Collection of basic formulas for a school chemistry course

G. P. Loginova

Elena Savinkina

E. V. Savinkina G. P. Loginova

Collection of basic formulas in chemistry

Student's Pocket Guide

general chemistry

The most important chemical concepts and laws

Chemical element- this is a certain type of atom with the same nuclear charge.

Relative atomic mass(A r) shows how many times the mass of an atom of a given chemical element is greater than the mass of a carbon-12 atom (12 C).

Chemical substance– a collection of any chemical particles.

Chemical particles

Formula unit– a conventional particle, the composition of which corresponds to the given chemical formula, for example:

Ar – argon substance (consists of Ar atoms),

H 2 O – the substance water (consists of H 2 O molecules),

KNO 3 – potassium nitrate substance (consists of K + cations and NO 3 ¯ anions).

Relationships between physical quantities

Atomic mass (relative) of the element B, A r (B):

Where *T(atom B) – mass of an atom of element B;

*t and– atomic mass unit;

*t and = 1/12 T(12 C atom) = 1.6610 24 g.

Quantity of substance B, n(B), mol:

Where N(B)– number of particles B;

N A– Avogadro’s constant (N A = 6.0210 23 mol -1).

Molar mass of a substance V, M(V), g/mol:

Where t(V)– mass B.

Molar volume of gas IN, V M l/mol:

Where V M = 22.4 l/mol (a consequence of Avogadro’s law), under normal conditions (no. – atmospheric pressure p = 101,325 Pa (1 atm); thermodynamic temperature T = 273.15 K or Celsius temperature t = 0 °C).

B for hydrogen, D(gas B by H 2):

*Density of gaseous substance IN by air, D(gas B over air): Mass fraction of element E in matter V, w(E):

Where x is the number of E atoms in the formula of substance B

The structure of the atom and the Periodic Law D.I. Mendeleev

Mass number (A) – the total number of protons and neutrons in the atomic nucleus:

A = N(p 0) + N(p +).

Atomic nuclear charge (Z) equal to the number of protons in the nucleus and the number of electrons in the atom:

Z = N(p+) = N(e¯).

Isotopes– atoms of the same element, differing in the number of neutrons in the nucleus, for example: potassium-39: 39 K (19 p + , 20n 0, 19e¯); potassium-40: 40 K (19 p+, 21n 0, 19e¯).

*Energy levels and sublevels

*Atomic orbital(AO) characterizes the region of space in which the probability of an electron having a certain energy being located is greatest.

*Shapes of s- and p-orbitals

Periodic law and periodic system D.I. Mendeleev

The properties of elements and their compounds are periodically repeated with increasing atomic number, which is equal to the charge of the nucleus of the element’s atom.

Period number corresponds number of energy levels filled with electrons, and stands for the last energy level to be filled(EU).

Group number A shows And etc.

Group number B shows number of valence electrons ns And (n – 1)d.

S-elements section– the energy sublevel (ESL) is filled with electrons ns-EPU– IA- and IIA-groups, H and He.

p-elements section– filled with electrons np-EPU– IIIA-VIIIA-groups.

D-elements section– filled with electrons (P- 1) d-EPU – IB-VIIIB2-groups.

f-elements section– filled with electrons (P-2) f-EPU – lanthanides and actinides.

Changes in the composition and properties of hydrogen compounds of elements of the 3rd period of the Periodic Table

Non-volatile, decomposes with water: NaH, MgH 2, AlH 3.

Volatile: SiH 4, PH 3, H 2 S, HCl.

Changes in the composition and properties of higher oxides and hydroxides of elements of the 3rd period of the Periodic Table

Basic: Na 2 O – NaOH, MgO – Mg(OH) 2.

Amphoteric: Al 2 O 3 – Al(OH) 3.

Acidic: SiO 2 – H 4 SiO 4, P 2 O 5 – H 3 PO 4, SO 3 – H 2 SO 4, Cl 2 O 7 – HClO 4.

Chemical bond

Electronegativity(χ) is a quantity characterizing the ability of an atom in a molecule to acquire a negative charge.

Mechanisms of covalent bond formation

Exchange mechanism- the overlap of two orbitals of neighboring atoms, each of which had one electron.

Donor-acceptor mechanism– overlap of a free orbital of one atom with an orbital of another atom that contains a pair of electrons.

Overlap of orbitals during bond formation

*Type of hybridization – geometric shape of the particle – angle between bonds

Hybridization of central atom orbitals– alignment of their energy and form.

sp– linear – 180°

sp 2– triangular – 120°

sp 3– tetrahedral – 109.5°

sp 3 d– trigonal-bipyramidal – 90°; 120°

sp 3 d 2– octahedral – 90°

Mixtures and solutions

Solution- a homogeneous system consisting of two or more substances, the content of which can be varied within certain limits.

Solution: solvent (eg water) + solute.

True solutions contain particles smaller than 1 nanometer.

Colloidal solutions contain particles ranging in size from 1 to 100 nanometers.

Mechanical mixtures(suspensions) contain particles larger than 100 nanometers.

Suspension=> solid + liquid

Emulsion=> liquid + liquid

Foam, fog=> gas + liquid

Heterogeneous mixtures are separated settling and filtering.

Homogeneous mixtures are separated evaporation, distillation, chromatography.

Saturated solution is or may be in equilibrium with the solute (if the solute is solid, then its excess is in the precipitate).

Solubility– the content of the dissolved substance in a saturated solution at a given temperature.

Unsaturated solution less,

Supersaturated solution contains solute more, than its solubility at a given temperature.

Relationships between physicochemical quantities in solution

Mass fraction of solute IN, w(B); fraction of a unit or %:

Where t(V)– mass B,

t(r)– mass of solution.

Weight of solution, m(p), g:

m(p) = m(B) + m(H 2 O) = V(p) ρ(p),

where F(p) is the volume of the solution;

ρ(p) – solution density.

Volume of solution, V(p), l:

Molar concentration, s(V), mol/l:

Where n(B) is the amount of substance B;

M(B) – molar mass of substance B.

Changing the composition of the solution

Diluting the solution with water:

> t"(V)= t(B);

> the mass of the solution increases by the mass of added water: m"(p) = m(p) + m(H 2 O).

Evaporating water from a solution:

> the mass of the solute does not change: t"(B) = t(B).

> the mass of the solution decreases by the mass of evaporated water: m"(p) = m(p) – m(H 2 O).

Merging two solutions: The masses of solutions, as well as the masses of the dissolved substance, add up:

t"(B) = t(B) + t"(B);

t"(p) = t(p) + t"(p).

Crystal Drop: the mass of the solute and the mass of the solution are reduced by the mass of precipitated crystals:

m"(B) = m(B) – m(sediment); m"(p) = m(p) – m(sediment).

The mass of water does not change.

Thermal effect of a chemical reaction

*Enthalpy of formation of a substance ΔH°(B), kJ/mol, is the enthalpy of the reaction of formation of 1 mole of a substance from simple substances in their standard states, that is, at constant pressure (1 atm for each gas in the system or at a total pressure of 1 atm in the absence of gaseous reaction participants) and constant temperature (usually 298 K , or 25 °C).

*Thermal effect of a chemical reaction (Hess’s law)

Q = ΣQ(products) – ΣQ(reagents).

ΔН° = ΣΔН°(products) – Σ ΔН°(reagents).

For reaction aA + bB +… = dD + eE +…

ΔH° = (dΔH°(D) + eΔH°(E) +…) – (aΔH°(A) + bΔH°(B) +…),

Where a, b, d, e– stoichiometric amounts of substances corresponding to the coefficients in the reaction equation.

Chemical reaction rate

If during time τ in volume V the amount of reactant or product changed by Δ n, speed reaction:

For a monomolecular reaction A → …:

v = k c(A).

For the bimolecular reaction A + B → ...:

v = k c(A) c(B).

For the trimolecular reaction A + B + C → ...:

v = k c(A) c(B) c(C).

Changing the rate of a chemical reaction

Speed reaction increase:

1) chemically active reagents;

2) promotion reagent concentrations;

3) increase

4) promotion temperature;

5) catalysts. Speed reaction reduce:

1) chemically inactive reagents;

2) demotion reagent concentrations;

3) decrease surfaces of solid and liquid reagents;

4) demotion temperature;

5) inhibitors.

*Temperature speed coefficient(γ) is equal to a number that shows how many times the reaction rate increases when the temperature increases by ten degrees:

Chemical equilibrium

*Law of mass action for chemical equilibrium: in a state of equilibrium, the ratio of the product of the molar concentrations of products in powers equal to

Their stoichiometric coefficients, to the product of the molar concentrations of the reactants in powers equal to their stoichiometric coefficients, at a constant temperature is a constant value (concentration equilibrium constant).

In a state of chemical equilibrium for a reversible reaction:

aA + bB + … ↔ dD + fF + …

K c = [D] d [F] f .../ [A] a [B] b ...

*Shift in chemical equilibrium towards the formation of products

1) Increasing the concentration of reagents;

2) reducing the concentration of products;

3) increase in temperature (for an endothermic reaction);

4) decrease in temperature (for an exothermic reaction);

5) increase in pressure (for a reaction occurring with a decrease in volume);

6) decrease in pressure (for a reaction occurring with an increase in volume).

Exchange reactions in solution

Electrolytic dissociation– the process of formation of ions (cations and anions) when certain substances are dissolved in water.

acids are formed hydrogen cations And acid anions, For example:

HNO 3 = H + + NO 3 ¯

During electrolytic dissociation reasons are formed metal cations and hydroxide ions, for example:

NaOH = Na + + OH¯

During electrolytic dissociation salts(medium, double, mixed) are formed metal cations and acid anions, for example:

NaNO 3 = Na + + NO 3 ¯

KAl(SO 4) 2 = K + + Al 3+ + 2SO 4 2-

During electrolytic dissociation acid salts are formed metal cations and acid hydroanions, for example:

NaHCO 3 = Na + + HCO 3 ‾

Some strong acids

HBr, HCl, HClO 4, H 2 Cr 2 O 7, HI, HMnO 4, H 2 SO 4, H 2 SeO 4, HNO 3, H 2 CrO 4

Some strong reasons

RbOH, CsOH, KOH, NaOH, LiOH, Ba(OH) 2, Sr(OH) 2, Ca(OH) 2

Dissociation degree α– the ratio of the number of dissociated particles to the number of initial particles.

At constant volume:

Classification of substances by degree of dissociation

Berthollet's rule

Exchange reactions in solution proceed irreversibly if the result is the formation of a precipitate, gas, or weak electrolyte.

Examples of molecular and ionic reaction equations

1. Molecular equation: CuCl 2 + 2NaOH = Cu(OH) 2 ↓ + 2NaCl

“Complete” ionic equation: Сu 2+ + 2Сl¯ + 2Na + + 2OH¯ = Cu(OH) 2 ↓ + 2Na + + 2Сl¯

“Short” ionic equation: Cu 2+ + 2OH¯ = Cu(OH) 2 ↓

2. Molecular equation: FeS (T) + 2HCl = FeCl 2 + H 2 S

“Complete” ionic equation: FeS + 2H + + 2Сl¯ = Fe 2+ + 2Сl¯ + H 2 S

“Short” ionic equation: FeS (T) + 2H + = Fe 2+ + H 2 S

3. Molecular equation: 3HNO 3 + K 3 PO 4 = H 3 PO 4 + 3KNO 3

“Complete” ionic equation: 3H + + 3NO 3 ¯ + 3K + + PO 4 3- = H 3 PO 4 + 3K + + 3NO 3 ¯

“Short” ionic equation: 3H + + PO 4 3- = H 3 PO 4

*Hydrogen index

(pH) pH = – log = 14 + log

*pH range for dilute aqueous solutions

pH 7 (neutral environment)

Examples of exchange reactions

Neutralization reaction- an exchange reaction that occurs when an acid and a base interact.

1. Alkali + strong acid: Ba(OH) 2 + 2HCl = BaCl 2 + 2H 2 O

Ba 2+ + 2ON¯ + 2H + + 2Сl¯ = Ba 2+ + 2Сl¯ + 2Н 2 O

H + + OH¯ = H 2 O

2. Slightly soluble base + strong acid: Cu(OH) 2(t) + 2HCl = CuCl 2 + 2H 2 O

Cu(OH) 2 + 2H + + 2Cl¯ = Cu 2+ + 2Cl¯ + 2H 2 O

Cu(OH) 2 + 2H + = Cu 2+ + 2H 2 O

*Hydrolysis– an exchange reaction between a substance and water without changing the oxidation states of atoms.

1. Irreversible hydrolysis of binary compounds:

Mg 3 N 2 + 6H 2 O = 3Mg(OH) 2 + 2NH 3

2. Reversible hydrolysis of salts:

A) Salt is formed a strong base cation and a strong acid anion:

NaCl = Na + + Сl¯

Na + + H 2 O ≠ ;

Cl¯ + H 2 O ≠

There is no hydrolysis; neutral environment, pH = 7.

B) Salt is formed a strong base cation and a weak acid anion:

Na 2 S = 2Na + + S 2-

Na + + H 2 O ≠

S 2- + H 2 O ↔ HS¯ + OH¯

Hydrolysis by anion; alkaline environment, pH >7.

B) Salt is formed a cation of a weak or slightly soluble base and an anion of a strong acid:

End of introductory fragment.

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Key words: Chemistry 8th grade. All formulas and definitions, symbols of physical quantities, units of measurement, prefixes for designating units of measurement, relationships between units, chemical formulas, basic definitions, briefly, tables, diagrams.

1. Symbols, names and units of measurement
some physical quantities used in chemistry

Physical quantity	Designation	Unit
Time	t	With
Pressure	p	Pa, kPa
Quantity of substance	ν	mole
Mass of substance	m	kg, g
Mass fraction	ω	Dimensionless
Molar mass	M	kg/mol, g/mol
Molar volume	Vn	m 3 /mol, l/mol
Volume of substance	V	m 3, l
Volume fraction		Dimensionless
Relative atomic mass	A r	Dimensionless
	Mr	Dimensionless
Relative density of gas A to gas B	D B (A)	Dimensionless
Density of matter	R	kg/m 3, g/cm 3, g/ml
Avogadro's constant	N A	1/mol
Absolute temperature	T	K (Kelvin)
Temperature in Celsius	t	°C (degrees Celsius)
Thermal effect of a chemical reaction	Q	kJ/mol

2. Relationships between units of physical quantities

3. Chemical formulas in 8th grade

4. Basic definitions in 8th grade

Atom- the smallest chemically indivisible particle of a substance.
Chemical element- a certain type of atom.
Molecule- the smallest particle of a substance that retains its composition and chemical properties and consists of atoms.
Simple substances- substances whose molecules consist of atoms of the same type.
Complex substances- substances whose molecules consist of atoms of different types.
Qualitative composition of the substance shows which atoms of elements it consists of.
Quantitative composition of the substance shows the number of atoms of each element in its composition.
Chemical formula- conventional recording of the qualitative and quantitative composition of a substance using chemical symbols and indices.
Atomic mass unit(amu) - a unit of measurement of atomic mass, equal to the mass of 1/12 of a carbon atom 12 C.
Mole- the amount of a substance that contains a number of particles equal to the number of atoms in 0.012 kg of carbon 12 C.
Avogadro's constant (Na = 6*10 23 mol -1) - the number of particles contained in one mole.
Molar mass of a substance (M ) is the mass of a substance taken in an amount of 1 mole.
Relative atomic mass element A r - the ratio of the mass of an atom of a given element m 0 to 1/12 of the mass of a carbon atom 12 C.
Relative molecular weight substances M r - the ratio of the mass of a molecule of a given substance to 1/12 of the mass of a carbon atom 12 C. The relative molecular mass is equal to the sum of the relative atomic masses of the chemical elements forming the compound, taking into account the number of atoms of a given element.
Mass fraction chemical element ω(X) shows what part of the relative molecular mass of substance X is accounted for by a given element.

ATOMIC-MOLECULAR TEACHING
1. There are substances with molecular and non-molecular structure.
2. There are gaps between the molecules, the sizes of which depend on the state of aggregation of the substance and temperature.
3. Molecules are in continuous motion.
4. Molecules are made up of atoms.
6. Atoms are characterized by a certain mass and size.
During physical phenomena, molecules are preserved; during chemical phenomena, as a rule, they are destroyed. Atoms rearrange during chemical phenomena, forming molecules of new substances.

LAW OF CONSTANT COMPOSITION OF MATTER
Each chemically pure substance of molecular structure, regardless of the method of preparation, has a constant qualitative and quantitative composition.

VALENCE
Valence is the property of an atom of a chemical element to attach or replace a certain number of atoms of another element.

CHEMICAL REACTION
A chemical reaction is a phenomenon as a result of which other substances are formed from one substance. Reactants are substances that enter into a chemical reaction. Reaction products are substances formed as a result of a reaction.
Signs of chemical reactions:
1. Release of heat (light).
2. Change in color.
3. Odor appears.
4. Formation of sediment.
5. Gas release.

Magnitude and its dimension	Ratio
Atomic mass of element X (relative)
Element serial number	Z= N(e –) = N(R +)
Mass fraction of element E in substance X, in fractions of a unit, in %)
Amount of substance X, mol
Amount of gas substance, mol	V m= 22.4 l/mol (n.s.) Well. – R= 101 325 Pa, T= 273 K
Molar mass of substance X, g/mol, kg/mol
Mass of substance X, g, kg	m(X) = n(X) M(X)
Molar volume of gas, l/mol, m 3 /mol	V m= 22.4 l/mol at N.S.
Gas volume, m 3	V = V m × n
Product yield
Density of substance X, g/l, g/ml, kg/m3
Density of gaseous substance X by hydrogen
Density of gaseous substance X in air	M(air) = 29 g/mol
United Gas Law
Mendeleev-Clapeyron equation	PV = nRT, R= 8.314 J/mol×K
Volume fraction of a gaseous substance in a mixture of gases, in fractions of a unit or in %
Molar mass of a mixture of gases
Mole fraction of a substance (X) in a mixture
Amount of heat, J, kJ	Q = n(X) Q(X)
Thermal effect of reaction	Q =–H
Heat of formation of substance X, J/mol, kJ/mol
Chemical reaction rate (mol/lsec)
Law of Mass Action (for a simple reaction)	a A+ V B= With C + d D u = k With a(A) With V(B)
Van't Hoff's rule
Solubility of the substance (X) (g/100 g solvent)
Mass fraction of substance X in mixture A + X, in fractions of a unit, in %
Weight of solution, g, kg	m(rr) = m(X)+ m(H2O) m(rr) = V(rr)  (rr)
Mass fraction of dissolved substance in solution, in fractions of a unit, in %
Solution density
Volume of solution, cm 3, l, m 3
Molar concentration, mol/l
Degree of electrolyte dissociation (X), in fractions of a unit or %
Ionic product of water	K(H2O) =
pH value	pH = –lg

Main:

Kuznetsova N.E. and etc. Chemistry. 8th grade-10th grade. – M.: Ventana-Graf, 2005-2007.

Kuznetsova N.E., Litvinova T.N., Levkin A.N. Chemistry.11th grade in 2 parts, 2005-2007.

Egorov A.S. Chemistry. A new textbook for preparing for higher education. Rostov n/d: Phoenix, 2004.– 640 p.

Egorov A.S. Chemistry: a modern course for preparing for the Unified State Exam. Rostov n/a: Phoenix, 2011. (2012) – 699 p.

Egorov A.S. Self-instruction manual for solving chemical problems. – Rostov-on-Don: Phoenix, 2000. – 352 p.

Chemistry/tutor manual for applicants to universities. Rostov-n/D, Phoenix, 2005– 536 p.

Khomchenko G.P., Khomchenko I.G.. Problems in chemistry for applicants to universities. M.: Higher school. 2007.–302p.

Additional:

Vrublevsky A.I.. Educational and training materials for preparing for centralized testing in chemistry / A.I. Vrublevsky –Mn.: Unipress LLC, 2004. – 368 p.

Vrublevsky A.I.. 1000 problems in chemistry with chains of transformations and control tests for schoolchildren and applicants. – Mn.: Unipress LLC, 2003. – 400 p.

Egorov A.S.. All types of calculation problems in chemistry for preparation for the Unified State Exam. – Rostov n/D: Phoenix, 2003. – 320 p.

Egorov A.S., Aminova G.Kh.. Typical tasks and exercises for preparing for the chemistry exam. – Rostov n/d: Phoenix, 2005. – 448 p.

Unified State Exam 2007. Chemistry. Educational and training materials for preparing students / FIPI - M.: Intellect-Center, 2007. – 272 p.

Unified State Exam 2011. Chemistry. Educational and training kit ed. A.A. Kaverina. – M.: National Education, 2011.

The only real options for tasks to prepare for the Unified State Exam. Unified State Examination 2007. Chemistry/V.Yu. Mishina, E.N. Strelnikova. M.: Federal Testing Center, 2007.–151 p.

Kaverina A.A. The optimal bank of tasks for preparing students. Unified State Exam 2012. Chemistry. Textbook./ A.A. Kaverina, D.Yu. Dobrotin, Yu.N. Medvedev, M.G. Snastina. – M.: Intellect-Center, 2012. – 256 p.

Litvinova T.N., Vyskubova N.K., Azhipa L.T., Solovyova M.V.. Test tasks in addition to tests for students of 10-month correspondence preparatory courses (methodological instructions). Krasnodar, 2004. – P. 18 – 70.

Litvinova T.N.. Chemistry. Unified State Exam 2011. Training tests. Rostov n/d: Phoenix, 2011.– 349 p.

Litvinova T.N.. Chemistry. Tests for the Unified State Exam. Rostov n/d.: Phoenix, 2012. - 284 p.

Litvinova T.N.. Chemistry. Laws, properties of elements and their compounds. Rostov n/d.: Phoenix, 2012. - 156 p.

Litvinova T.N., Melnikova E.D., Solovyova M.V.., Azhipa L.T., Vyskubova N.K. Chemistry in tasks for applicants to universities. – M.: Onyx Publishing House LLC: Mir and Education Publishing House LLC, 2009. – 832 p.

Educational and methodological complex in chemistry for students of medical and biological classes, ed. T.N. Litvinova. – Krasnodar.: KSMU, – 2008.

Chemistry. Unified State Exam 2008. Entrance tests, teaching aid / ed. V.N. Doronkina. – Rostov n/a: Legion, 2008.– 271 p.

List of websites on chemistry:

1. Alhimik. http:// www. alhimik. ru

2. Chemistry for everyone. Electronic reference book for a complete chemistry course.

http:// www. informika. ru/ text/ database/ chemistry/ START. html

3. School chemistry - reference book. http:// www. schoolchemistry. by. ru

4. Chemistry tutor. http://www. chemistry.nm.ru

Internet resources

Alhimik. http:// www. alhimik. ru

Chemistry for everyone. Electronic reference book for a complete chemistry course.

http:// www. informika. ru/ text/ database/ chemistry/ START. html

School chemistry - reference book. http:// www. schoolchemistry. by. ru

http://www.classchem.narod.ru

Chemistry tutor. http://www. chemistry.nm.ru

http://www.alleng.ru/edu/chem.htm- educational Internet resources on chemistry

http://schoolchemistry.by.ru/- school chemistry. This site has the opportunity to take On-line testing on various topics, as well as demo versions of the Unified State Exam

Chemistry and life—XXI century: popular science magazine. http:// www. hij. ru

several basic concepts and formulas.

All substances have different mass, density and volume. A piece of metal from one element can weigh many times more than an exactly the same size piece of another metal.

Mole(number of moles)

designation: mole, international: mol- a unit of measurement for the amount of a substance. Corresponds to the amount of substance that contains N.A. particles (molecules, atoms, ions) Therefore, a universal quantity was introduced - number of moles. A frequently encountered phrase in tasks is “received... mole of substance"

N.A.= 6.02 1023

N.A.- Avogadro's number. Also “a number by agreement.” How many atoms are there in the tip of a pencil? About a thousand. It is not convenient to operate with such quantities. Therefore, chemists and physicists around the world agreed - let’s designate 6.02 × 1023 particles (atoms, molecules, ions) as 1 mole substances.

1 mole = 6.02 1023 particles

This was the first of the basic formulas for solving problems.

Molar mass of a substance

Molar mass substance is the mass of one mole of substance.

Denoted as Mr. It is found according to the periodic table - it is simply the sum of the atomic masses of a substance.

For example, we are given sulfuric acid - H2SO4. Let's calculate the molar mass of a substance: atomic mass H = 1, S-32, O-16.
Mr(H2SO4)=1 2+32+16 4=98 g\mol.

The second necessary formula for solving problems is

substance mass formula:

That is, to find the mass of a substance, you need to know the number of moles (n), and we find the molar mass from the Periodic Table.

Law of conservation of mass - The mass of substances that enter into a chemical reaction is always equal to the mass of the resulting substances.

If we know the mass(es) of the substances that reacted, we can find the mass(es) of the products of that reaction. And vice versa.

The third formula for solving chemistry problems is

volume of substance:

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Where did the number 22.4 come from? From Avogadro's law:

equal volumes of different gases taken at the same temperature and pressure contain the same number of molecules.

According to Avogadro's law, 1 mole of an ideal gas under normal conditions (n.s.) has the same volume Vm= 22.413 996(39) l

That is, if in the problem we are given normal conditions, then, knowing the number of moles (n), we can find the volume of the substance.

So, basic formulas for solving problems in chemistry

Avogadro's numberN.A.

6.02 1023 particles

Quantity of substance n (mol)

n=V\22.4 (l\mol)

Mass of substance m (g)

Volume of substance V(l)

V=n 22.4 (l\mol)

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These are formulas. Often, to solve problems, you first need to write the reaction equation and (required!) arrange the coefficients - their ratio determines the ratio of moles in the process.

Chemistry– the science of the composition, structure, properties and transformations of substances.

Atomic-molecular science. Substances consist of chemical particles (molecules, atoms, ions), which have a complex structure and consist of elementary particles (protons, neutrons, electrons).

Atom– a neutral particle consisting of a positive nucleus and electrons.

Molecule– a stable group of atoms connected by chemical bonds.

Chemical element– a type of atoms with the same nuclear charge. Element denote

where X is the symbol of the element, Z– serial number of the element in the Periodic Table of Elements D.I. Mendeleev, A– mass number. Serial number Z equal to the charge of the atomic nucleus, the number of protons in the atomic nucleus and the number of electrons in the atom. Mass number A equal to the sum of the numbers of protons and neutrons in an atom. The number of neutrons is equal to the difference A–Z.

Isotopes– atoms of the same element having different mass numbers.

Relative atomic mass(A r) is the ratio of the average mass of an atom of an element of natural isotopic composition to 1/12 of the mass of an atom of the carbon isotope 12 C.

Relative molecular weight(M r) is the ratio of the average mass of a molecule of a substance of natural isotopic composition to 1/12 of the mass of an atom of the 12 C carbon isotope.

Atomic mass unit(a.u.m) – 1/12 of the mass of an atom of the carbon isotope 12 C. 1 a.u. m = 1.66? 10 -24 years

Mole– the amount of a substance containing as many structural units (atoms, molecules, ions) as there are atoms in 0.012 kg of the carbon isotope 12 C. Mole– the amount of a substance containing 6.02 10 23 structural units (atoms, molecules, ions).

n = N/N A, Where n– amount of substance (mol), N– number of particles, a N A– Avogadro’s constant. The amount of a substance can also be denoted by the symbol v.

Avogadro's constant N A = 6.02 10 23 particles/mol.

Molar massM(g/mol) – ratio of the mass of the substance m(d) to the amount of substance n(mol):

M = m/n, where: m = M n And n = m/M.

Molar volume of gasV M(l/mol) – gas volume ratio V(l) to the amount of substance of this gas n(mol). Under normal conditions V M = 22.4 l/mol.

Normal conditions: temperature t = 0°C, or T = 273 K, pressure p = 1 atm = 760 mm. rt. Art. = 101,325 Pa = 101.325 kPa.

V M = V/n, where: V = V Mn And n = V/V M .

The result is a general formula:

n = m/M = V/V M = N/N A .

Equivalent- a real or fictitious particle that interacts with one hydrogen atom, or replaces it, or is equivalent to it in some other way.

Molar mass equivalents M e– the ratio of the mass of a substance to the number of equivalents of this substance: M e = m/n (eq) .

In charge exchange reactions, the molar mass of substance equivalents is

with molar mass M equal to: M e = M/(n ? m).

In redox reactions, the molar mass of equivalents of a substance with molar mass M equal to: M e = M/n(e), Where n(e)– number of transferred electrons.

Law of equivalents– the masses of reactants 1 and 2 are proportional to the molar masses of their equivalents. m 1 / m 2= M E1/M E2, or m 1 /M E1 = m 2 /M E2, or n 1 = n 2, Where m 1 And m 2– masses of two substances, M E1 And M E2– molar masses of equivalents, n 1 And n 2– the number of equivalents of these substances.

For solutions, the law of equivalents can be written as follows:

c E1 V 1 = c E2 V 2, Where with E1, with E2, V 1 And V 2– molar concentrations of equivalents and volumes of solutions of these two substances.

United gas law: pV = nRT, Where p– pressure (Pa, kPa), V– volume (m 3, l), n– amount of gas substance (mol), T – temperature (K), T(K) = t(°C) + 273, R– constant, R= 8.314 J/(K? mol), with J = Pa m 3 = kPa l.

2. Atomic structure and Periodic Law

Wave-particle duality matter - the idea that every object can have both wave and corpuscular properties. Louis de Broglie proposed a formula connecting the wave and corpuscular properties of objects: ? = h/(mV), Where h– Planck’s constant, ? – wavelength that corresponds to each body with mass m and speed V. Although wave properties exist for all objects, they can be observed only for micro-objects with masses on the order of the mass of an atom and an electron.

Heisenberg Uncertainty Principle: ?(mV x) ?х > h/2n or ?V x ?x > h/(2?m), Where m– particle mass, x– its coordinate, Vx– speed in direction x, ?– uncertainty, error of determination. The uncertainty principle means that it is impossible to simultaneously indicate the position (coordinate) x) and speed (V x) particles.

Particles with small masses (atoms, nuclei, electrons, molecules) are not particles in the sense of Newtonian mechanics and cannot be studied by classical physics. They are studied by quantum physics.

Principal quantum numbern takes values 1, 2, 3, 4, 5, 6 and 7, corresponding to the electronic levels (layers) K, L, M, N, O, P and Q.

Level– the space where electrons with the same number are located n. Electrons of different levels are spatially and energetically separated from each other, since the number n determines electron energy E(the more n, the more E) and distance R between electrons and nucleus (the more n, the more R).

Orbital (side, azimuthal) quantum numberl takes values depending on the number n:l= 0, 1,…(n- 1). For example, if n= 2, then l = 0, 1; If n= 3, then l = 0, 1, 2. Number l characterizes the sublevel (sublayer).

Sublevel– the space where electrons with certain n And l. Sublevels of a given level are designated depending on the number l:s- If l = 0, p- If l = 1, d- If l = 2, f- If l = 3. The sublevels of a given atom are designated depending on the numbers n And l, for example: 2s (n = 2, l = 0), 3d(n= 3, l = 2), etc. Sublevels of a given level have different energies (the more l, the more E): E s< E < Е А < … and the different shapes of the orbitals that make up these sublevels: the s-orbital has the shape of a ball, p-the orbital is shaped like a dumbbell, etc.

Magnetic quantum numberm 1 characterizes the orientation of the orbital magnetic moment, equal to l, in space relative to the external magnetic field and takes the following values: – l,…-1, 0, 1,…l, i.e. total (2l + 1) value. For example, if l = 2, then m 1 =-2, -1, 0, 1, 2.

Orbital(part of a sublevel) – the space where electrons (no more than two) are located with certain n, l, m 1. Sublevel contains 2l+1 orbital. For example, d– the sublevel contains five d-orbitals. Orbitals of the same sublevel having different numbers m 1, have the same energy.

Magnetic spin numberm s characterizes the orientation of the electron’s own magnetic moment s, equal to?, relative to the external magnetic field and takes two values: +? And _ ?.

Electrons in an atom occupy levels, sublevels and orbitals according to the following rules.

Pauli's Rule: In one atom, two electrons cannot have four identical quantum numbers. They must differ in at least one quantum number.

From the Pauli rule it follows that an orbital can contain no more than two electrons, a sublevel can contain no more than 2(2l + 1) electrons, a level can contain no more 2n 2 electrons.

Klechkovsky's rule: electronic sublevels are filled in in order of increasing amount (n + l), and in case of the same amount (n+l)– in ascending order of number n.

Graphic form of Klechkovsky's rule.

According to Klechkovsky’s rule, sublevels are filled in in the following order: 1s, 2s, 2р, 3s, Зр, 4s, 3d, 4р, 5s, 4d, 5р, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, 8s,…

Although the filling of sublevels occurs according to the Klechkovsky rule, in the electronic formula the sublevels are written sequentially by level: 1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f etc. Thus, the electronic formula of the bromine atom is written as follows: Br(35e) 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 5 .

The electronic configurations of a number of atoms differ from those predicted by Klechkovsky's rule. So, for Cr and Cu:

Сr(24e) 1s 2 2s 2 2p 6 3s 2 3p 6 3d 5 4s 1 and Cu(29e) 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 1.

Rule of Hunda (Gunda): The filling of the orbitals of a given sublevel is carried out so that the total spin is maximum. The orbitals of a given sublevel are filled first with one electron at a time.

Electronic configurations of atoms can be written by levels, sublevels, orbitals. For example, the electronic formula P(15e) can be written:

a) by levels)2)8)5;

b) by sublevels 1s 2 2s 2 2p 6 3s 2 3p 3;

c) by orbital

Examples of electronic formulas of some atoms and ions:

V(23e) 1s 2 2s 2 2p 6 3s 2 3p 6 3d 3 4s 2;

V 3+ (20e) 1s 2 2s 2 2p 6 3s 2 3p 6 3d 2 4s 0.

3. Chemical bond

3.1. Valence bond method

According to the valence bond method, a bond between atoms A and B is formed by sharing a pair of electrons.

Covalent bond. Donor-acceptor connection.

Valence characterizes the ability of atoms to form chemical bonds and is equal to the number of chemical bonds formed by an atom. According to the valence bond method, valence is equal to the number of shared pairs of electrons, and in the case of a covalent bond, valence is equal to the number of unpaired electrons in the outer level of an atom in its ground or excited states.

Valence of atoms

For example, for carbon and sulfur:

Saturability covalent bond: atoms form a limited number of bonds equal to their valence.

Hybridization of atomic orbitals– mixing of atomic orbitals (AO) of different sublevels of the atom, the electrons of which participate in the formation of equivalent?-bonds. Hybrid orbital (HO) equivalence explains the equivalence of the chemical bonds formed. For example, in the case of a tetravalent carbon atom there is one 2s– and three 2p-electron. To explain the equivalence of the four?-bonds formed by carbon in the molecules CH 4, CF 4, etc., atomic one s- and three R- orbitals are replaced by four equivalent hybrid ones sp 3-orbitals:

Focus A covalent bond is that it is formed in the direction of maximum overlap of the orbitals that form a common pair of electrons.

Depending on the type of hybridization, hybrid orbitals have a specific location in space:

sp– linear, the angle between the axes of the orbitals is 180°;

sp 2– triangular, angles between the axes of the orbitals are 120°;

sp 3– tetrahedral, angles between the axes of the orbitals are 109°;

sp 3 d 1– trigonal-bipyramidal, angles 90° and 120°;

sp 2 d 1– square, angles between the axes of the orbitals are 90°;

sp 3 d 2– octahedral, the angles between the axes of the orbitals are 90°.

3.2. Molecular orbital theory

According to the theory of molecular orbitals, a molecule consists of nuclei and electrons. In molecules, electrons are located in molecular orbitals (MO). The MOs of the outer electrons have a complex structure and are considered as a linear combination of the outer orbitals of the atoms that make up the molecule. The number of formed MOs is equal to the number of AOs involved in their formation. The energies of MOs can be lower (bonding MOs), equal (non-bonding MOs) or higher (antibonding MOs), than the energies of the AOs that form them.

Terms of interaction of JSC

1. AO interact if they have similar energies.

2. AOs interact if they overlap.

3. AO interact if they have the appropriate symmetry.

For a diatomic molecule AB (or any linear molecule), the symmetry of MO can be:

If a given MO has an axis of symmetry,

If a given MO has a plane of symmetry,

If the MO has two perpendicular planes of symmetry.

The presence of electrons on the bonding MOs stabilizes the system, as it reduces the energy of the molecule compared to the energy of the atoms. The stability of the molecule is characterized bond order n, equal to: n = (n light – n size)/2, Where n light and n size - number of electrons in bonding and antibonding orbitals.

The filling of MOs with electrons occurs according to the same rules as the filling of AOs in an atom, namely: Pauli’s rule (there cannot be more than two electrons on a MO), Hund’s rule (the total spin must be maximum), etc.

The interaction of 1s-AO atoms of the first period (H and He) leads to the formation of bonding?-MO and antibonding?*-MO:

Electronic formulas of molecules, bond orders n, experimental bond energies E and intermolecular distances R for diatomic molecules from atoms of the first period are given in the following table:

Other atoms of the second period contain, in addition to 2s-AO, also 2p x -, 2p y – and 2p z -AO, which upon interaction can form?– and?-MO. For O, F, and Ne atoms, the energies of the 2s– and 2p-AOs differ significantly, and the interaction between the 2s-AO of one atom and the 2p-AO of another atom can be neglected, considering the interaction between the 2s-AO of two atoms separately from the interaction of their 2p-AO. The MO scheme for molecules O 2, F 2, Ne 2 has the following form:

For atoms B, C, N, the energies of 2s– and 2p-AO are close in their energies, and the 2s-AO of one atom interacts with the 2p z-AO of another atom. Therefore, the order of MOs in molecules B 2, C 2 and N 2 differs from the order of MOs in molecules O 2, F 2 and Ne 2. Below is the MO scheme for molecules B 2, C 2 and N 2:

Based on the given MO schemes, it is possible, for example, to write down the electronic formulas of the molecules O 2 , O 2 + and O 2 ?:

O 2 + (11e)? s2? s *2 ? z 2 (? x 2 ? y 2)(? x *1 ? y *0)

n = 2 R = 0.121 nm;

O 2 (12e)? s2? s *2 ? z 2 (? x 2 ? y 2)(? x *1 ? y *1)

n = 2.5 R = 0.112 nm;

O 2 ?(13e)? s2? s *2 ? z 2 (? x 2 ? y 2)(? x *2 ? y *1)

n = 1.5 R = 0.126 nm.

In the case of the O 2 molecule, MO theory allows us to foresee greater strength of this molecule, since n = 2, the nature of changes in binding energies and internuclear distances in the series O 2 + – O 2 – O 2 ?, as well as the paramagnetism of the O 2 molecule, the upper MOs of which have two unpaired electrons.

3.3. Some types of connections

Ionic bond– electrostatic bond between ions of opposite charges. An ionic bond can be considered an extreme case of a polar covalent bond. An ionic bond is formed if the difference in electronegativity of the atoms? X is greater than 1.5–2.0.

An ionic bond is non-directional non-saturable communication In a NaCl crystal, the Na+ ion is attracted by all the Cl ions? and is repelled by all other Na + ions, regardless of the direction of interaction and the number of ions. This determines the greater stability of ionic crystals compared to ionic molecules.

Hydrogen bond– a bond between a hydrogen atom of one molecule and an electronegative atom (F, CI, N) of another molecule.

The existence of a hydrogen bond explains the anomalous properties of water: the boiling point of water is much higher than that of its chemical analogues: t kip (H 2 O) = 100 °C, and t kip (H 2 S) = -61 ° C. No hydrogen bonds are formed between H 2 S molecules.

4. Patterns of chemical processes

4.1. Thermochemistry

Energy(E)- ability to produce work. Mechanical work (A) is performed, for example, by gas during its expansion: A = p?V.

Reactions that occur with the absorption of energy are: endothermic.

Reactions that involve the release of energy are: exothermic.

Types of energy: heat, light, electrical, chemical, nuclear energy, etc.

Energy types: kinetic and potential.

Kinetic energy– the energy of a moving body, this is the work that a body can do before it reaches rest.

Heat (Q)– a type of kinetic energy – associated with the movement of atoms and molecules. When communicating to a body of mass (m) and specific heat capacity (c) of heat? Q its temperature increases by? t: ?Q = m with ?t, where? t = ?Q/(c t).

Potential energy- energy acquired by a body as a result of a change in position in space by it or its component parts. The energy of chemical bonds is a type of potential energy.

First law of thermodynamics: energy can pass from one type to another, but cannot disappear or arise.

Internal energy (U) – the sum of the kinetic and potential energies of the particles that make up the body. The heat absorbed in the reaction is equal to the difference in the internal energy of the reaction products and reagents (Q = ?U = U 2 – U 1), provided that the system has not done any work on the environment. If the reaction occurs at constant pressure, then the released gases do work against external pressure forces, and the heat absorbed during the reaction is equal to the sum of the changes in internal energy ?U and work A = p?V. This heat absorbed at constant pressure is called the enthalpy change: ? Н = ?U + p?V, defining enthalpy How H = U + pV. Reactions of liquid and solid substances occur without significant changes in volume (?V = 0), so what about these reactions? N close to ?U (?Н = ?U). For reactions with a change in volume we have ?Н > ?U, if expansion is in progress, and ?N< ?U , if there is compression.

The change in enthalpy is usually referred to the standard state of a substance: that is, for a pure substance in a certain state (solid, liquid or gaseous), at a pressure of 1 atm = 101,325 Pa, a temperature of 298 K and a concentration of substances of 1 mol/l.

Standard enthalpy of formation?– heat released or absorbed during the formation of 1 mole of a substance from the simple substances that constitute it, under standard conditions. For example, ?N arr.(NaCl) = -411 kJ/mol. This means that in the reaction Na(s) + ?Cl 2 (g) = NaCl(s) when 1 mole of NaCl is formed, 411 kJ of energy is released.

Standard enthalpy of reaction?H– change in enthalpy during a chemical reaction, determined by the formula: ?N = ?N arr.(products) – ?N arr.(reagents).

So for the reaction NH 3 (g) + HCl (g) = NH 4 Cl (tv), knowing? H o 6 p (NH 3) = -46 kJ/mol, ? H o 6 p (HCl) = -92 kJ /mol and?H o 6 p (NH 4 Cl) = -315 kJ/mol we have:

H = ?H o 6 p (NH 4 Cl) – ?H o 6 p (NH 3) – ?H o 6 p (HCl) = -315 – (-46) – (-92) = -177 kJ.

If? N< 0, then the reaction is exothermic. If? N> 0, then the reaction is endothermic.

Law Hess: The standard enthalpy of a reaction depends on the standard enthalpies of the reactants and products and does not depend on the path of the reaction.

Spontaneous processes can be not only exothermic, i.e. processes with a decrease in energy (?N< 0), but can also be endothermic processes, i.e. processes with increasing energy (?N> 0). In all these processes, the “disorder” of the system increases.

EntropyS – a physical quantity characterizing the degree of disorder of the system. S – standard entropy, ?S – change in standard entropy. If?S > 0, disorder increases if AS< 0, то беспорядок системы уменьшается. Для процессов в которых растет число частиц, ?S >0. For processes in which the number of particles decreases, ?S< 0. Например, энтропия меняется в ходе реакций:

CaO(solid) + H 2 O(l) = Ca(OH) 2 (solid), ?S< 0;

CaCO 3 (tv) = CaO (tv) + CO 2 (g), ?S > 0.

Processes occur spontaneously with the release of energy, i.e. for which? N< 0, and with increasing entropy, i.e. for which?S > 0. Taking both factors into account leads to the expression for Gibbs energy: G = H – TS or? G = ?H – T?S. Reactions in which the Gibbs energy decreases, i.e. ?G< 0, могут идти самопроизвольно. Реакции, в ходе которых энергия Гиббса увеличивается, т. е. ?G >0, do not go spontaneously. The condition?G = 0 means that equilibrium has been established between the products and reactants.

At low temperatures, when the value T is close to zero, only exothermic reactions occur, since T?S– little and?G = ? N< 0. At high temperatures the values T?S great, and, neglecting the size? N, we have?G = – T?S, i.e., processes with increasing entropy will occur spontaneously, for which?S > 0, a?G< 0. При этом чем больше по абсолютной величине значение?G, тем более полно проходит данный процесс.

The value of AG for a particular reaction can be determined by the formula:

G = ?С arr (products) – ?G o b p (reagents).

In this case, the values of ?G o br, as well as? N arr. and?S o br for a large number of substances are given in special tables.

4.2. Chemical kinetics

Chemical reaction rate(v) is determined by the change in the molar concentration of reactants per unit time:

Where v– reaction rate, s – molar concentration of the reagent, t- time.

The rate of a chemical reaction depends on the nature of the reactants and the reaction conditions (temperature, concentration, presence of a catalyst, etc.)

Effect of concentration. IN In the case of simple reactions, the reaction rate is proportional to the product of the concentrations of the reactants, taken in powers equal to their stoichiometric coefficients.

For reaction

where 1 and 2 are the directions of the forward and reverse reactions, respectively:

v 1 = k 1 ? [A] m ? [B]n and

v 2 = k 2 ? [C]p ? [D]q

Where v- speed reaction, k– rate constant, [A] – molar concentration of substance A.

Molecularity of the reaction– the number of molecules participating in the elementary act of the reaction. For simple reactions, for example: mA + nB> рС + qD, molecularity is equal to the sum of the coefficients (m + n). Reactions can be single-molecule, double-molecule, and rarely triple-molecule. Reactions of higher molecular weight do not occur.

Reaction order is equal to the sum of the exponents of the degrees of concentration in the experimental expression of the rate of a chemical reaction. So, for a complex reaction

mA + nB > рС + qD the experimental expression for the reaction rate is

v 1 = k 1 ? [A] ? ? [IN] ? and the reaction order is (? + ?). Wherein? And? are found experimentally and may not coincide with m And n accordingly, since the equation of a complex reaction is the result of several simple reactions.

Effect of temperature. The rate of a reaction depends on the number of effective collisions between molecules. An increase in temperature increases the number of active molecules, giving them the necessary energy for the reaction to occur. activation energy E act and increases the rate of a chemical reaction.

Van't Hoff's rule. When the temperature increases by 10°, the reaction rate increases by 2–4 times. Mathematically this is written as:

v 2 = v 1 ? ?(t 2 – t 1)/10

where v 1 and v 2 are the reaction rates at the initial (t 1) and final (t 2) temperatures, ? – temperature coefficient of reaction rate, which shows how many times the reaction rate increases with an increase in temperature by 10°.

More precisely, the dependence of the reaction rate on temperature is expressed Arrhenius equation:

k = A? e - E/(RT)

Where k– rate constant, A– constant independent of temperature, e = 2.71828, E– activation energy, R= 8.314 J/(K? mol) – gas constant; T– temperature (K). It can be seen that the rate constant increases with increasing temperature and decreasing activation energy.

4.3. Chemical equilibrium

A system is in equilibrium if its state does not change over time. Equality of the rates of forward and reverse reactions is a condition for maintaining the equilibrium of the system.

An example of a reversible reaction is the reaction

N 2 + 3H 2 - 2NH 3 .

Law of mass action: the ratio of the product of concentrations of reaction products to the product of concentrations of starting substances (all concentrations are indicated in powers equal to their stoichiometric coefficients) is a constant called equilibrium constant.

The equilibrium constant is a measure of the progress of a forward reaction.

K = O – direct reaction does not occur;

K =? – the direct reaction goes to completion;

K > 1 – balance shifted to the right;

TO< 1 – balance is shifted to the left.

Reaction equilibrium constant TO is related to the magnitude of the change in the standard Gibbs energy?G for the same reaction:

G= – RT ln K, or?G = -2.3RT lg K, or K= 10 -0.435?G/RT

If K > 1, then lg K> 0 and?G< 0, т. е. если равновесие сдвинуто вправо, то реакция – переход от исходного состояния к равновесному – идет самопроизвольно.

If TO< 1, then lg K < 0 и?G >0, i.e. if the equilibrium is shifted to the left, then the reaction does not spontaneously go to the right.

Law of equilibrium shift: If an external influence is exerted on a system in equilibrium, a process arises in the system that counteracts the external influence.

5. Redox reactions

Redox reactions– reactions that occur with a change in the oxidation states of elements.

Oxidation– process of electron donation.

Recovery– the process of adding electrons.

Oxidizer– an atom, molecule, or ion that accepts electrons.

Reducing agent– an atom, molecule, or ion that donates electrons.

Oxidizing agents, accepting electrons, go into a reduced form:

F 2 [approx. ] + 2e > 2F? [restored].

Reductants, giving up electrons, go into the oxidized form:

Na 0 [recovery ] – 1e > Na + [approx.].

The equilibrium between the oxidized and reduced forms is characterized by Nernst equations for redox potential:

Where E 0– standard value of redox potential; n– number of transferred electrons; [restored ] and [approx. ] are the molar concentrations of the compound in reduced and oxidized forms, respectively.

Values of standard electrode potentials E 0 are given in tables and characterize the oxidative and reduction properties of compounds: the more positive the value E 0, the stronger the oxidizing properties, and the more negative the value E 0, the stronger the restorative properties.

For example, for F 2 + 2e - 2F? E 0 = 2.87 volts, and for Na + + 1e - Na 0 E 0 =-2.71 volts (the process is always recorded for reduction reactions).

A redox reaction is a combination of two half-reactions, oxidation and reduction, and is characterized by an electromotive force (emf) ? E 0:?E 0= ?E 0 ok – ?E 0 restore, Where E 0 ok And? E 0 restore– standard potentials of the oxidizing agent and reducing agent for this reaction.

E.m.f. reactions? E 0 is related to the change in the Gibbs free energy?G and the equilibrium constant of the reaction TO:

?G = – nF?E 0 or? E = (RT/nF) ln K.

E.m.f. reactions at non-standard concentrations? E equal to: ? E =?E 0 – (RT/nF) ? Ig K or? E =?E 0 –(0,059/n)lg K.

In the case of equilibrium?G = 0 and?E = 0, where does it come from? E =(0.059/n)lg K And K = 10 n?E/0.059 .

For the reaction to proceed spontaneously, the following relations must be satisfied: ?G< 0 или K >> 1, to which the condition corresponds? E 0> 0. Therefore, to determine the possibility of a given redox reaction, it is necessary to calculate the value? E 0. If? E 0 > 0, the reaction is in progress. If? E 0< 0, no response.

Chemical current sources

Galvanic cells– devices that convert the energy of a chemical reaction into electrical energy.

Daniel's galvanic cell consists of zinc and copper electrodes immersed in solutions of ZnSO 4 and CuSO 4, respectively. Electrolyte solutions communicate through a porous partition. In this case, oxidation occurs on the zinc electrode: Zn > Zn 2+ + 2e, and reduction occurs on the copper electrode: Cu 2+ + 2e > Cu. In general, the reaction goes: Zn + CuSO 4 = ZnSO 4 + Cu.

Anode– electrode on which oxidation occurs. Cathode– the electrode on which the reduction takes place. In galvanic cells, the anode is negatively charged and the cathode is positively charged. On element diagrams, metal and mortar are separated by a vertical line, and two mortars are separated by a double vertical line.

So, for the reaction Zn + CuSO 4 = ZnSO 4 + Cu, the circuit diagram of the galvanic cell is written: (-)Zn | ZnSO 4 || CuSO 4 | Cu(+).

The electromotive force (emf) of the reaction is? E 0 = E 0 ok – E 0 restore= E 0(Cu 2+ /Cu) – E 0(Zn 2+ /Zn) = 0.34 – (-0.76) = 1.10 V. Due to losses, the voltage created by the element will be slightly less than? E 0. If the concentrations of solutions differ from the standard ones, equal to 1 mol/l, then E 0 ok And E 0 restore are calculated using the Nernst equation, and then the emf is calculated. corresponding galvanic cell.

Dry element consists of a zinc body, NH 4 Cl paste with starch or flour, a mixture of MnO 2 with graphite and a graphite electrode. During its operation, the following reaction occurs: Zn + 2NH 4 Cl + 2MnO 2 = Cl + 2MnOOH.

Element diagram: (-)Zn | NH4Cl | MnO 2 , C(+). E.m.f. element - 1.5 V.

Batteries. A lead battery consists of two lead plates immersed in a 30% sulfuric acid solution and coated with a layer of insoluble PbSO 4 . When charging a battery, the following processes occur on the electrodes:

PbSO 4 (tv) + 2e > Pb (tv) + SO 4 2-

PbSO 4 (tv) + 2H 2 O > PbO 2 (tv) + 4H + + SO 4 2- + 2e

When the battery is discharged, the following processes occur on the electrodes:

Pb(tv) + SO 4 2- > PbSO 4 (tv) + 2e

PbO 2 (tv) + 4H + + SO 4 2- + 2e > PbSO 4 (tv) + 2H 2 O

The total reaction can be written as:

To operate, the battery requires regular charging and monitoring of the concentration of sulfuric acid, which may decrease slightly during battery operation.

6. Solutions

6.1. Concentration of solutions

Mass fraction of substance in solution w equal to the ratio of the mass of the solute to the mass of the solution: w = m water / m solution or w = m in-va /(V ? ?), because m solution = V p-pa ? ?r-ra.

Molar concentration With equal to the ratio of the number of moles of solute to the volume of solution: c = n(mol)/ V(l) or c = m/(M? V( l )).

Molar concentration of equivalents (normal or equivalent concentration) with e is equal to the ratio of the number of equivalents of a dissolved substance to the volume of solution: with e = n(mol eq.)/ V(l) or with e = m/(M e? V(l)).

6.2. Electrolytic dissociation

Electrolytic dissociation– decomposition of the electrolyte into cations and anions under the influence of polar solvent molecules.

Degree of dissociation?– ratio of the concentration of dissociated molecules (with diss) to the total concentration of dissolved molecules (with vol): ? = with diss / with ob.

Electrolytes can be divided into strong(? ~ 1) and weak.

Strong electrolytes(for them? ~ 1) – salts and bases soluble in water, as well as some acids: HNO 3, HCl, H 2 SO 4, HI, HBr, HClO 4 and others.

Weak electrolytes(for them?<< 1) – Н 2 O, NH 4 OH, малорастворимые основания и соли и многие кислоты: HF, H 2 SO 3 , H 2 CO 3 , H 2 S, CH 3 COOH и другие.

Ionic reaction equations. IN In ionic equations of reactions, strong electrolytes are written in the form of ions, and weak electrolytes, poorly soluble substances and gases are written in the form of molecules. For example:

CaCO 3 v + 2HCl = CaCl 2 + H 2 O + CO 2 ^

CaCO 3 v + 2H + + 2Cl? = Ca 2+ + 2Cl? + H 2 O + CO 2 ^

CaCO 3 v + 2H + = Ca 2+ + H 2 O + CO 2 ^

Reactions between ions go towards the formation of a substance that produces fewer ions, i.e. towards a weaker electrolyte or a less soluble substance.

6.3. Dissociation of weak electrolytes

Let us apply the law of mass action to the equilibrium between ions and molecules in a solution of a weak electrolyte, for example acetic acid:

CH 3 COOH - CH 3 COO? +H+

The equilibrium constants for dissociation reactions are called dissociation constants. Dissociation constants characterize the dissociation of weak electrolytes: the lower the constant, the less the weak electrolyte dissociates, the weaker it is.

Polybasic acids dissociate stepwise:

H 3 PO 4 - H + + H 2 PO 4 ?

The equilibrium constant of the total dissociation reaction is equal to the product of the constants of the individual stages of dissociation:

N 3 PO 4 - ZN + + PO 4 3-

Ostwald's dilution law: the degree of dissociation of a weak electrolyte (a) increases with decreasing its concentration, i.e., with dilution:

Effect of a common ion on the dissociation of a weak electrolyte: the addition of a common ion reduces the dissociation of the weak electrolyte. So, when adding CH 3 COOH to a solution of a weak electrolyte

CH 3 COOH - CH 3 COO? +H+ ?<< 1

a strong electrolyte containing an ion common to CH 3 COOH, i.e. an acetate ion, for example CH 3 COONa

CH 3 COOna - CH 3 COO? + Na + ? = 1

the concentration of acetate ion increases, and the CH 3 COOH dissociation equilibrium shifts to the left, i.e., acid dissociation decreases.

6.4. Dissociation of strong electrolytes

Ion activity A – concentration of an ion, manifested in its properties.

Activity factorf– ion activity ratio A to concentration with: f= a/c or A = fc.

If f = 1, then the ions are free and do not interact with each other. This occurs in very dilute solutions, in solutions of weak electrolytes, etc.

If f< 1, то ионы взаимодействуют между собой. Чем меньше f, тем больше взаимодействие между ионами.

The activity coefficient depends on the ionic strength of solution I: the higher the ionic strength, the lower the activity coefficient.

Ionic strength of solution I depends on charges z and concentrations from ions:

I = 0.52?s z2.

The activity coefficient depends on the charge of the ion: the greater the charge of the ion, the lower the activity coefficient. Mathematically, the dependence of the activity coefficient f on ionic strength I and ion charge z written using the Debye-Hückel formula:

Ion activity coefficients can be determined using the following table:

6.5 Ionic product of water. pH value

Water, a weak electrolyte, dissociates, forming H+ and OH? ions. These ions are hydrated, that is, connected to several water molecules, but for simplicity they are written in non-hydrated form

H 2 O - H + + OH?.

Based on the law of mass action, for this equilibrium:

The concentration of water molecules [H 2 O], i.e. the number of moles in 1 liter of water, can be considered constant and equal to [H 2 O] = 1000 g/l: 18 g/mol = 55.6 mol/l. From here:

TO[H 2 O] = TO(H 2 O ) = [H + ] = 10 -14 (22°C).

Ionic product of water– the product of concentrations [H + ] and – is a constant value at a constant temperature and equal to 10 -14 at 22°C.

The ionic product of water increases with increasing temperature.

pH value– negative logarithm of the concentration of hydrogen ions: pH = – log. Similarly: pOH = – log.

Taking the logarithm of the ionic product of water gives: pH + pHOH = 14.

The pH value characterizes the reaction of the medium.

If pH = 7, then [H + ] = is a neutral medium.

If pH< 7, то [Н + ] >– acidic environment.

If pH > 7, then [H + ]< – щелочная среда.

6.6. Buffer solutions

Buffer solutions are solutions that have a certain concentration of hydrogen ions. The pH of these solutions does not change when diluted and changes little when small amounts of acids and alkalis are added.

I. A solution of the weak acid HA, concentration – from the acid, and its salt with the strong base BA, concentration – from the salt. For example, an acetate buffer is a solution of acetic acid and sodium acetate: CH 3 COOH + CHgCOONa.

pH = pK acidic + log(salt/s sour).

II. A solution of the weak base BOH, concentration - from basic, and its salt with a strong acid BA, concentration - from salt. For example, an ammonia buffer is a solution of ammonium hydroxide and ammonium chloride NH 4 OH + NH 4 Cl.

pH = 14 – рК basic – log(with salt/with basic).

6.7. Hydrolysis of salts

Hydrolysis of salts– interaction of salt ions with water to form a weak electrolyte.

Examples of hydrolysis reaction equations.

I. A salt is formed by a strong base and a weak acid:

Na 2 CO 3 + H 2 O - NaHCO 3 + NaOH

2Na + + CO 3 2- + H 2 O - 2Na + + HCO 3 ? +OH?

CO 3 2- + H 2 O - HCO 3 ? + OH?, pH > 7, alkaline environment.

In the second stage, hydrolysis practically does not occur.

II. A salt is formed by a weak base and a strong acid:

AlCl 3 + H 2 O - (AlOH)Cl 2 + HCl

Al 3+ + 3Cl? + H 2 O - AlOH 2+ + 2Cl? + H + + Cl?

Al 3+ + H 2 O - AlOH 2+ + H +, pH< 7.

In the second stage, hydrolysis occurs less, and in the third stage there is practically no hydrolysis.

III. A salt is formed by a strong base and a strong acid:

K + + NO 3 ? + H 2 O ? no hydrolysis, pH? 7.

IV. A salt is formed by a weak base and a weak acid:

CH 3 COONH 4 + H 2 O - CH 3 COOH + NH 4 OH

CH 3 COO? + NH 4 + + H 2 O - CH 3 COOH + NH 4 OH, pH = 7.

In some cases, when the salt is formed by very weak bases and acids, complete hydrolysis occurs. In the solubility table for such salts the symbol is “decomposed by water”:

Al 2 S 3 + 6H 2 O = 2Al(OH) 3 v + 3H 2 S^

The possibility of complete hydrolysis should be taken into account in exchange reactions:

Al 2 (SO 4) 3 + 3Na 2 CO 3 + 3H 2 O = 2Al(OH) 3 v + 3Na 2 SO 4 + 3CO 2 ^

Degree of hydrolysish – the ratio of the concentration of hydrolyzed molecules to the total concentration of dissolved molecules.

For salts formed by a strong base and a weak acid:

= chрOH = – log, рН = 14 – рOH.

From the expression it follows that the degree of hydrolysis h(i.e. hydrolysis) increases:

a) with increasing temperature, as K(H 2 O) increases;

b) with a decrease in the dissociation of the acid forming the salt: the weaker the acid, the greater the hydrolysis;

c) with dilution: the smaller the c, the greater the hydrolysis.

For salts formed by a weak base and a strong acid

[H + ] = ch pH = – log.

For salts formed by a weak base and a weak acid

6.8. Protolytic theory of acids and bases

Protolysis– proton transfer process.

Protoliths– acids and bases that donate and accept protons.

Acid– a molecule or ion capable of donating a proton. Each acid has a corresponding conjugate base. The strength of acids is characterized by the acid constant K k.

H 2 CO 3 + H 2 O - H 3 O + + HCO 3 ?

K k = 4 ? 10 -7

3+ + H 2 O - 2+ + H 3 O +

K k = 9 ? 10 -6

Base– a molecule or ion that can accept a proton. Each base has a corresponding conjugate acid. The strength of bases is characterized by the base constant K 0.

NH3? H 2 O (H 2 O) - NH 4 + + OH?

K 0 = 1,8 ?10 -5

Ampholytes– protoliths capable of releasing and acquiring a proton.

HCO3? + H 2 O - H 3 O + + CO 3 2-

HCO3? – acid.

HCO3? + H 2 O - H 2 CO 3 + OH?

HCO3? – foundation.

For water: H 2 O+ H 2 O - H 3 O + + OH?

K(H 2 O) = [H 3 O + ] = 10 -14 and pH = – log.

Constants K k And K 0 for conjugate acids and bases are linked.

HA + H 2 O - H 3 O + + A?,

A? + H 2 O - HA + OH?,

7. Solubility constant. Solubility

In a system consisting of a solution and a precipitate, two processes take place - dissolution of the precipitate and precipitation. The equality of the rates of these two processes is a condition of equilibrium.

Saturated solution– a solution that is in equilibrium with the precipitate.

The law of mass action applied to the equilibrium between precipitate and solution gives:

Since = const,

TO = K s (AgCl) = .

In general we have:

A m B n(TV) - m A +n+n B -m

K s ( A m B n)= [A +n ] m[IN -m ] n .

Solubility constantK s(or solubility product PR) - the product of ion concentrations in a saturated solution of a slightly soluble electrolyte - is a constant value and depends only on temperature.

Solubility of a sparingly soluble substance s can be expressed in moles per liter. Depending on the size s substances can be divided into poorly soluble – s< 10 -4 моль/л, среднерастворимые – 10 -4 моль/л? s? 10 -2 mol/l and highly soluble s>10 -2 mol/l.

The solubility of compounds is related to their solubility product.

Condition for precipitation and dissolution of sediment

In the case of AgCl: AgCl - Ag + + Cl?

K s= :

a) condition of equilibrium between precipitate and solution: = Ks.

b) deposition condition: > Ks; during precipitation, ion concentrations decrease until equilibrium is established;

c) the condition for the dissolution of the precipitate or the existence of a saturated solution:< Ks; As the precipitate dissolves, the ion concentration increases until equilibrium is established.

8. Coordination compounds

Coordination (complex) compounds are compounds with a donor-acceptor bond.

For K 3:

ions of the outer sphere – 3K +,

inner sphere ion – 3-,

complexing agent – Fe 3+,

ligands – 6CN?, their dentation – 1,

coordination number – 6.

Examples of complexing agents: Ag +, Cu 2+, Hg 2+, Zn 2+, Ni 2+, Fe 3+, Pt 4+, etc.

Examples of ligands: polar molecules H 2 O, NH 3, CO and anions CN?, Cl?, OH? and etc.

Coordination numbers: usually 4 or 6, less often 2, 3, etc.

Nomenclature. The anion is named first (in the nominative case), then the cation (in the genitive case). Names of some ligands: NH 3 - ammin, H 2 O - aquo, CN? – cyano, Cl? – chloro, OH? – hydroxo. Names of coordination numbers: 2 – di, 3 – three, 4 – tetra, 5 – penta, 6 – hexa. The oxidation state of the complexing agent is indicated:

Cl—diamminesilver(I) chloride;

SO 4 – tetrammine copper(II) sulfate;

K 3 – potassium hexacyanoferrate(III).

Chemical connection.

Valence bond theory assumes hybridization of the orbitals of the central atom. The location of the resulting hybrid orbitals determines the geometry of the complexes.

Diamagnetic complex ion Fe(CN) 6 4-.

Cyanide ion – donor

The iron ion Fe 2+ – acceptor – has the formula 3d 6 4s 0 4p 0. Taking into account the diamagnetic nature of the complex (all electrons are paired) and the coordination number (6 free orbitals are needed), we have d 2 sp 3-hybridization:

The complex is diamagnetic, low-spin, intraorbital, stable (no external electrons are used), octahedral ( d 2 sp 3-hybridization).

Paramagnetic complex ion FeF 6 3-.

Fluoride ion is a donor.

The iron ion Fe 3+ – acceptor – has the formula 3d 5 4s 0 4p 0 . Taking into account the paramagneticity of the complex (electrons are coupled) and the coordination number (6 free orbitals are needed), we have sp 3 d 2-hybridization:

The complex is paramagnetic, high-spin, outer-orbital, unstable (outer 4d orbitals are used), octahedral ( sp 3 d 2-hybridization).

Dissociation of coordination compounds.

Coordination compounds in solution completely dissociate into ions of the inner and outer spheres.

NO 3 > Ag(NH 3) 2 + + NO 3 ?, ? = 1.

The ions of the inner sphere, i.e., complex ions, dissociate into metal ions and ligands, like weak electrolytes, in stages.

Where K 1 , TO 2 , TO 1 _ 2 are called instability constants and characterize the dissociation of complexes: the lower the instability constant, the less the complex dissociates, the more stable it is.