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 → States of matter ↓


Real gases and deviations from ideal behaviour


The study of gases is an essential part of chemistry, and understanding the behavior of gases provides a foundation for understanding many other concepts in this subject. In an ideal world, gases behave in a way described by the ideal gas law, which is a simple model that works under certain standard conditions. However, in reality, gases do not always strictly follow this model. Real gases deviate from ideal behavior due to a number of factors. In this lesson, we will explore the reasons behind these deviations, how they are taken into account, and the importance of understanding real gas behavior in chemistry.

Ideal gas law

Before we learn about real gases, let's revisit the basics of the ideal gas law. This law is often expressed in this equation:

PV = nRT

Where:

  • P is the pressure of the gas
  • V is the volume of the gas
  • n is the number of moles
  • R is the ideal gas constant
  • T is the temperature in Kelvin

This equation assumes that gas particles are point particles that do not interact with each other. In many situations, this assumption simplifies the behavior of the gas and proves useful in calculations. However, it is important to remember that the ideal gas law describes an "ideal" situation that does not always match reality.

Characteristics of real gases

Real gases differ from ideal gases mainly due to the following reasons:

  1. Molecular size: Gases have molecules that occupy space, and this space becomes important at high pressures or low temperatures.
  2. Intermolecular forces: Real gases experience attractive and repulsive forces between their molecules.

Van der Waals equation

The van der Waals equation for real gases adjusts the ideal gas law to take into account the volume occupied by the gas molecules and the intermolecular forces. This equation is given as:

(P + a(n/V)^2)(V - nb) = nRT

Here:

  • a is a constant that corrects the intermolecular forces
  • b is a constant that corrects the volume occupied by the gas molecules

The terms a(n/V)^2 and nb in the ideal gas law adjust for pressure and volume, giving a more accurate description of the behavior of a gas under different conditions.

Visual example: pressure versus volume at constant temperature

Below is a graphical representation of how pressure and volume are related for ideal and real gases. The graph highlights the deviations from ideal behavior as pressure is increased.

Volume Pressure ideal gas Real gas

As shown in this graph, the ideal gas follows a smooth curve. The real gas, on the other hand, experiences a sharp drop in volume as intermolecular forces become significant.

Conditions for real gas divergence

There are certain specific conditions under which real gases deviate the most from ideal behaviour:

  • High Pressure: At high pressure the molecules are forced closer to each other such that the volume occupied by the molecules becomes negligible.
  • Low Temperatures: At low temperatures, the intermolecular forces have a greater effect because the kinetic energy is low, making attractive forces more significant.

If we consider two gas containers at different pressure and temperature, the container with higher pressure or lower temperature will show more deviation from the ideal gas behaviour.

Lesson example: comparison of ideal and real gases

Consider two containers:

  • Container A contains an ideal gas at 1 atm and 273 K.
  • Container B contains real gas at 1 atm and 273 K.

Upon analysis, container A strictly follows the ideal gas law equation. However, container B will require adjustments according to the van der Waals equation, as the volume and interactions of the molecules will affect the calculation of pressure or volume.

Mathematical adjustments

The need to mathematically correct real gases comes from the need to understand and predict how gases will behave under different conditions. This understanding is important for applications ranging from chemical reactions to industrial processes where accurate pressure and volume measurements are required.

Practical implications

Understanding the behavior of real gases is important in a variety of fields. For example, in engineering and technology, systems involving gases require careful calculations to ensure safety and effectiveness. In medical applications, it is important to control gas mixtures for patients. Thus an accurate understanding of real gas behavior becomes indispensable, and science constantly absorbs new findings to refine existing models.

Visual example: the effects of intermolecular forces

The concept of intermolecular forces in gases can be represented graphically.

ideal gas Real gas

In this illustration, ideal gas particles are small and well-spaced, exhibiting uniform motion. Real gas particles exhibit more compact shapes, and their proximity leads to strong interactions, significantly affecting their behavior.

Conclusion

The study of real gases and their deviations from ideal behavior is important in advancing chemical knowledge. While the ideal gas law provides a foundation, real gases and van der Waals adjustments provide a more complete and applicable understanding, especially under non-ideal conditions of high pressure and low temperature. From scientific research to applied sciences, these concepts form a vital mindset for discovering advanced theories and implementing solutions that require a deeper chemical understanding.


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