The fundamentals of atomic-molecular science were first outlined by Lomonosov. In 1741, in one of his first works - “Elements of Mathematical Chemistry” - Lomonosov formulated the most important provisions of the so-called corpuscular theory of the structure of matter that he created.
According to Lomonosov’s ideas, all substances consist of tiny “insensitive” particles, physically indivisible and capable of mutual adhesion. The properties of substances are determined by the properties of these particles. Lomonosov distinguished two types of such particles: smaller ones - “elements”, corresponding to atoms in the modern understanding of this term, and larger ones - “corpuscles”, which we now call molecules.
Each corpuscle has the same composition as the whole substance. Chemically different substances also have corpuscles of different composition. “Corpuscules are homogeneous if they consist of the same number of the same elements, connected in the same way,” and “corpuscles are heterogeneous when their elements are different and connected in different ways or in different numbers.”
From the above definitions it is clear that Lomonosov believed that the reason for the differences in substances was not only the difference in the composition of the corpuscles, but also the different arrangement of elements in the corpuscle.
Lomonosov emphasized that corpuscles move according to the laws of mechanics; Without motion, the corpuscles cannot collide with each other or otherwise act on each other and change. Since all changes in substances are caused by the movement of corpuscles, chemical transformations should be studied not only by the methods of chemistry, but also by the methods of physics and mathematics.
Over the more than 200 years that have passed since Lomonosov lived and worked, his ideas about the structure of matter have undergone comprehensive testing, and their validity has been fully confirmed. Currently, all our ideas about the structure of matter, the properties of substances and the nature of physical and chemical phenomena are based on atomic-molecular science.
The basis of atomic-molecular teaching is the principle of discreteness (discontinuity of structure) of matter: every substance is not something continuous, but consists of individual very small particles. The difference between substances is due to the difference between their particles; Particles of one substance are the same, particles of different substances are different. Under all conditions, particles of matter are in motion; the higher the body temperature, the more intense this movement.
For most substances, the particles are molecules. A molecule is the smallest particle of a substance that has its chemical properties. Molecules, in turn, are made up of atoms. An atom is the smallest particle of an element that has its chemical properties. A molecule can contain a different number of atoms. Thus, the molecules of noble gases are monoatomic, the molecules of substances such as hydrogen, nitrogen are diatomic, water is triatomic, etc. The molecules of the most complex substances - higher proteins and nucleic acids - are built from a number of atoms that is measured in hundreds of thousands.
In this case, atoms can combine with each other not only in different ratios, but also in different ways. Therefore, with a relatively small number of chemical elements, the number of different substances is very large.
Students often wonder why the molecule of a given substance does not have its physical properties. In order to better understand the answer to this question, consider several physical properties of substances, for example, melting and boiling points, heat capacity, mechanical strength, hardness, density, electrical conductivity.
Properties such as melting and boiling points, mechanical strength and hardness are determined by the strength of the bonds between the molecules in a given substance at its given state of aggregation; therefore, applying such concepts to a single molecule does not make sense. Density is a property that an individual molecule has that can be calculated. However, the density of a molecule is always greater than the density of a substance (even in the solid state), because in any substance there is always some free space between the molecules. And such properties as electrical conductivity and heat capacity are determined not by the properties of molecules, but by the structure of the substance as a whole. In order to be convinced of this, it is enough to remember that these properties change greatly when the state of aggregation of a substance changes, while the molecules do not undergo profound changes. Thus, the concepts of some physical properties are not applicable to an individual molecule, while others are applicable, but these properties themselves are different in magnitude for the molecule and for the substance as a whole.
Not in all cases the particles that make up a substance are molecules. Many substances in solid and liquid states, for example most salts, have an ionic structure rather than a molecular one. Some substances have an atomic structure. The structure of solids and liquids will be discussed in more detail in Chapter V, but here we will only point out that in substances with an ionic or atomic structure, the bearer of chemical properties is not molecules, but those combinations of ions or atoms that form the given substance.
Atomic-molecular science- a set of provisions, axioms and laws that describe all substances as a set of molecules consisting of atoms.
Ancient Greek philosophers Long before the beginning of our era, they already put forward the theory of the existence of atoms in their works. Rejecting the existence of gods and otherworldly forces, they tried to explain all incomprehensible and mysterious natural phenomena by natural causes - the connection and separation, interaction and mixing of particles invisible to the human eye - atoms. But for many centuries, church ministers persecuted adherents and followers of the doctrine of atoms and subjected them to persecution. But due to the lack of necessary technical devices, ancient philosophers could not scrupulously study natural phenomena, and under the concept of “atom” they hid the modern concept of “molecule”.
Only in the middle of the 18th century the great Russian scientist M.V. Lomonosov substantiated atomic-molecular concepts in chemistry. The main provisions of his teaching are set out in the work “Elements of Mathematical Chemistry” (1741) and a number of others. Lomonosov named the theory corpuscular-kinetic theory.
M.V. Lomonosov clearly distinguished between two stages in the structure of matter: elements (in the modern sense - atoms) and corpuscles (molecules). The basis of his corpuscular-kinetic theory (modern atomic-molecular teaching) is the principle of discontinuity of the structure (discreteness) of matter: any substance consists of individual particles.
In 1745 M.V. Lomonosov wrote:“An element is a part of a body that does not consist of any smaller and different bodies... Corpuscles are a collection of elements into one small mass. They are homogeneous if they consist of the same number of the same elements connected in the same way. Corpuscles are heterogeneous when their elements are different and connected in different ways or in different numbers; the infinite variety of bodies depends on this.
Molecule is the smallest particle of a substance that has all its chemical properties. Substances having molecular structure, consist of molecules (most non-metals, organic substances). A significant part of inorganic substances consists of atoms(atomic crystal lattice) or ions (ionic structure). Such substances include oxides, sulfides, various salts, diamond, metals, graphite, etc. The carrier of chemical properties in these substances is a combination of elementary particles (ions or atoms), that is, a crystal is a giant molecule.
Molecules are made up of atoms. Atom- the smallest, chemically indivisible component of a molecule.
It turns out that molecular theory explains the physical phenomena that occur with substances. The study of atoms comes to the aid of molecular theory in explaining chemical phenomena. Both of these theories - molecular and atomic - are combined into the atomic-molecular theory. The essence of this doctrine can be formulated in the form of several laws and regulations:
- substances are made up of atoms;
- when atoms interact, simple and complex molecules are formed;
- during physical phenomena, molecules are preserved, their composition does not change; with chemicals - they are destroyed, their composition changes;
- molecules of substances consist of atoms; in chemical reactions, atoms, unlike molecules, are preserved;
- the atoms of one element are similar to each other, but different from the atoms of any other element;
- chemical reactions involve the formation of new substances from the same atoms that made up the original substances.
Thanks to its atomic-molecular theory M.V. Lomonosov is rightfully considered the founder of scientific chemistry.
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Lecture topic: BASIC CONCEPTS AND LAWS OF CHEMISTRY.
Plan:
BASIC CONCEPTS OF CHEMISTRY. ATOMIC-MOLECULAR TEACHING
BASIC LAWS OF CHEMISTRY
BASIC GAS LAWS
CHEMICAL EQUIVALENT. LAW OF EQUIVALENT RELATIONS
CHEMICAL REACTIONS. CLASSIFICATION OF CHEMICAL REACTIONS
THE PLACE OF CHEMISTRY AMONG OTHER SCIENCES
Chemistry refers to the natural sciences that study the material world around us, its phenomena and laws.
The basic law of nature is the law of the eternity of matter and its motion. Separate forms of motion of matter are studied by separate sciences. The place of chemistry, which deals primarily with the molecular (and atomic) level of organization of matter, is between particle physics (subatomic level) and biology (supramolecular level).
Chemistry- the science of substances, their composition, structure, properties and transformations associated with changes in the composition, structure and properties of the particles that form them.
The great Russian scientist M.V. Lomonosov said: “Chemistry extends its hands widely into human affairs.” Indeed, there is practically no technical discipline that could do without knowledge of chemistry. Even such modern and seemingly distant sciences as electronics and computer science have today received a new impetus in their development by concluding an “alliance” with chemistry (recording information at the molecular level, developing biocomputers, etc.). What then can we say about the fundamental disciplines: physics, biology, etc., where independent sections bordering on chemistry have long existed (chemical physics, biochemistry, geochemistry, etc.).
BASIC CONCEPTS OF CHEMISTRY.
ATOMIC-MOLECULAR TEACHING
The idea of atoms as structural elements of the material world originated in ancient Greece (Leucippus, Democritus, 1st-3rd centuries BC). But only at the end of the 18th - beginning of the 19th centuries. Atomic-molecular science was created. The most important contribution to the generalization of the accumulated material was made by M. V. Lomonosov.
Atomic-molecular teaching includes the following basic principles:
1. All substances are not solid, but consist of particles (molecules, atoms, ions).
2. Molecules are made up of atoms (elements).
3. Differences between substances are determined by the differences in the particles that form them, which differ from each other in composition, structure and properties.
4. All particles are in constant motion, the speed of which increases when heated.
Atom- the smallest particle of a chemical element that is the carrier of its properties. This is an electrically neutral microsystem, the behavior of which obeys the laws of quantum mechanics.
Chemical element- a type of atoms that have the same positive nuclear charge and are characterized by a certain set of properties.
Isotopes- atoms of the same element that differ in mass (the number of neutrons in the nucleus).
Any chemical element in nature is represented by a certain isotopic composition, therefore its mass is calculated as a certain average value from the masses of isotopes, taking into account their content in nature.
Molecule- the smallest particle of a substance that is the bearer of its properties and is capable of independent existence.
Simple substance- a substance whose molecules consist only of atoms of one element.
Allotropy- the ability of an element to form simple substances having different composition, structure and properties.
Varieties of allotropic modifications are defined:
A different number of atoms of an element in the molecule of a simple substance, for example, oxygen (O 2) and ozone (O 3).
Differences in the structure of the crystal lattice of a simple substance, for example, a carbon compound: graphite (flat, or two-dimensional, lattice) and diamond (volumetric, or three-dimensional lattice).
Complex substance- a substance whose molecules consist of atoms of different elements.
Complex substances consisting of only two elements are called binary, for example:
Ø oxides: CO, CO 2, CaO, Na 2 O, FeO, Fe 2 O 3;
Ø sulfides: ZnS, Na 2 S, CS 2;
Ø hydrides: CaH 2, LiH, NaH;
Ø nitrides: Li 3 N, Ca 3 N 2, AlN;
Ø phosphides: Li 3 P, Mg 3 P 2, AlP;
Ø carbides: Be 2 C, Al 4 C 3, Ag 2 C 2;
Ø silicides: Ca 2 Si, Na 4 Si.
Complex compounds consisting of more than two elements belong to the main classes of inorganic compounds. These are hydroxides (acids and bases) and salts, including complex compounds.
Atoms and molecules have absolute mass, for example, the mass of a C 12 atom is 2·10 -26 kg.
It is inconvenient to use such quantities in practice, which is why the relative mass scale is adopted in chemistry.
Atomic mass unit(a.u.m.) is equal to 1/12 of the mass of the C 12 isotope.
Relative atomic mass (A r- dimensionless quantity) is equal to the ratio of the average mass of an atom to a. eat.
Relative molecular weight (M r- dimensionless quantity) is equal to the ratio of the average mass of a molecule to a. eat.
Mole(ν - “nude” or n) - the amount of a substance containing the same number of structural units (atoms, molecules or ions) as there are atoms in 12 g of the C 12 isotope.
Avogadro's number- the number of particles (atoms, molecules, ions, etc.) contained in 1 mole of any substance.
N A = 6.02·10 23.
More precise values of some fundamental constants are given in the tables in the appendix.
Molar mass of the substance (M) is the mass of 1 mole of a substance. It is calculated as the ratio of the mass of a substance to its quantity:
The molar mass is numerically equal A r(for atoms) or M r(for molecules).
From equation 1, you can determine the amount of a substance if its mass and molar mass are known:
(2)
Molar volume (V m for gases) is the volume of one mole of a substance. It is calculated as the ratio of the volume of gas to its quantity:
(3)
Volume of 1 mole of any gas under normal conditions (P = 1 atm = 760 mm. rt. Art. = 101.3 kPa; T = 273TS = 0°C) is equal to 22.4 l.
(4)
The density of a substance is equal to the ratio of its mass to volume.
(5)
§ 1 M.V. Lomonosov as the founder of atomic-molecular science
Since the 17th century, science has had molecular teaching, which has been used to explain physical phenomena. The practical application of molecular theory in chemistry was limited by the fact that its provisions could not explain the essence of the occurrence of chemical reactions or answer the question of how new substances are formed from some substances during a chemical process.
The solution to this issue turned out to be possible on the basis of atomic-molecular theory. In 1741, in the book “Elements of Mathematical Chemistry,” Mikhail Vasilyevich Lomonosov actually formulated the foundations of atomic-molecular science. The Russian scientist-encyclopedist considered the structure of matter not as a specific combination of atoms, but as a combination of larger particles - corpuscles, which, in turn, consist of smaller particles - elements.
Lomonosov's terminology underwent changes over time: what he called corpuscles began to be called molecules, and the term element was replaced by the term atom. However, the essence of the ideas and definitions he expressed brilliantly stood the test of time.
§ 2 History of the development of atomic-molecular science
The history of the development and establishment of atomic-molecular science in science turned out to be very difficult. Working with objects of the microworld caused enormous difficulties: atoms and molecules were impossible to see and, thus, verify their existence, and attempts to measure atomic masses often ended in obtaining erroneous results. 67 years after Lomonosov's discovery, in 1808, the famous English scientist John Dalton put forward the atomic hypothesis. According to it, atoms are the smallest particles of matter that cannot be divided into their component parts or converted into each other. According to Dalton, all atoms of one element have exactly the same weight and are different from the atoms of other elements. By combining the theory of atoms with the theory of chemical elements developed by Robert Boyle and Mikhail Vasilyevich Lomonosov, Dalton provided a solid foundation for further theoretical research in chemistry. Unfortunately, Dalton denied the existence of molecules in simple substances. He believed that only complex substances consist of molecules. This did not contribute to the further development and application of atomic-molecular teaching.
The conditions for the dissemination of the ideas of atomic-molecular science in natural sciences developed only in the second half of the 19th century. In 1860, at the International Congress of Natural Scientists in the German city of Karlsruhe, scientific definitions of the atom and molecule were adopted. There was no study of the structure of substances at that time, so it was accepted that all substances consist of molecules. It was believed that simple substances, such as metals, consist of monatomic molecules. Subsequently, such a complete extension of the principle of molecular structure to all substances turned out to be erroneous.
§ 3 Basic provisions of atomic-molecular teaching
1. A molecule is the smallest part of a substance that retains its composition and most important properties.
2. Molecules are made up of atoms. Atoms of one element are similar to each other, but different from atoms of other chemical elements.
Basic concepts of chemistry, laws of stoichiometry
Chemical atomism (atomic-molecular theory) is historically the first fundamental theoretical concept that forms the basis of modern chemical science. The formation of this theory took more than a hundred years and is associated with the activities of such outstanding chemists as M.V. Lomonosov, A.L. Lavoisier, J. Dalton, A. Avogadro, S. Cannizzaro.
Modern atomic-molecular theory can be presented in the form of a number of provisions:
1. Chemical substances have a discrete (discontinuous) structure. Particles of matter are in constant chaotic thermal motion.
2. The basic structural unit of a chemical substance is the atom.
3. Atoms in a chemical substance are bonded to each other to form molecular particles or atomic aggregates (supramolecular structures).
4. Complex substances (or chemical compounds) consist of atoms of different elements. Simple substances consist of atoms of one element and should be considered as homonuclear chemical compounds.
When formulating the basic principles of the atomic-molecular theory, we had to introduce several concepts that need to be discussed in more detail, since they are fundamental in modern chemistry. These are the concepts of “atom” and “molecule,” more precisely, atomic and molecular particles.
Atomic particles include the atom itself, atomic ions, atomic radicals, and atomic radical ions.
An atom is the smallest electrically neutral particle of a chemical element, which is the carrier of its chemical properties, and consists of a positively charged nucleus and an electron shell.
Atomic ion is an atomic particle that has an electrostatic charge, but does not have unpaired electrons, for example, Cl - is a chloride anion, Na + is a sodium cation.
Atomic radical- an electrically neutral atomic particle containing unpaired electrons. For example, the hydrogen atom is actually an atomic radical - H × .
An atomic particle that has an electrostatic charge and unpaired electrons is called atomic radical ion. An example of such a particle is the Mn 2+ cation, which contains five unpaired electrons at the d-sublevel (3d 5).
One of the most important physical characteristics of an atom is its mass. Since the absolute value of the mass of an atom is negligible (the mass of a hydrogen atom is 1.67 × 10 -27 kg), chemistry uses a relative mass scale, in which 1/12 of the mass of a carbon atom of isotope-12 is chosen as a unit. Relative atomic mass is the ratio of the mass of an atom to 1/12 the mass of a carbon atom of the 12 C isotope.
It should be noted that in the periodic system D.I. Mendeleev presents the average isotopic atomic masses of elements, which are mostly represented by several isotopes that contribute to the atomic mass of an element in proportion to their content in nature. Thus, the element chlorine is represented by two isotopes - 35 Cl (75 mol.%) and 37 Cl (25 mol.%). The average isotopic mass of the element chlorine is 35.453 amu. (atomic mass units) (35×0.75 + 37×0.25).
Similar to atomic particles, molecular particles include molecules themselves, molecular ions, molecular radicals, and radical ions.
A molecular particle is the smallest stable collection of interconnected atomic particles, which is the bearer of the chemical properties of a substance. The molecule is devoid of electrostatic charge and has no unpaired electrons.
molecular ion is a molecular particle that has an electrostatic charge, but does not have unpaired electrons, for example, NO 3 - is a nitrate anion, NH 4 + is an ammonium cation.
molecular radical is an electrically neutral molecular particle containing unpaired electrons. Most radicals are reaction particles with a short lifetime (on the order of 10 -3 -10 -5 s), although quite stable radicals are currently known. So methyl radical × CH 3 is a typical unstable particle. However, if the hydrogen atoms in it are replaced by phenyl radicals, then a stable molecular radical triphenylmethyl is formed
Molecules with an odd number of electrons, such as NO or NO 2 , can also be considered highly stable free radicals.
A molecular particle that has an electrostatic charge and unpaired electrons is called molecular radical ion. An example of such a particle is the oxygen radical cation – ×O 2 + .
An important characteristic of a molecule is its relative molecular weight. Relative molecular mass (M r) is the ratio of the average isotopic mass of a molecule, calculated taking into account the natural content of isotopes, to 1/12 of the mass of a carbon atom of the 12 C isotope.
Thus, we have found out that the smallest structural unit of any chemical substance is an atom, or rather an atomic particle. In turn, in any substance, excluding inert gases, atoms are connected to each other by chemical bonds. In this case, the formation of two types of substances is possible:
· molecular compounds in which it is possible to isolate the smallest carriers of chemical properties that have a stable structure;
· compounds of a supramolecular structure, which are atomic aggregates in which atomic particles are linked by covalent, ionic or metallic bonds.
Accordingly, substances having a supramolecular structure are atomic, ionic or metallic crystals. In turn, molecular substances form molecular or molecular-ionic crystals. Substances that are under normal conditions in a gaseous or liquid state of aggregation also have a molecular structure.
In fact, when working with a specific chemical substance, we are not dealing with individual atoms or molecules, but with a collection of a very large number of particles, the levels of organization of which can be represented by the following diagram:
For a quantitative description of large arrays of particles, which are macrobodies, a special concept of “amount of matter” was introduced, as a strictly defined number of its structural elements. The unit of quantity of a substance is the mole. A mole is an amount of substance(n) , containing as many structural or formula units as there are atoms contained in 12 g of carbon isotope 12 C. Currently, this number is quite accurately measured and is 6.022 × 10 23 (Avogadro's number, N A). Atoms, molecules, ions, chemical bonds and other objects of the microworld can act as structural units. The concept of “formula unit” is used for substances with a supramolecular structure and is defined as the simplest relationship between its constituent elements (gross formula). In this case, the formula unit takes on the role of a molecule. For example, 1 mole of calcium chloride contains 6.022×10 23 formula units - CaCl 2.
One of the important characteristics of a substance is its molar mass (M, kg/mol, g/mol). Molar mass is the mass of one mole of a substance. The relative molecular mass and molar mass of a substance are numerically the same, but have different dimensions, for example, for water M r = 18 (relative atomic and molecular masses are dimensionless values), M = 18 g/mol. The amount of substance and molar mass are related by a simple relationship:
The basic stoichiometric laws that were formulated at the turn of the 17th and 18th centuries played a major role in the formation of chemical atomism.
1. Law of conservation of mass (M.V. Lomonosov, 1748).
The sum of the masses of the reaction products is equal to the sum of the masses of the substances that interacted. In mathematical form, this law is expressed by the following equation:
An addition to this law is the law of conservation of mass of an element (A. Lavoisier, 1789). According to this law During a chemical reaction, the mass of each element remains constant.
Laws M.V. Lomonosova and A. Lavoisier found a simple explanation within the framework of atomic theory. Indeed, during any reaction, the atoms of chemical elements remain unchanged and in constant quantities, which entails both the constancy of the mass of each element individually and the system of substances as a whole.
The laws under consideration are of decisive importance for chemistry, since they allow one to model chemical reactions using equations and perform quantitative calculations based on them. It should be noted, however, that the law of conservation of mass is not absolutely accurate. As follows from the theory of relativity (A. Einstein, 1905), any process that occurs with the release of energy is accompanied by a decrease in the mass of the system in accordance with the equation:
where DE is the released energy, Dm is the change in the mass of the system, c is the speed of light in vacuum (3.0×10 8 m/s). As a result, the equation of the law of conservation of mass should be written in the following form:
Thus, exothermic reactions are accompanied by a decrease in mass, and endothermic reactions are accompanied by an increase in mass. In this case, the law of conservation of mass can be formulated as follows: in an isolated system the sum of masses and reduced energies is a constant quantity. However, for chemical reactions whose thermal effects are measured in hundreds of kJ/mol, the mass defect is 10 -8 -10 -9 g and cannot be detected experimentally.
2. Law of Constancy of Composition (J. Proust, 1799-1804).
An individual chemical substance of molecular structure has a constant qualitative and quantitative composition, independent of the method of its preparation.. Compounds that obey the law of constant composition are called colorblind. Daltonides are all currently known organic compounds (about 30 million) and part (about 100 thousand) of inorganic substances. Substances having a non-molecular structure ( Bertolides), do not obey this law and may have a variable composition, depending on the method of obtaining the sample. These include the majority (about 500 thousand) of inorganic substances. These are mainly binary compounds of d-elements (oxides, sulfides, nitrides, carbides, etc.). An example of a compound of variable composition is titanium(III) oxide, the composition of which varies from TiO 1.46 to TiO 1.56. The reason for the variable composition and irrationality of the Bertolide formulas are changes in the composition of some of the elementary cells of the crystal (defects in the crystal structure), which do not entail a sharp change in the properties of the substance. For Daltonids, such a phenomenon is impossible, since a change in the composition of the molecule leads to the formation of a new chemical compound.
3. Law of equivalents (I. Richter, J. Dalton, 1792-1804).
The masses of reacting substances are directly proportional to their equivalent masses.
where E A and E B are the equivalent masses of the reacting substances.
The equivalent mass of a substance is the molar mass of its equivalent.
An equivalent is a real or conditional particle that donates or gains one hydrogen cation in acid-base reactions, one electron in redox reactions, or interacts with one equivalent of any other substance in exchange reactions. For example, when metallic zinc reacts with an acid, one zinc atom displaces two hydrogen atoms, giving up two electrons:
Zn + 2H + = Zn 2+ + H 2
Zn 0 - 2e - = Zn 2+
Therefore, the equivalent of zinc is 1/2 of its atom, i.e. 1/2 Zn (conditional particle).
The number showing which part of the molecule or formula unit of a substance is its equivalent is called the equivalence factor - f e. Equivalent mass, or molar mass of equivalent, is defined as the product of the equivalence factor and the molar mass:
For example, in a neutralization reaction, sulfuric acid gives up two hydrogen cations:
H 2 SO 4 + 2KOH = K 2 SO 4 + 2H 2 O
Accordingly, the equivalent of sulfuric acid is 1/2 H 2 SO 4, the equivalence factor is 1/2, and the equivalent mass is (1/2) × 98 = 49 g/mol. Potassium hydroxide binds one hydrogen cation, so its equivalent is the formula unit, the equivalence factor is equal to one, and the equivalent mass is equal to the molar mass, i.e. 56 g/mol.
From the examples considered, it is clear that when calculating the equivalent mass, it is necessary to determine the equivalence factor. There are a number of rules for this:
1. The equivalence factor of an acid or base is equal to 1/n, where n is the number of hydrogen cations or hydroxide anions involved in the reaction.
2. The salt equivalence factor is equal to the quotient of unity divided by the product of the valency (v) of the metal cation or acid residue and their number (n) in the salt (stoichiometric index in the formula):
For example, for Al 2 (SO 4) 3 - f e = 1/6
3. The equivalence factor of an oxidizing agent (reducing agent) is equal to the quotient of unity divided by the number of electrons attached (donated) by it.
Attention should be paid to the fact that the same compound may have a different equivalence factor in different reactions. For example, in acid-base reactions:
H 3 PO 4 + KOH = KH 2 PO 4 + H 2 O f e (H 3 PO 4) = 1
H 3 PO 4 + 2KOH = K 2 HPO 4 + 2H 2 O f e (H 3 PO 4) = 1/2
H 3 PO 4 + 3KOH = K 3 PO 4 + 3H 2 O f e (H 3 PO 4) = 1/3
or in redox reactions:
KMn 7+ O 4 + NaNO 2 + H 2 SO 4 ® Mn 2+ SO 4 + NaNO 3 + K 2 SO 4 + H 2 O
MnO 4 - + 8H + + 5e - ® Mn 2+ + 4H 2 O f e (KMnO 4) = 1/5
