What is a chemical bond in science?

The fundamental questions in study chemistry ever since the beginning to study the nature of forces responsible for the construction of bond to form a molecule.

After nearly a century of confusion, Kekul, Van't Hoff , Le Bel, Lewis, and London, etc in the nineteenth century given the concept of the construction of chemical bonds in chemistry.
It was easily realized that the number of atoms or groups of atoms combines to forming the ions or molecular species.

Every element has a saturation capacity for the construction of bonds. The valency is commonly used for the saturation capacity of an element.

Definition of chemical bond in chemistry

Chemical bond defines as the force holding together two atoms or groups of atoms forming an aggregate of ions or molecular species such that there occur lowering of energy.

A chemical bond represents the forces between atom or ions in a molecule. There will be many chemical compounds whose properties would indicate intermediate types.

Different types of bond

To study different types of force holding together on atoms or ions to form a molecule in our definition the chemical compounds form mainly three types of bond.
  1. Ionic bond or electrovalent bond or electrostatic bond.
  2. Covalent bond.
  3. Metallic bond.
The ionic bond is electrostatic forces that bind together oppositely charged ions forms by the transfer of electron or electrons from an electropositive metal to an electronegative non-metal atom.
A covalent bond defined as a force holding together atoms through the sharing of electrons.
Types of chemical bonding
Chemical bonding

Ionic bond definition and example

Ionic compounds are constructed by the transference of electron or electrons from one atom to another.
Elements that have the tendency to lose one or more electrons are called electropositive and elements that have a tendency to gain electrons are called electronegative.

Crystallographic studies show that there is no discrete sodium chloride molecule in the crystal of sodium chloride. each of sodium ion surrounded by six chlorine atom or vice versa. The two oppositely charged ions are held together by the electrostatic force of attraction.

Each sodium atom loses one electron to form uni positive sodium ion and neutral chlorine atom gains this electron to form uni negative ion. The two ions constructed a close-packed type ionic compound.
Na → Na⁺ + e
Cl + e → Cl⁻

Na⁺ + Cl⁻ → NaCl

What type of elements form covalent bonds?

Covent bond is formed by the sharing of electrons. Lewis represents the structure of the covalent bond of hydrogen and hydrogen fluoride.

A single covalent bond is formed between two hydrogen atom and hydrogen and a fluorine atom. This type of bond formed by the sharing of only one electron between the bonded atom.

H⋅ + ⋅H → H⋅ ⋅H or H-H
H⋅ + ⋅F → H⋅ ⋅F or H-F

Double and triple covalent bonds formed when the atoms bonded together share two or three electrons. This type of bond formed in oxygen and nitrogen molecules.

It is not essential for covalent bonding, the sharing of electron equally to the partner. For the compound formation between boron trifluoride and ammonia both the electrons come from ammonia. Such type of bond is called a coordinate covalent bond. here ammonia as a donner and boron trifluoride is an acceptor.
NH₃ + BF₃ → BF₃←NH₃
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How are metallic bonds formed?

Metals are a good conductor of electricity and thermal energy and formed crystalline solid with high coordination numbers of 12 or 14.

Since all the atoms of metal, crystal are identical and they can not bound by an ionic bond. Two different types of atom formed this type of bond.

Covalent bonding also not possible for the formation of metallic crystals due to much weak van der Waals forces acting between covalent atoms.

Metallic crystal may be a collection of positive atomic cores immersed in a fluid of mobile electrons or sea of mobile electrons.

The force that binds a metal ion to the mobile electrons or sea of electrons is a known metallic bond. This concept is called the electrons sea model.
This model can explain the conductivity and heat conduction in the metal.
  • Under the influence of the applied electric field, it is possible to move the electrons through the crystal lattice. Thereby metals are the conductor of electricity.
  • Heat conduction by the consequence of freedom of motion in electrons. The higher energy transfers some energy to mobile electrons, which transfer one atomic core of the metal atom to another atomic core at another distinct core.
Most of the properties of the metal can explain this type of bonding but the heat capacity of metals difficult to explain by these types of bonding.

Importance of environmental chemistry

Environmental chemistry is the branch of science which deals with the chemical changes in the environment. It includes our surroundings such as air, water, soil, forest, and sunlight. Broadly speaking the environment is three main components.
  1. Abiotic components.
  2. Biotic components.
  3. Energy components.

Physical-chemical and biological components

The abiotic or non-living component or factor of ecosystems is any non-living factor which used or present in an ecosystem. Sunlight, oxygen, nitrogen, temperature, pH, and water is the most common abiotic factors present in our ecosystem. These nonliving components present in the lithosphere or atmosphere.

The biotic or living components are plants and animals including the man in our ecosystem. The most common abiotic factors are temperature, air currents, and minerals.

Energy components are globally leading end-to-end hydrocarbon production data management and accounting software, tracking hydrocarbons from production and transport to sales for revenue generation. These include solar energy,  geochemical, thermochemical, hydroelectric and nuclear energy.

Evolution of life on earth timeline

Life originally appeared on our earth in an overall reducing atmosphere. In 1953 Miller and Urey showed that lighting discharges through a mixture of methane, water and ammonia, and hydrogen produce a significant amount of amino acids essential product of life cycle.

Abelson and other latter showed that solar ultraviolet ration radiation acts on carbon monoxide, carbon dioxide, nitrogen and a small amount of hydrogen cyanide. Hydrogen cyanide subsequently gives rise to glycine, adenine, and other biological significant product of the life cycle.
These compounds undergo a series of chemical complex evaluations over millions of years to produce living organisms.

Photosynthesis organisms appeared approximately 2.5 billion years ago when the atmosphere becomes gradually reach become dioxygen and sustain the aerobic of life. The diverse biological process of today has largely developed with this form of life.
Importance of environmental chemistry
Environmental chemistry

Ecosystem diversity definition environmental science

The coexistence animal, plants and microorganisms or biotic component living organisms and abiotic component non-living material or factors which may be inorganic carbon dioxide,  nitrogen, sulfur phosphorus or organic protein and carbohydrates and climate factors like temperature and humidity is called an ecosystem.
  • In short, an ecosystem is the coexistence of the population of all species of living and nonliving components that live together in a particular area.
  • An ecosystem is the living organism's presence in his physical environment.
  • Ecosystems are commonly different types and size namely marine, aquatic, or terrestrial. The marine ecosystem is present in sea and ocean to connect living organisms in the sea and non-living organisms in a seawater environment.
  • The law of conservation of energy follows in every ecosystem by conservation of matter into energy and energy into matter.
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Environmental protection from pollution

The main aim of the environmental chemistry studies the course of environmental pollution and remedial measure necessity to free it from this environmental pollution.

A pollutant is a substance, chemical or factor which has the potential to adversely affect the natural characteristic of environmental, natural resources and assets.

To save our environment from this pollution we need to recycle household wastage, which included sewage and garbage, much toxic industrial wastage.

In 1990 the concept of green chemistry was introduced for protecting our environment from toxic elements used in or daily life. The production of substances of daily use by chemical reactions which neither employ toxic chemicals nor release toxic elements in the atmosphere.

The effort has been made by use chemicals from the various chemical reactions in the presence of ultraviolet light, sound waves, microwaves, and enzymes harmful to our environment.

What are the isotopes of radioactive elements?

Isotopes of an element are atoms of the same element with different atomic weights. Isotopes posts identical chemical properties because of their identical electronic structure. Isotopes of a particular element have the same number of protons but varying the number of neutrons inside the nucleus of an atom.
  1. When an Alpha particle emits from within the nucleus the mother element loss two units of atomic number and four units of mass number.
    If a radioactive element with mass number M and atomic number Z ejected an alpha particle the newborn element has mass number = (M - 4) and atomic number = (Z - 2).
  2. When a beta particle emits from the nucleus, the daughter element nucleus has an atomic number one unit greater than that of the mother element nucleus.
    If a radioactive element with mass number M and atomic number Z ejected a beta particle the newborn element has mass number the same and atomic number = (Z + 1).
₈₈Ra²²⁶ → ₈₈₋₂Rn²²²⁻⁴ + ₂He⁴(ɑ)
₈₈Ra²²⁶ → ₈₈Rn²²² + ₂He⁴(ɑ)
₉₀Th²³⁴ → ₉₁Pa²³⁴ + ₋₁e⁰(β)

Isotopes of lead and uranium

Uranium is the first discovered radioactive elements. Uranium in the 6th group or actinides of the periodic table with atomic number 92 and mass number 238. Uranium undergoes successive disintegration till the daughter elements become stable, non-radioactive isotopes of lead.
The mother element along with all the daughter elements down to the stable isotope of lead is called a radioactive disintegration series.

Radioisotopes of uranium - 235 and uranium - 238

Uranium - 238 disintegrate ultimately to an isotope of lead. The entire route involves eight alpha and six beta emissions to form the isotopes of lead with atomic number 82 and mass number 206.
₉₂U²³⁸ → ₈₂Pb²⁰⁶ + 8 ɑ + 6 β
Radioisotopes of lead - uranium -238 disintegration series
Radioisotopes of lead - uranium
The mass number of all the above disintegration products are given by (4n +2) where n = 59 for Uranium - 238. This disintegration series is known as (4n + 2) series.

Uranium - 235 or (4n+3) series starts with uranium - 235 and ends with the stable isotope of lead - 207. Seven alpha and four beta emissions in the entire route of the overall process,
₉₂U²³⁵ → ₈₂Pb²⁰⁷ + 7 ɑ + 4 β
Isotopes of lead-207 and uranium-235 in 4n + 3 series
Isotopes of lead-207 and uranium-235

Isotopes of thorium- 232 in radioactive disintegration

Thorium - 232 undergoes successive disintegration till the daughter elements become stable, non-radioactive isotopes of lead with mass number 208.
The entire route involves six alpha and four beta emission called the thorium- 232 disintegration series or 4n series.
₉₀Th²³² → ₈₂Pb²⁰⁸ + 6 ɑ + 4 β
Isotopes of thorium-232 and lead-208 in 4n + 3 series
Isotopes of thorium 232 and lead 208
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Periodic table and group displacement law

In 1913 Soddy proposed the law for the position of radioisotopes in the periodic table when the knowledge of atomic structure was still incomplete. extensive chemical studies on the disintegration products of different series preceded the announcement of this law.

When an alpha particle is emitted in a radioactive disintegration step, the product is displaced two places to the left in the periodic table but the emission of a beta particle results in a displacement of the product to one place to the right.

Soddy observed that more than one product belonging to the same group on the periodic table. He further established that the product elements belonging to the same group had identical chemical properties though their radioactivity's were different. Soddy coined the term isotope for such elements occupying the same place on the periodic table.

₉₀Th²³² → ₈₈Ra²²⁸ + ɑ → ₈₉Ac²²⁸ + β → ₉₀Th²²⁸ + β
₉₂U²³⁸ → ₉₀Th²³⁴ + ɑ → ₈₉Ac²³⁴ + β → ₉₂U²³⁴ + β

A study of the displacement law further reveals that when a parent radio element emits one alpha and two beta particles successively the product isotope occupies the same group in the periodic table with the parent element.

Uses of radioactive isotopes

Isotopes have been used in a variety filed like medicine, biology, agriculture, trace analysis, and many other fields. The uses of isotopes broadly classified under the heads,

Medicinal uses of isotopes

  1. Radioactive iodine-131 is used in the diagnosis and treatment of thyroid gland disorder. After drinking a solution of sodium iodide containing sodium-131. The radioactive iodine moves preferentially to the thyroid gland. The radiation or beta emission destroys the malignant cells without affecting the rest of the body.
  2. Cobalt-60 is a good gamma-ray emitter. Cobalt-60 used to inhibit the growth of malignant tissue in the treatment of cancer.
  3. For abnormality of the circulation of blood, a small amount of a sodium chloride solution labeled with sodium-24 a beta emitter used. Sodium chloride solution injected into a vein of the patient.

Ionization energy trend in the periodic table

The study of ionization energy is an important article in inorganic chemistry for school and college-level courses.

The electrons are raised to higher energy levels by absorption of energy from external sources. If energy supplied to electrons sufficient, electrons go completely out of the influence of the nucleus of an atom.

The amount of energy required to remove the most loosely bound electron or the outermost electron from an isolated gaseous atom of an element in its lowest energy state or ground state to produce a cation is known ionization energy.

M (g) + Ionization energy → M⁺ (g) + e

The process of ionization is an endothermic process since energy is supplied during ionization. Ionization energy generally represented I or IE and measured in electron volt or kilocalories per gram atom.

What is electron volt simple definition?

One electron volt is the energy consumption by an electron falling through a potential difference of one volt. Electron volt simply represented eV.

∴ 1 eV = charge of an electron × 1 volt
= (1.6 × 10⁻¹⁹ coulomb) × (1 volt)
= 1.6 × 10⁻¹⁹ Joule

1 eV = 1.6 × 10⁻¹² erg

Removal of an electron from the hydrogen atom

The energy required for removing an electron from energy levels of the hydrogen atom called the ionization energy. Simply the energy corresponding to the transition from n = ∞ to n = 1 gives the ionization energy of the hydrogen atom.

The ionization energy of the hydrogen atom
= (2π²me⁴/h²)[(1/n₁²) - (1/n₂²)]
where n₁ = 1 and n₂ = ∞.

∴ EH = 2.179 × 10⁻¹¹ erg
= 2.179 × 10⁻¹⁸ Joule
= (2.179 × 10⁻¹⁸)/(1.6 × 10⁻¹⁹) eV.

∴ EH = 13.6 eV.

Second and third ionization energy

  1. The electrons are removed in stages one by one from an atom. The amount of energy required to remove the first electron from a gaseous atom called its first ionization energy.
  2. M (g) + IE₁ → M⁺ (g) + e
  3. The energy required to remove the second electron from a cation called second Ionization energy.
    M⁺ (g) + IE₂ → M⁺² (g) + e
  4. Similarly, we have third, fourth ionization.
    M⁺² (g) + IE₃ → M⁺³ (g) + e
    M⁺ (g) + IE₄ → M⁺⁴ (g) + e
How to calculate the second ionization energy of helium atom if ionization energy of hydrogen is13.6 eV?

The ground state electronic configuration of helium 1S². The second ionization potential means the removal of the second electron from the 1S orbital against the nuclear charge of +2.

∴ IEHe = (2π²mZ²e⁴/h²)[(1/n₁²) - (1/n₂²)]
= Z² × IEH.

∴ Second Ionization energy of helium = 2² × 13.6
= 54.4 eV.

First ionization energy trend in the periodic table

First ionization energy trend in the periodic table
Ionization energy and the periodic table
The trend of ionization energy in periodic table influenced by the following factors
  • Atomic radius.
  • Change on the nucleus or atomic number.
  • Completely-filled and half-filled orbitals.
  • Shielding effect of the inner electrons.
  • Overall charge on the ionizing species.

How are the atomic radius and ionization energy related?

Greater the atomic radius or the distance of an electron from the positive charge nucleus of an element, the weaker will be the attraction. Hence the energy required to remove the electron lower.

An atom raised to an excited state by promoting one electron to a higher energy level than the excited electron was more easily detached because of the distance between the electron and nucleus increases.

The Atomic radius decreases from left to right along a period of the periodic table because of the increasing charge on the nucleus of an atom. Thus when we move left to right along with period normally ionization energy increases.

When we moving from top to bottom in a group the ionization energy of the elements decreases with the increasing size of the atom.

Atomic number and ionization energy relationship

With the increasing atomic number change on the nucleus increases and more difficult to remove an electron from an atom. Hence grater would be the value of ionization.

Normally the value of ionization increases in moving from left to right in a period since with the increasing atomic number the change on the nucleus also increases.

The increase in the magnitude of ionization due to the increase in the electrostatic attraction between the outermost electrons and the nucleus of an atom. Thus it becomes more difficult to remove an electron.

Half filled and completely filled orbitals

According to Hund's rule, an atom having half-filled or completely filled orbital comparatively more stable and hence more energy consumption to remove an electron from such atom.

The ionization of such an atom is therefore relatively difficult than expected normally from their position in the periodic table.
Few exceptions in the value of ionization energy in the periodic table can be explained on the basis of the half-filled and completely filled orbitals.

The ionization energy of group-15 elements is higher than the group-16 elements and group-2 elements are higher than the group-3 elements in the periodic table.
Boron and nitrogen in the second period and magnesium and phosphorus in the third period have a slightly higher value of ionization energy than those normally expected.

Nitrogen and phosphorus in group-15 elements with atomic number 7 and 15 have the electronic configuration

1S² 2S² 2P³
1S² 2S² 2P⁶ 3S² 3P³.

Removal of an electron from half-filled 2P and 3P suborbital of nitrogen and phosphorus required more energy.

Removal of an electron from the group-2 element of beryllium and magnesium with completely-filled S-subshell required more energy.
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Shielding effect of the inner electrons

The study of electrostatic attraction between the electrons and nucleus shows that an outer electron attracted by the nucleus and repelled by the electrons of the inner shell.
The combined effect of this attractive and repulsive force acting on the outer electron experiences less attraction from the nucleus. This is known as the shielding effect.
Thus a larger number of electrons in the inner shell, lesser the attractive force for holding outer electron.

The radial distribution functions of the S, P, d subshell show that for the same principal quantum number the S-subshell most shielding than the p-subshell and least shielding the d - orbital.

∴ Shielding efficiency: S〉P〉d.

As we move down a group, the number of inner-shells increases and hence the ionization tends to decreases.

Group-2 elements

What trend in ionization energy occurs across a period?

What trend in ionization energy occurs across a period?
Ionization energy trend
The greater the charge on the nucleus of an atom the more energy consumed for removing an electron from the atom.

More energy consumed means more energy required for removing an electron from the atom. With the increase atomic number electrostatic attraction between the outermost electrons and the nucleus of an atom increases. Thus removal of an electron from an atom more difficult.

The values of ionization energy generally increase in moving left to right in a period since the nuclear charge of an element also increases in the same direction.

Due to the presence of a completely filled and half-filled orbital of beryllium and nitrogen, the ionization energy of beryllium and nitrogen slightly higher than the neighbor element boron and oxygen.
Ionization energy trend for the second period in the periodic table


The overall charge of an atom

An increase in the overall charge on the ionizing species (M⁺, M⁺², M⁺³, etc) will enormously influence the ionization since electron withdrawal from a positively charged species more difficult than from a neutral atom.

The first ionization of the elements varies with their positions in the periodic table. In each of the tables, the noble gas has the highest value and the alkali metals the lowest value for the ionization energy.

Describe how ionization energy impacts ionic bonding

The study of the ionization energy of the element in a particular group of the periodic table is essential for the properties of the elements.

Lithium, sodium, potassium, rubidium, and cesium or alkali metal in the periodic table with a low value of ionization energy, point to the high reactivity of alkali metals for the formation of the ionic bonding.

Examples of crystalline and amorphous solids

All the branches of chemical science and all the science, technology depend on the structure of atom or molecules. Thus study crystalline solids is an important article for school or college level students who want to study this article in different books or websites.

Solids are characterized by their definite shape and also their considerable mechanical strength and rigidity. The rigidity due to the absence of translatory motion of the structural units (atoms, ions, etc) of the solids. Here we study crystalline solids and amorphous solids.

These properties are due to the existence of very strong forces of attraction amongst the molecules or ions. It is because of these strong forces that the structural units (atoms, ions, etc) of the solids do not possess any translatory motion but can only have the vibrational motion about their mean position.

Liquids can be obtained by heating up to or beyond their melting points. In solids, molecules do not possess any translatory energy but posses only vibrational energy. The forces of attraction amongst them are very strong.

The effect of heating is to impart sufficient energy to molecules so that they can overcome these strong forces of attraction. Thus solids are less compressible than liquids and denser than the liquid.
Solids are generally classified into two broad categories: crystalline and amorphous substances.

What is the definition of crystalline solid?

The definition of crystalline solids is the solid which posses a definite structure, sharp melting point, and the constituents may be atoms, ions, molecules have order arrangement of the constituents extends in long-range order called crystalline solids.

Sodium chloride, potassium chloride, sugar, and ice, quartz are examples of crystalline solids possess a sharp melting point.

The pattern of such crystal having observed in some small crystal region to predict accurately the position of the particle in any region under observation.

Properties of crystalline solids

In the crystalline, the constituents may be atoms, ions, molecules.
  1. Crystalline solids are a sharp melting point, flat faces and sharp edges which is a well-developed form, are usually arranged symmetrically.
  2. Definite and the ordered arrangement of the constituents extends over a large distance in the crystal and called the long-range order.
  3. Crystalline solids those belonging to the cubic class are enantiotropic in nature. The magnitude of the enantiotropic property depends on the direction along which is measured.

Why amorphous solids called supercooled liquid?

The solids which do not possess a definite structure, sharp melting point, and the constituents may be atoms ions, molecules do not have order arrangement of the constituents extends over a short-range the solids called amorphous solids.

Amorphous solids such as glass, pitch, rubber, plastics possessing many characteristics of crystalline such as definite shape rigidity and hardness, do not have this ordered arrangement and melt gradually over a range of temperatures. For this reason, they are not considered as solids but rather highly supercooled liquids.

Difference between crystalline and amorphous solids

  1. Crystalline solids possess definite structure and sharp melting point but amorphous solids that do not possess a definite structure and sharp melting point.
  2. Crystalline solids constituents(atoms, molecules) have order arrangement of the constituents extends over a long-range in solids but amorphous solids the constituents may be atoms, molecules do not have order arrangement.
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Classify of crystalline on the basis of forces

Study the basics of the nature of force operating between constituent particles or atoms, ions, molecules of matter, crystalline solids are classified into four categories.
Types of crystalline solids for study online
Types of crystalline solids

Molecular crystals types

Forces that hold the constituents of molecular crystals are of Van der Waals types. These are weaker forces because of which molecular crystals are soft and possess low melting points.

Carbon dioxide, carbon tetrachloride, argon, and most of the organic compounds are examples of these types of crystals.
This class further classified into three category
  1. Non-polar binding crystals
    The constituent particles of these types of crystalline solids are non-directional. Hydrogen, helium atom or non-polar hydrogen, oxygen, chlorine, carbon dioxide, methane molecules are examples of these types of crystal. The force operating between constituent particles atoms or molecules is a weak London force of attraction.
  2. Polar binding crystals
    The polarity of bond shows in these types of crystalline solids. Sulfur dioxide and ammonia are examples where force operating between constituent particles is the dipole-dipole attraction force.
  3. Hydrogen-bonded crystals
    The constituent molecule of these types of crystalline solids is polar molecule and these molecules are bounded each other by hydrogen bonding. An example of this type of crystal ice.

Ionic crystal structure

The forces involved here are of electrostatic forces of attraction. These are stronger than the non-directional type. Therefore ionic crystals strong and likely to be brittle.

They have little electricity with high melting and boiling point and can not be bent. The melting point of the ionic crystal increases with the decreasing size of the constituent particles.

In ionic crystals, some of the atoms may be held together by covalent bonds to form ions having a definite position and orientation in the crystal lattice. Calcium carbonate is an example of these types of crystalline solids.

Covalent crystal or covalent bonding crystal

The forces involved here are chemical nature or covalent bonds extended in three dimensions. They are strong and consequently, the crystals are strong and hard with high melting points. Diamond, graphite, silicon are examples of these types of crystalline solid.

Metallic crystalline solids

Electrons are held loosely in these types of crystals. Therefore they are good conductors of electricity. Metallic crystalline solids can be bent and are also strong.

Since the forces have non-directional characteristics the arrangement ao atoms frequently correspond to the closet packing of the sphere.

Crystalline allotropes of carbon

Carbon has several crystalline isotropic forms only two of them are common diamond and graphite. There are four other rare and poorly understood allotropes, β-graphite, Lonsdaleite or hexagonal diamond, Chaoite (very rare mineral) and carbon VI.
The last two forms appear to contain -C≡C-C≡C- and are closer to the diamond in their properties.

Structure of graphite crystal

The various amorphous forms of carbon like carbon black, soot, etc. are all microcrystalline forms of graphite.
Graphite consists of a layer structure in each layer the C-atoms are arranged in hexagonal planner arrangement with SP² hybridized with three sigma bonds to three neighbors and one π-bonds to one neighbor.
The resonance between structures having an alternative mode of π bonding makes all C-C bonds equal, 114.5 pm equal, consistent with a bond order of 1.33.
The π electrons are responsible for the electrical conductivity of graphite. Successive layers of Carbon-atoms are held by weak van der Waals forces at the separation of 335pm and can easily slide over one another.

Structure of diamond crystal

In diamond, each SP³ hybridized carbon is tetrahedrally surrounded by four other carbon atoms with C-C bond distance 154 pm. These tetrahedral belong to the cubic unit cell.
Natural diamond commonly contains traces of nitrogen or sometimes very rarely through traces of al in blue diamonds.

How much Van't Hoff equation - effect on temperature?

Van't Hoff equation proposed equilibrium of a chemical reaction is constant at a given temperature. The equilibrium constant, Kp values can be changed with the change of temperature.

This will be evident from the study of Kp values at different temperatures of a chemical reaction.
N₂ + O₂ ⇆ 2NO

TemperatureKp × 10⁴
2000° K4.08
2200° K11.00
2400° K25.10
2600° K50.30

The quantitative relation, known Van't Hoff equation connecting chemical equilibrium and temperature can be derived thermodynamically starting from Gibbs - Helmholtz equation.
The Gibbs - Helmholtz equation
ΔG⁰ = ΔH⁰ + T[d(ΔG⁰)/dT]p
Zero superscripts are indicating stranded values.

or,- (ΔH⁰/T² )= -(ΔG⁰/T² )+(1/T)[d(ΔG⁰)/dT]p
or, - (ΔH⁰/T² ) = [d/dT(ΔG⁰/T)]p.

Van't Hoff isotherm

- RT lnKp = ΔG⁰

or, - R lnKp = ΔG⁰/T.

Differentiating with respect to temperature at constant pressure
- R [dlnKp/dT]p = [d/dT(ΔG⁰/T)]p.

Comparing the above two-equation

dlnKp/dT = ΔH⁰/T²

This is the differential form of Van't Hoff equation.

The integrated form of van't Hoff equation

The greater the value of standard enthalpy of a reaction, the faster the chemical reaction reaching an equilibrium point.

dlnKp/dT = ΔH⁰/T²

Separating the variables and integrating
∫ dlnKp = (ΔH⁰/R)∫ (dT/T²)

ΔH⁰ independent of temperature.
or, lnKp = - (ΔH⁰/R)(1/T) + C
where C = integrating constant.

The integration constant can be evaluated and identified the value of ΔS⁰/R, using the relation
ΔG⁰ = ΔH⁰ - TΔS⁰.

∴ Van't hoff equation

lnKp = - (ΔH⁰/RT) + (ΔS⁰/R).

The standard free energy of chemical reaction 2A + B ⇆ 2C at 500 K = 2 KJ mol⁻¹. Calculate Kp at 500 K for the chemical reaction A + ½B ⇆ C.

Standard free energy at 500 K for the chemical reaction A + ½B ⇆ C
= (2 kJ mol⁻¹)/2
= 1 kJ mol⁻¹.

ΔG⁰ = - RT lnKp.
∴ 1 = - 8.31 × 10⁻³ × 500 × lnKp
or, lnKp = 1/(8.31 × 0.5)
= 0.2406.

∴ Kp = 1.27.

Heat absorption and emission in a chemical reaction

Heat absorption and emission in a chemical reaction can be studied from the following analysis.

Reactants → Products

We may study the following possibilities
  • Heat absorption, ΔH⁰ = positive.
Low enthalpy side → High enthalpy side.

If heat absorbed, the forward direction of the chemical reaction is the endothermic direction and the reverse one is the exothermic direction. The dissociation of hydrogen iodide into hydrogen and Iodine is an example of this type of chemical reaction.

HI ⇆ H₂ + I₂ ΔH⁰ = (+) ve
  • Heat emission, ΔH⁰ = negative.
High enthalpy side → Low enthalpy side.

If heat emission, the forward direction of the chemical reaction is the exothermic direction and the reverse one is the endothermic direction.
The formation of ammonia from hydrogen and nitrogen is an example of this type of chemical reaction.

N₂ + H₂ ⇆ 2NH₃ ΔH⁰ = (-) ve
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Endothermic and exothermic chemical reaction

Van't Hoff equation drowns the relation between equilibrium constant and endothermic and exothermic chemical reactions.
  1. For an endothermic reaction, ΔH⁰ 〉 0 and the right-hand side of the equation positive. This leads to the fact that lnKp increases with increasing temperature.
  2. For an exothermic reaction, ΔH⁰ 〈 0 and the right-hand side of the equation negative. This leads to the fact that lnKp decreases with increasing temperature.
Van't Hoff equation and equilibrium point
Van't Hoff equation

Heat change of a chemical reaction in two temperature

For the ideal system, the heat change or enthalpy change is not a function of pressure.

∴ Standard enthalpy change = enthalpy change
or, ΔH⁰ = ΔH

dlnKp/dt = ΔH/RT²

lnKp = (ΔH/RT) + ΔS/R

However, the entropy of an ideal gas depends strongly on pressure and ΔS and ΔG per mole of reaction in the mixture differ quite substantially from ΔS⁰ and ΔG⁰.

The integrated form of the Van't Hoff equation at two temperature

ln(Kp₂/Kp₁) = (ΔH/R){(T₂ - T₁)/T₁T₂)}

where Kp₁ and Kp₂ are the equilibrium constants of the reaction at two different temperatures T₁ and T₂ respectively.

Determination of Kp₁ and Kp₂ at two temperatures helps to calculate the value of change of enthalpy of the chemical reaction.

The above relation called Van't Hoff reaction isobar since pressure remains constant during the change of temperature.

Show that the equilibrium point for any chemical reaction given by ΔG = 0.

Van't Hoff reaction isotherm
ΔG = - RT lnKa + RT lnQa.
When the reaction attains equilibrium point,
Qa = Ka.

∴ ΔG = 0

Assumptions from Van't Hoff equation

  1. The reacting system of the chemical reaction behaves ideally.
  2. ΔH has taken independent of temperature for a small range of temperature change.
Due to the assumption involved ΔH and ΔU do not produce the precise value of these reactions. As ΔG independent of pressure for ideal system ΔH and ΔU also independent of pressure.

ΔG⁰ = - RT lnKp
or, [dlnKp/dT]T = 0.

Use Gibbs - Helmholtz equation to derive the Van't Hoff reaction isochore. What condition do you expect a linear relationship between log k and 1/T?

Again Kp = Kc (RT)ΔƔ
or, lnKp = lnKc + ΔƔ lnR + ΔƔ lnT
Differentiating with respect to T,
dlnKp/dT = dlnKc/dT + ΔƔ/T.

dlnKp/dT = ΔH⁰/RT²
or, dlnKc/dT = ΔH⁰/RT² - ΔƔ/T
or, dlnKc/dT = (ΔH⁰ - ΔƔRT)/RT²

∴ dlnKc/dT = ΔU⁰/RT²

ΔU⁰ = standers heat of reaction at constant volume. This is the differential form of Van't Hoff reaction isochore.

The integrated form of the equation at two temperature
ln(Kc₂/Kc₁) = (ΔU⁰/R){(T₂ - T₁)/T₁T₂)}.

For ideal system ΔU⁰ = ΔU. Since the reaction occurs at constant volume and the equation called Van't Hoff reaction isochore.

The heat of a reaction and Le-Chatelier principal

Van't Hoff equations give a quantitative expression of the Le-Chatelier principle.
lnKp = - (ΔH/R)(1/T) + C.
  1. Endothermic reaction, ΔH〉0, an increase in temperature increases the value of lnKp of the chemical reactions.
  2. An exothermic reaction, ΔHㄑ 0, with rising in temperature, lnKp decreased.
Change of Kp provides the calculation of the quantitative change of equilibrium point yield of products.

According to the Le - Chatelier Principle, whenever stress placed on any system in a state of the equilibrium point, the system always reacts in a direction to reduce the applied stress.
  1. The temperature increased in a chemical reaction, the system at equilibrium point will try to move in a direction in which heat absorbed, which is endothermic reaction favors.
  2. When the temperature decreased in a chemical reaction, the system at equilibrium point will try to move in a direction in which heat emitted, which is exothermic reaction favors.

What is the zero-order kinetics reactions?

    Chemical kinetics is the branch of physical chemistry that deals with a study of the speed of chemical reaction. Such studies also enable us to understand the mechanism by which the reaction occurs.
    Study of chemical equilibrium only initial and final states was considered, the energy relation between reactants and product is governed by thermodynamics where the time or the intermediate states were of no concern.
    The velocity of a reaction is the amount of chemical change occurring per unit time. The rate is generally expressed as the decrease in the concentration of the reactant or increase in concentration per unit time.
    Some surface reactions the rate has been found to be independent of concentration. These are zero-order kinetic reactions.

The concentration of zero-order reactions

    Let us take a reaction represented as
    A → Product
    Let the initial concentration of the reactant a and product is zero. After the time interval t, the concentration of the reactant is (a-x) and the concentration of the product is x. Thus x is decreased concentration in zero-order reaction.
    If the rate of the reaction is equal to the rate constant. What is the order of the reaction?
    Zero-order reaction.

The zero-order reaction in terms of product

    The mathematical equation of zero-order kinetics in terms of product,
dx/dt = k₀
Where k₀ is the rate constant of the zero-order reaction.
or, dx = k₀dt

Integrating the above reaction,
∫dx = k₀ ∫dt
or, x = k₀t + c
where c is the integration constant of the reaction.

When t = o, x is also zero thus, C = o Thus the above equation is,
x = k₀ t
    This is the relationship between decreases of concentration of the reactant(x) within time(t).

Zero-order kinetics reactions in terms of reactant

Rate equation in terms of reactant,
-d[A]/dt = k₀ [A]⁰ = k₀
Where [A] is the concentration of the reactant at the time t.
or, - d[A] = k₀dt

Integrating the above equation,
We have - ∫d[A] = k₀ ∫ dt
or, - [A] = k₀t + c
where c is the integration constant of the reaction.

If initial at the time t = 0 concentration of the reactant [A]₀ Then from the above equation,
- [A]₀ = 0 + c
or, c = -[A]₀
    Putting the value on the above equation,
- [A] = kt - [A]₀
    This is another form of the rate equation in zero-order kinetics.

Half-life and zero-order kinetics reactions

    The time required for half of the reaction to be completed is known as the half-life of the zero-order reaction. It means 50% of reactants disappear in that time interval.
    If in a chemical reaction initial concentration is [A]₀ and after t time interval the concentration of the reactant is [A].
Then, [A]₀ - [A] = kt
    Thus when t = t½, that is the half-life of the reaction, the concentration of the reactant [A] = [A]₀/2. Putting the value on the above equation,
We have [A]₀ - [A]₀/2 = k t½
or, k t½ = [A]₀/2
t½ = [A]₀/2k
    Thus for the zero-order kinetics the half-life of the reaction proportional to its initial concentration.

Examples of zero-order of reactions

    The only heterogeneous catalyzed reactions may have zero-order kinetics.
Study zero-order kinetics reaction in chemical kinetics
Zero-order kinetics reaction
    The half-life of a zero-order reaction is x and the reaction is completed on t₁ time. What is the relation between x and t₁?
    2x = t₁
    For the reaction H₂ + Cl₂ → 2HCl on sunlight and taking place on the water. What is the order of the reaction?
    This is a zero-order reaction.
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Unit of the rate constant in a chemical reaction

    The rate equation in terms of product for the nth-order reaction is,
d[A]/dt = k [A]n
or, k = (d[A]/dt) × (1/[A]n)
    Thus the unit of rate constant(k) = (unit of concentration)/{unit of time × (unit of concentration)n}
    = (unit of concentration)1-n/unit of time
    Zero-order kinetics reaction the concentration is expressed in lit mole⁻¹ and time in sec
Then the rate constant = (lit mol⁻¹)/sec
= mol lit⁻¹sec⁻¹
    For the reaction N₂O₅ → 2NO₂ + ½ O₂, the rate of disappearance of N₂O₅ is 6.25 × 10⁻³ mol lit⁻¹sec⁻¹, what is the rate of formation of NO₂ and O₂ respectively?
    1.25 × 10⁻² and 3.125 × 10⁻³ mol lit⁻¹sec⁻¹
    The rate constant of a chemical reaction is 5 × 10⁻⁸ mol lit⁻¹sec⁻¹. What is the order of this reaction? How long does it take to change concentration from 4 × 10⁻⁴ moles lit⁻¹ to 2 × 10⁻² moles lit⁻¹?
    The reaction is a zero-order reaction and 3.92 × 10⁵ sec takes to change concentration from 4 × 10⁻⁴ moles lit⁻¹ to 2 × 10⁻² moles lit⁻¹.
    For a reaction, N₂ + 3 H₂ → 2NH₃, if d[NH₃]/dt = 2 × 10⁻⁴mol lit⁻¹sec⁻¹, what is the order and the value of - d[H₂]/dt of this reaction?
    Zero-order reaction and the value of d[H₂]/dt = 3 × 10⁻⁴ mol lit⁻¹sec⁻¹

Characteristics of zero-order kinetics

  1. The rate of the reaction is independent of concentration.
  2. Half-life is proportional to the initial concentration of the reactant.
  3. The rate of the reaction is always equal to the rate constant of the reaction at all concentrations.

Online college courses for soft and hard acids bases

Soft and hard acids and bases (SHAB) principles are very helpful for study the stability of the complex between acid and bases and it is very useful for study online college courses. This principle was proposed in 1963 by Ralph G. Pearson.

A + :B → A : B

According to the SHAB principle, the complex most stable when participating acid and base are either both soft or both hard and least stable when one of the reactants (namely acids and base) is very hard and the other one is very soft.

To study the donner properties of different bases and preferences of a particular base to bind acid. Hydrogen ion and methyl mercury (II) ion is used for this comparison study.

Proton and methyl mercury cation have only one coordination position to accommodate only one coordinate bond but the two cations vary widely in their preferences to bases.

This preference was estimated from the experimental determination of equilibrium constants for the exchange reactions.

BH⁺ + [CH₃Hg(H₂O)]⁺ ⇄ [CH₃HgB]⁺ + H₃O⁺

Experimental results indicate that bases in which nitrogen be a donor atom, oxygen or fluorine prefer to coordinate with the hydrogen ion. Bases which has donor atom phosphorus, sulfur, iodine, bromine, chlorine or carbon prefers to coordinate with mercury.

The neutralization reaction of acids and bases

Lewis defined, an acid-base neutralization reaction involves an interaction of a vacant orbital of an acid and a filled or unshared orbital of a base.

A + : B A: B
Lewis acid Lewis base

The species A is called Lewis acid or a generalized acid and B is called Lewis base or a generalized base. Strong acid and a strong base will form a stable complex.

What are soft and hard bases?

The donor atoms of the second category are of low electronegativity, high polarizability, and are easy to oxidize. Such donors have been called ‘soft bases' by Pearson since they are holding on to their valence electrons rather loosely.

The donor atoms in the first group have high electronegativity, low polarisability and hard to oxidize. Such donors have been named ‘hard bases' by Pearson since they hold on to their electrons strongly.

Classify the following as soft and hard acids and bases.

  1. Hydride ion.
  2. Nickel (IV) ion.
  3. Iodine (+1) ion.
  4. Hydride ion.

  1. The hydride ion has a negative charge and too large in size compared to the hydrogen atom. Electronegativity of hydride ion quite low. Due to high polarizability and large size, the valence electron is loosely bound in hydride ion and it is a soft base.
  2. The nickel (IV) has quite a high positive charge and small size compared to the nickel (II). Electronegativity of nickel (IV) will be very high and polarisability will low. Hence it is hard acid.
  3. Mono-positive iodine has a low positive charge and has a large size. It has a low electronegativity and high polarizability.
  4. Hydrogen ion has the smallest size with a high positive charge density and absence of unshared pair of electrons in its valence shell. All these will give a high electronegativity and very low polarizability. Hence hydrogen ion is a hard acid.

Study the properties of soft and hard bases

In simple terms, hardness associated with a tightly held electron shell with little tendency to polarize. On the other hand, softness associated with a loosely bound polarizable electron shell.

It will be seen that within a group of the periodic table softness of the Lewis bases increases with the increase in the size of the donor atoms. Among the halide ions, softness increases in the order.
Online college courses for soft and hard acids bases
Soft and hard acids and bases
Study online for schools and college-level

What are soft and hard acids?

After having gone through a classification of bases, a classification of Lewis acids is necessary. The preferences of a given Lewis acid towards ligands of different donor atoms are usually determined from the stability constant values of the respective complexes or from some other useful equilibrium constant measurements.

When this is done, metal complexes with different donor atoms can be classified into two sets based on the sequences of their stability.

Hard acids have small acceptor atoms, are of high positive charge and do not contain unshared pair of electrons in their valence shell, although all these properties may not appear in one and the same acid.
These properties lead to high electronegativity and low polarizability. In keeping with the naming of the bases, such acids are termed as 'hard acids'.

N≫P; O≫S; F〉Cl〉Br〉I

Soft acids have large acceptor atoms, are of low positive charge and contain ushered pairs of electrons in their valence shell. These properties lead to high polarizability and low electronegative. Again in keeping with the naming of the bases, such acids are termed 'Soft acids'.

N≫P; O≫S; F〉Cl〉Br〉I
Hard AcidsBorderline acidsSoft Acids
H⁺, Li⁺, Na⁺
K⁺, Be⁺², Mg⁺², Ca⁺², Sr⁺², Mn⁺², Al⁺³, Ga⁺³, In⁺³, La⁺³, Lu⁺³, Cr⁺³, Co⁺³ Fe⁺³, As⁺³, Si⁺⁴, Ti⁺⁴, U⁺⁴, Ce⁺³, Sn⁺⁴, VO⁺², UO₂⁺², MoO⁺³
Fe⁺, Co⁺², Ni⁺², Cu⁺², Zn⁺², Pb⁺², Sn⁺², Sb⁺², Bi⁺², Rh⁺², B(CH₃)₃, SO₂, NO⁺, GaH₃Cu⁺, Ag⁺, Au⁺, Tl⁺, Hg⁺, Pd⁺, Cd⁺, Pt⁺, CH₃Hg⁺, Tl⁺³, BH₃, GaCl₃, InCl₃, I⁺, Br⁺, I₂, Br₂, and zerovalent metal atom

SHAB principle for soft and hard acids and bases

This principle also means that if there is a choice of the chemical reaction between an acid and two bases and two acids and a base, A hard acid will prefer to combine with a hard base and a soft acid will prefer to combine with soft base and thus a more stable product will be obtained.

The hard acid - hard base may interact with strong ionic forces. Hard acids have small acceptor atoms and positive charge while the hard bases have small-donor atoms but often with a negative charge. Hence a strong ionic interaction will lead to the hard acid-base combination.

On the other hand, a soft acid - soft base combination mainly a covalent interaction. Soft acids have large acceptor atoms, are of low positive charge and contain ushered pairs of electrons in their valence shell.

Application of SHAB principle in acid chemistry

The SHAB concept is extremely useful in elucidating many properties of chemical elements in acid chemistry and will be often referred to at appropriate places.
  1. Boron trifluoride and boron trihydride the behavior of boron is different in these two compounds.
    The presence of hard fluoride ions in boron trifluoride easy to add hard bases.
    The presence of soft hydride ions in boron trihydride easy to add soft bases.
  2. [CoF₆]⁻³ more stable than [CoI₆]⁻³. It will be seen that cobalt (III) ion is a hard acid, fluoride ion is a hard base and iodide ion is a soft base.
    In [CoF₆]⁻³, hard acid, and hard base form a stable complex than the [CoI₆]⁻³ form by a hard acid and soft base.
  3. The existence of certain ores can also be rationalized by applying the SHAB principle. Thus hard acids such as magnesium, calcium, and aluminum occur in nature as magnesium carbonate, calcium carbonate, and aluminum oxide but not as magnesium calcium and aluminum sulfides
    Since the anion CO₃⁻² and O⁻² are hard bases and S⁻² is a soft base. Soft acids such as Cu⁺, Ag⁺ and Hg⁺², on the other hand, occur in nature as sulfides.
  4. The borderline acids such as Ni⁺², Cu⁺², and Pb⁺² occur in nature both as carbonates and sulfides. The combination of hard acids and hard bases occurs mainly through ionic bonding as in Mg(OH)₂ and that of soft acids and soft bases occurs mainly by covalent bonding as in HgI₂.
Why AgI2- stable, but AgF2- does not exist

We know that mono positive silver ion is a soft acid, fluoride ion is hard to base and iodide ion is the soft base.
Hence AgI₂⁻ (soft acid + soft base) is a stable complex and AgF₂⁻ (soft acid + hard base) does not exist.

Mercury hydroxide dissolved readily in acidic solution but mercury sulfide does not?

In the case of mercury hydroxide and mercury sulfide, mercury is a soft acid and hydroxide and sulfide are a hard base and soft base respectively.

Mercury sulfide formed by soft acid and soft base will be more stable than mercury hydroxide formed by soft acid and hard base.

More stability of mercury sulfide than that of mercury hydroxide explains why mercury hydroxide dissolved readily in acidic solution but mercury sulfide does not dissolve readily in acidic solution.

f block elements names and symbols

The f-block in the periodic table appears in two series characterized by the filling of 4f and 5f sublevel in the respective third inner principal quantum number from outermost.

The 4f block contains fourteen elements cerium to lutetium with the atomic number from 58 to 71 and is called Lanthanum's as they appear after lanthanum.

The 5f block contains fourteen elements thorium to lawrencium with the atomic number from 90 to 103 and is called actinides as they appear after actinium.

General electronic configuration of 4f block elements

The 4f block in the periodic table has been variously called rare earth, lanthanum’s, and lanthanum. The lanthanum atoms and their trivalent ions have the following general electronic configuration.

Lanthanum atoms
[Pd] 4fn 5S² 5P⁶ 5d¹ 6S²
where n has values 1 to 14.

Lanthanum (M⁺³) ions
[Pd] 4fn 5S² 5P⁶
where n has values 1 to 14.
Electronic configuration of 4f-block elements in the periodic table
4f-block elements in the periodic table
4f-block or inner transition elements with increasing atomic number, electrons are added to the deep-seated 4f-orbital. The outer electronic configuration of 4f-elements is 6S² and inner orbitals contain f -electrons.
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Cerium, Gadolinium, and Lutetium electronic configuration

Only Cerium, Gadolinium, and Lutetium contain one electron in 5d orbital with atomic number 58, 64 and 87. The electronic configuration of these elements is outside of the general electronic configuration.

Electrons of similar spin developed an exchange interaction which leads to the stabilization of the system. For the electrons of similar spin, repulsion is less by an amount called the exchange energy of an electron.

The greater the number of electrons with parallel spins the greater is exchanged interaction and the greater stability. The basis of Hound's rules of maximum spin municipality.

[Pd] 4f¹ 5S² 5P⁶ 5d¹ 6S²

Gadolinium atom contains one electron in a 5d orbital. 4f and 5d are very close in terms of the energy of 4f and 5d orbital. In such a case, the half-filled orbital is slightly more stable than orbital with one additional electron by increasing exchange energy.

Maximum stability of f-shell when there are seven electrons with parallel spins in the seven f-orbital. This half-filled energy level stabilizes by exchange energy.

[Pd] 4f⁷ 5S² 5P⁶ 5d¹ 6S²

Lutetium also has the f¹⁴d¹ configuration where the last electrons have added the capacity of the f-shell.

[Pd] 4f¹⁴ 5S² 5P⁶ 5d¹ 6S².

Electronic configuration of praseodymium

Praseodymium possesses electronic configuration 4f³ 6s² instead of the expected one 4f² 5d¹ 6s². This can be explained by (n + l) rules, the orbital which has a higher value of (n + l) is the higher energy orbitals.

n + l = 4+3 = 7 for 4f-orbital.
n + l = 5+7 =7 for 5d-orbital

4f and 5d-shell sum of principal and azimuthal quantum number the same. In this case, the highest number of principal quantum numbers is the higher energy quantum level of an atom and 5d-orbital is the higher energy quantum shell.

Again electrons are fed into orbitals in order of increasing energy until all the electrons have been accommodated.

Electron filling process for praseodymium f-electron filling first and possess electronic configuration 4f³ 6s².

Why +3 oxidation number is so common and stable in lanthanum?

The nature of lanthanum's elements is such that three electrons are removed comparatively easy to give the normal trivalent state.

The ground state electronic configuration of the natural lanthanum's atoms and trivalent ions

Lanthanum's [Pd] 4fn 5S² 5P⁶ 5d¹ 6S²

Lanthanum ions [Pd] 4fn 5S² 5P⁶
where n is 0 to 14 from Lanthanum to Lutetium.

As a consequence, the f-electrons can not participate in the chemical reactions thus +3 oxidation numbers common and stable in lanthanums.

General electronic configuration of 5f block elements

Electronic configuration of 5f-block elements in the periodic table
5f-block elements in the periodic table
The second series f block elements result from the filling of 5f-orbital and consist of elements thorium to lawrencium with atomic number 90 to 103.

All of them are radioactive but most abundant isotopes of thorium and uranium have very long half-lives.
General electronic configuration of these elements and ion are

Actinides atoms
[Rn] 4fn 5d1-2 6S²
where n has values 1 to 14

Actinides (M⁺³) ions
[Rn] 4fn
where n has values 1 to 14.

Chemistry 1

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