Analytical chemistry is the study of the separation, identification, and quantification of the chemical components of natural and artificial materials. Qualitative analysis gives an indication of the identity of the chemical species in the sample and quantitative analysis determines the amount of...
, compounds with higher equivalent weights are generally more desirable because weighing errors are reduced. An example is the volumetric standardisation of a solution of sodium hydroxide which has been prepared to approximately 0.1 . It is necessary to calculate the mass of a solid acid which will react with about 20 cm3 of this solution (for a titration using a 25 cm3 burette
Burette
A burette is a vertical cylindrical piece of laboratory glassware with a volumetric graduation on its full length and a precision tap, or stopcock, on the bottom. It is used to dispense known amounts of a liquid reagent in experiments for which such precision is necessary, such as a titration...
): suitable solid acids include oxalic acid dihydrate
Oxalic acid
Oxalic acid is an organic compound with the formula H2C2O4. This colourless solid is a dicarboxylic acid. In terms of acid strength, it is about 3,000 times stronger than acetic acid. Oxalic acid is a reducing agent and its conjugate base, known as oxalate , is a chelating agent for metal cations...
, potassium hydrogen phthalate
Potassium hydrogen phthalate
Potassium hydrogen phthalate, often called simply KHP, is an acidic salt compound. It forms white powder, colorless crystals, a colorless solution, and an ionic solid that is the monopotassium salt of phthalic acid...
and potassium hydrogen iodate. The equivalent weights of the three acids 63.04 g, 204.23 g and 389.92 g respectively, and the masses required for the standardisation are 126.1 mg, 408.5 mg and 779.8 mg respectively. Given that the measurement uncertainty
Measurement uncertainty
In metrology, measurement uncertainty is a non-negative parameter characterizing the dispersion of the values attributed to a measured quantity. The uncertainty has a probabilistic basis and reflects incomplete knowledge of the quantity. All measurements are subject to uncertainty and a measured...
in the mass measured on a standard analytical balance is ±0.1 mg, the relative uncertainty in the mass of oxalic acid dihydrate would be about one part in a thousand, similar to the measurement uncertainty in the volume measurement in the titration. However the measurement uncertainty in the mass of potassium hydrogen iodate would be five times lower, because its equivalent weight is five times higher: such an uncertainty in the measured mass is negligible in comparison to the uncertainty in the volume measured during the titration (see example below).
For sake of example, it shall be assumed that 22.45±0.03 cm3 of the sodium hydroxide solution reacts with 781.4±0.1 mg of potassium hydrogen iodate. As the equivalent weight of potassium hydrogen iodate is 389.92 g, the measured mass is 2.004 milliequivalents. The concentration of the sodium hydroxide solution is therefore 2.004 meq/0.02245 l = 89.3 meq/l. In analytical chemistry, a solution of any substance which contains one equivalent per litre is known as a normal solution (abbreviated N), so the example sodium hydroxide solution would be 0.0893 N. The relative uncertainty
Measurement uncertainty
In metrology, measurement uncertainty is a non-negative parameter characterizing the dispersion of the values attributed to a measured quantity. The uncertainty has a probabilistic basis and reflects incomplete knowledge of the quantity. All measurements are subject to uncertainty and a measured...
(ur) in the measured concentration can be estimated by assuming a Gaussian distribution of the measurement uncertainties
Measurement uncertainty
In metrology, measurement uncertainty is a non-negative parameter characterizing the dispersion of the values attributed to a measured quantity. The uncertainty has a probabilistic basis and reflects incomplete knowledge of the quantity. All measurements are subject to uncertainty and a measured...
:
This sodium hydroxide solution can be used to measure the equivalent weight of an unknown acid. For example, if it takes 13.20±0.03 cm3 of the sodium hydroxide solution to neutralise 61.3±0.1 mg of an unknown acid, the equivalent weight of the acid is:
Because each mole of acid can only release an integer number of moles of hydrogen ions, the molar mass of the unknown acid must be an integer multiple of 52.0±0.1 g.
Use in gravimetric analysis
The term "equivalent weight" had a distinct sense in gravimetric analysisGravimetric analysis
Gravimetric analysis describes a set of methods in analytical chemistry for the quantitative determination of an analyte based on the mass of a solid...
: the it was the mass of precipitate which corresponds to one gram of analyte (the species of interest). The different definitions came from the practice of quoting gravimetric results as mass fractions of the analyte, often expressed as a percentage
Percentage
In mathematics, a percentage is a way of expressing a number as a fraction of 100 . It is often denoted using the percent sign, “%”, or the abbreviation “pct”. For example, 45% is equal to 45/100, or 0.45.Percentages are used to express how large/small one quantity is, relative to another quantity...
. A related term was the equivalence factor, one gram divided by equivalent weight, which was the numerical factor by which the mass of precipitate had to be multiplied to obtain the mass of analyte.
For example, in the gravimetric determination of nickel
Nickel
Nickel is a chemical element with the chemical symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge. Nickel belongs to the transition metals and is hard and ductile...
, the molar mass of the precipitate bis(dimethylglyoximato
Dimethylglyoxime
Dimethylglyoxime is a chemical compound described by the formula CH3CCCH3. This colourless solid is the dioxime derivative of the diketone diacetyl . DmgH2 is used in the analysis of palladium or nickel. Its coordination complexes are of theoretical interest as models for enzymes and as catalysts...
)nickel [Ni(dmgH)2] is 288.915(7) , while the molar mass of nickel is 58.6934(2) : hence 288.915(7)/58.6934(2) = 4.9224(1) grams of [Ni(dmgH)2] precipitate is equivalent to one gram of nickel and the equivalence factor is 0.203151(5). For example, 215.3±0.1 mg of [Ni(dmgH)2] precipitate is equivalent to (215.3±0.1 mg) × 0.203151(5) = 43.74±0.2 mg of nickel: if the original sample size was 5.346±0.001 g, the nickel content in the original sample would be 0.8182±0.0004%.
Gravimetric analysis is one of the most precise of the common methods of chemical analysis, but it is time-consuming and labour-intensive. It has been largely superseded by other techniques such as atomic absorption spectroscopy
Atomic absorption spectroscopy
Atomic absorption spectroscopy is a spectroanalytical procedure for the qualitative and quantitative determination of chemical elements employing the absorption of optical radiation by free atoms in the gaseous state. In analytical chemistry the technique is used for determining the concentration...
, in which the mass of analyte is read off from a calibration curve
Calibration curve
In analytical chemistry, a calibration curve is a general method for determining the concentration of a substance in an unknown sample by comparing the unknown to a set of standard samples of known concentration...
.
Use in polymer chemistry
Polymer chemistry
Polymer chemistry or macromolecular chemistry is a multidisciplinary science that deals with the chemical synthesis and chemical properties of polymers or macromolecules. According to IUPAC recommendations, macromolecules refer to the individual molecular chains and are the domain of chemistry...
, the equivalent weight of a reactive polymer is the mass of polymer which has one equivalent of reactivity (often, the mass of polymer which corresponds to one mole of reactive side-chain groups). It is widely used to indicate the reactivity of polyol
Polyol
A polyol is an alcohol containing multiple hydroxyl groups. In two technological disciplines the term "polyol" has a special meaning: food science and polymer chemistry.- Polyols in food science :...
, isocyanate
Isocyanate
Isocyanate is the functional group of elements –N=C=O , not to be confused with the cyanate functional group which is arranged as –O–C≡N or with isocyanide, R-N≡C. Any organic compound which contains an isocyanate group may also be referred to in brief as an isocyanate. An isocyanate may have more...
, or epoxy
Epoxy
Epoxy, also known as polyepoxide, is a thermosetting polymer formed from reaction of an epoxide "resin" with polyamine "hardener". Epoxy has a wide range of applications, including fiber-reinforced plastic materials and general purpose adhesives....
thermoset resins which would undergo crosslinking reactions through those functional groups.
It is particularly important for ion-exchange polymers (also called ion-exchange resins): one equivalent of an ion-exchange polymer will exchange one mole of singly charged ions, but only half a mole of doubly charged ions.
Nevertheless, given the decline in use of the term "equivalent weight" in the rest of chemistry, it has become more usual to express the reactivity of a polymer as the inverse of the equivalent weight, that is in units of mmol/g or meq/g.