Grade 11
  1. Basic concepts of chemistry  1.1. Importance of Chemistry  1.2. Nature and scope of chemistry  1.3. laws of chemical combination  1.3.1. Law of conservation of mass  1.3.2. Law of definite proportions  1.3.3. Law of multiple proportions  1.3.4. Law of gaseous volume  1.3.5. Avogadro's Law  1.4. Dalton's atomic theory  1.5. Mole concept and molar mass  1.6. Percent composition  1.7. Empirical and molecular formula  1.8. Stoichiometry and Stoichiometric Calculations  1.9. Limiting reagent concept
  2. Structure of the atom  2.1. Discovery of the electron, proton, and neutron  2.2. Atomic Model  2.2.1. Thomson's model  2.2.2. Rutherford's model  2.2.3. Bohr's model  2.3. Quantum mechanical model of the atom  2.4. Dual nature of matter and radiation  2.5. Heisenberg's uncertainty principle  2.6. Quantum numbers  2.7. Atomic orbitals and their shapes  2.8. Electronic configuration of elements  2.9. Aufbau principle  2.10. Pauli's exclusion principle  2.11. Hund's maximum multiplicity rule  2.12. de Broglie's hypothesis  2.13. Photoelectric effect
  3. Classification of elements and periodicity in properties  3.1. Historical development of the periodic table  3.2. Modern Periodic Law and Periodic Table  3.3. Periodic trends in properties  3.3.1. Atomic and Ionic Radius  3.3.2. Ionization enthalpy  3.3.3. Electron gain enthalpy  3.3.4. Electronegativity  3.3.5. Valency  3.3.6. Metallic and Non-Metallic Properties  3.3.7. Oxidation states  3.4. Unusual Properties of the First Elements
  4. Chemical Bonding and Molecular Structure  4.1. Kossel–Lewis approach to chemical bonding  4.2. Ionic or electrovalent bond  4.3. Covalent bond and its features  4.4. Bond parameters  4.5. VSEPR Theory  4.6. Valence bond theory  4.7. Hybridization and its types  4.8. Molecular orbital theory  4.8.1. Bond order and stability  4.9. Hydrogen bonding
  5. States of matter  5.1. Intermolecular forces  5.2. Gas Laws  5.2.1. Boyle's law  5.2.2. Charles's Law  5.2.3. Avogadro's Law  5.2.4. Dalton's law of partial pressure  5.2.5. Graham's law of spread  5.3. Ideal Gas Equation and Applications  5.4. Real gases and deviations from ideal behaviour  5.5. Kinetic molecular theory of gases  5.6. Liquefaction of gases  5.7. Properties of Liquids  5.8. Surface tension and viscosity
  6. Thermodynamics  6.1. System and environment  6.2. Types of systems in thermodynamics  6.3. Types of procedures  6.4. First law of thermodynamics  6.5. Internal energy and enthalpy  6.6. Heat capacity and specific heat  6.7. Hess's law of constant heat summation  6.8. Bond dissociation enthalpy  6.9. Enthalpy of formation and combustion  6.10. Enthalpy of solution and neutralization  6.11. Spontaneity and the second law of thermodynamics  6.12. Gibbs free energy and its applications
  7. Balance  7.1. The concept of balance  7.2. Equilibrium constant and its applications  7.3. Le Chatelier's principle  7.4. Ionic equilibrium in solutions  7.5. Acid and Base Theory  7.5.1. Arrhenius concept  7.5.2. Bronsted-Lowry concept  7.5.3. Lewis concept  7.6. pH Scale and pOH  7.7. Common ion effect  7.8. Hydrolysis of salts  7.9. Buffer solutions and their mechanism of action  7.10. Solubility equilibrium of sparingly soluble salts
  8. Redox reactions  8.1. Oxidation and reduction concepts  8.2. Oxidation number and its applications  8.3. Redox reactions in terms of electron transfer  8.4. Balancing redox reactions (oxidation number and ion-electron methods)  8.5. Types of redox reactions  8.6. Electrochemical Cells and Redox Reactions
  9. Hydrogen  9.1. Position of Hydrogen in the Periodic Table  9.2. Isotopes of hydrogen  9.3. Preparation of Hydrogen  9.4. Properties of Hydrogen  9.5. Hydrides and their classification  9.6. Water and heavy water  9.7. Hydrogen peroxide and its properties  9.8. Uses of Hydrogen and Its Compounds
  10. S-block elements (alkali and alkaline earth metals)  10.1. Group 1 Elements - Properties and Trends  10.2. Group 2 Elements - Properties and Trends  10.3. Unusual properties of lithium and beryllium  10.4. Important compounds of sodium and their uses  10.5. Important Compounds of Magnesium and Calcium
  11. Some p-block elements  11.1. General Introduction to p-Block Elements  11.2. Group 13 Elements  11.2.1. Boron and its compounds  11.3. Group 14 Elements  11.3.1. Carbon and its allotropes  11.3.2. Important Compounds of Carbon and Silicon
  12. Organic Chemistry - Some Basic Principles and Techniques  12.1. Classification and Nomenclature of Organic Compounds  12.2. Structural representation of organic compounds  12.3. Classification of organic reactions  12.4. Electronic Effects in Organic Chemistry  12.4.1. Inductive effect  12.4.2. Resonance effect  12.4.3. Hyperconjugation  12.5. Reaction mechanism and intermediate species  12.6. Purification and qualitative analysis of organic compounds
  13. Hydrocarbons  13.1. Hydrocarbons  13.1.1. Preparation and Properties of Alkenes  13.2. alkene  13.2.1. Preparation and Properties of Alkenes  13.2.2. Electrophilic addition reactions  13.3. Alkynes  13.3.1. Preparation and Properties of Alkynes  13.4. Aromatic hydrocarbons  13.4.1. Structure and properties of benzene  13.4.2. Electrophilic substitution reactions of benzene
  14. Environmental Chemistry  14.1. Environmental Pollution  14.2. Atmospheric pollution and the greenhouse effect  14.3. Water pollution and treatment methods  14.4. Soil pollution and its effects  14.5. Industrial waste and its treatment  14.6. Strategies for pollution control

Grade 11 → Chemical Bonding and Molecular Structure → Molecular orbital theory ↓


Bond order and stability


Molecular orbital theory (MOT) is an essential concept in chemistry that helps us understand how atoms combine to form molecules. It provides information about the electronic structure of molecules and allows us to predict many of their properties. Two important aspects of this theory are bond order and stability. Let us explore these concepts in detail.

Introduction to molecular orbitals

Before diving into bond order and stability, it's important to understand what molecular orbitals are. When atoms combine to form molecules, their atomic orbitals (such as s and p orbitals) overlap to form molecular orbitals that extend throughout the molecule.

There are mainly two types of molecular orbitals:

  • Bonding molecular orbitals (sigma, pi): These orbitals lower the energy of the system and help hold the atoms together.
  • Antibonding molecular orbitals (sigma*, pi*): These orbitals increase the energy of the system and can weaken or prevent bonding.
H₂ → 1 H + 1 H → H₂ Orbital overlap: H 1s + H 1s = σ(1s), σ*(1s)

Consider the simplest molecule, dihydrogen (H₂). Each hydrogen atom has one electron in its 1s orbital. When these orbitals overlap, they form a bonding orbital (sigma(1s)) and an antibonding orbital (sigma*(1s)).

Bond order

Bond order is a concept used to determine the strength and stability of bonds in a molecule. It is calculated based on the electrons present in the bonding and antibonding molecular orbitals. The formula for bond order is:

Bond order = (Number of electrons in bonding orbitals - Number of electrons in antibonding orbitals) / 2

The bond order gives us valuable information:

  • Bond length: Higher bond order usually indicates shorter bond length.
  • Bond strength: Higher bond order means stronger bonds.
  • Molecular stability: Molecules with positive bond order are generally more stable.

Example

Let us calculate the bond order for some molecules.

Hydrogen molecule (H₂)

In H₂ molecule, we have the following:

  • Bonding electrons in sigma(1s) orbital: 2
  • Antibonding electrons in sigma*(1s) orbital: 0
Bond order = (2 - 0) / 2 = 1

The bond order of H₂ is 1, which suggests a single bond between the two hydrogen atoms.

Helium molecule (He₂)

Consider the hypothetical He₂ molecule:

  • Bonding electrons in sigma(1s) orbital: 2
  • Antibonding electrons in sigma*(1s) orbital: 2
Bond order = (2 - 2) / 2 = 0

The bond order of He₂ is 0, which indicates that the molecule is not stable and does not exist under normal conditions.

Oxygen molecule (O₂)

O₂ molecule is involved in pi-bonding due to its orbitals:

  • Bonding electrons: 8 (sigma(2s), sigma(2p_z), pi(2p_x, 2p_y))
  • Antibonding electrons: 4 (sigma*(2s), pi*(2p_x, 2p_y))
Bond order = (8 - 4) / 2 = 2

The bond order of O₂ is 2, indicating the double bond between the oxygen atoms.

Molecular stability

Molecular stability is closely related to bond order. Positive bond order means that bonding orbitals have more electrons than nonbonding orbitals, which contributes to the molecule's stability. In contrast, zero or negative bond order usually indicates instability.

Factors affecting stability

  • Bond energy: Higher bond orders correlate with higher bond energy, making the bonds stronger.
  • Electronic structure: The balanced distribution of electrons in bonding and barrier orbitals contributes to stability.
  • Atomic configuration: Even if the bond order is positive, the configuration of the atoms and their interactions can affect the overall stability.

Real-world applications

Understanding bond order and stability has practical applications in chemistry and materials science. These concepts help predict molecular behavior in various chemical reactions and processes.

Synthesis of new compounds

By calculating bond orders, chemists can predict the strength and stability of new compounds, which aids the synthesis process.

Physics

The stability and properties of substances, such as their hardness and melting point, are often linked to the bond order of their constituent molecules.

Biological systems

In biological systems, the stability of DNA, proteins, and other molecules is important for function. Molecular orbital theory helps in understanding these aspects.

Conclusion

Molecular orbital theory beautifully describes how bonds are formed and broken in the context of quantum-mechanical systems. The bond order, derived from this theory, is a powerful tool for predicting molecular properties and stability. As we have seen, higher bond orders generally lead to stronger and more stable bonds, which serve as a guideline for understanding new and complex molecular systems.

In conclusion, by exploring bond order and its relationship with molecular stability, students gain a deeper understanding of chemical bonding, equipping them with vital knowledge for advanced study and applications in chemistry.


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