Behaviour of Gases & Energetics

Behaviour of Gases & Energetics

Behaviour of Gases

1. Boyle’s law:

• At constant temperature, the volume of a definite mass of a gas is inversely proportional to pressure.

• V ∝ 1/p (at constant T)

2. Charles’s law:

• At constant pressure, the volume of a definite mass of a gas is directly proportional to absolute temperature.

• V ∝ T (at constant p)

3. Gay-Lussac’s law:

• At constant volume, the pressure of a given mass of gas is directly proportional to the temperature in Kelvin.

• p ∝ T (at constant V)

4. Avogadro’s gas law:

• At constant temperature and pressure, the volume of a gas is directly proportional to the number of molecules.

• V ∝ n (at constant T & p)

5. Ideal gas equation:

• pV = nRT

• Where:

  • p = Pressure

  • V = Volume

  • n = Number of moles

  • T = Temperature in Kelvin

  • R = Gas constant

  • R = 0.0821 L·atm·K⁻¹·mol⁻¹

  • R = 8.314 J·K⁻¹·mol⁻¹

  • R = 1.987 cal·K⁻¹·mol⁻¹

A gas will behave as an ideal gas at very low pressure and high temperature.

6. STP & NTP:

• STP - Standard Temperature and Pressure

• NTP – Normal Temperature and Pressure

• At STP, for 1 mole of gas:

  • V = 22.4 litre = 22400 ml

  • p = 1 atm = 76 mm of Hg = 760 mm of Hg

  • T = 273 K

Diffusion of Gases

The process of intermixing of gases, irrespective of the density relationship and without the effect of external agency, is called diffusion of gases.

In a gas, the molecules are far apart, and the space between them is huge. Therefore, molecules of one gas can move into the empty spaces or voids of another gas and vice versa. This leads to diffusion.

Graham's Law of Diffusion

Under the same conditions of temperature and pressure, the rates of diffusion of gases are inversely proportional to the square roots of their densities.

Let r₁ and r₂ be the rates of diffusion of two gases A and B, and d₁ and d₂ be their respective densities; then, according to Graham’s law:

• r₁ / r₂ = √(d₂ / d₁) = √(M₂ / M₁)

• Where M is the molecular mass, which is 2 × vapour density.

Dalton’s Law of Partial Pressure

It states that if two or more gases that do not react chemically are enclosed in a vessel, the total pressure of the gaseous mixture is equal to the sum of the partial pressures of each gas if they were enclosed separately at the same temperature.

Let P₁, P₂, and P₃ be the pressures of three non-reactive gases; then the total pressure P is:

• P = P₁ + P₂ + P₃

Energetics (Thermodynamics)

Thermodynamics is the branch of chemistry that deals with the energy changes in a chemical reaction. Some key terms in thermodynamics are:

1. System:

• The specific part of the universe where energy changes are happening.

2. Surroundings:

• The rest of the universe, excluding the system. If a chemical reaction happens in a tube, the materials in the tube are the system, and the rest of the surroundings are the surroundings. The glass tube is the boundary between the system and its surroundings.

3. Types of Systems:

1. Open system

2. Closed system

3. Isolated system

• An open system is one where both matter (mass) and energy can be exchanged with the surroundings.

  • Example: A reaction of sodium carbonate and hydrochloric acid in an open container.

• In a closed system, only energy can be exchanged with the surroundings, but not mass.

• An isolated system is one where neither mass nor energy is exchanged with the surroundings.

  • Example: Hot tea or coffee in a thermos flask.

Intensive and Extensive Properties

Intensive Properties:

• Intensive properties of a system are the properties that do not depend upon either the size of the system or the quantity of matter present in it, but depend on the nature of substances present in the system.

Example: Pressure, temperature, specific heat, surface tension, viscosity, refractive index, boiling point, melting point, pH, etc.

Extensive Properties:

• Extensive properties of a system are the properties that depend upon the quantity of matter present in the system.

Example: Mass, volume, energy, enthalpy, etc.

Thermodynamic Processes

1. Isothermal Process:

• A process is said to be isothermal if the temperature of the system remains constant.

• This means the operation is carried out at a constant temperature.

2. Adiabatic Process:

• In an adiabatic process, no exchange of heat between the system and surroundings is possible.

• The system is completely isolated or insulated from the surroundings.

3. Isobaric Process:

• A process is said to be isobaric if the pressure remains constant throughout.

• This means dp = 0.

4. Isochoric Process:

• A process carried out at constant volume is called an isochoric process.

• Thus, for an isochoric process, dV = 0.

5. Cyclic Process:

• When a system undergoes a series of changes and finally returns to its initial state, it is called a cyclic process.

• There is no change in energy in a cyclic process, i.e., dE = 0.

6. Reversible Process:

• A process is said to be reversible if it is carried out infinitesimally slowly so that each change occurring in the direct method can be exactly reversed, and the system and surroundings remain in a state of equilibrium at any stage in the process.

7. Irreversible Process:

• It is a process in which the change is brought about rapidly, and the system does not have the chance to achieve equilibrium.

• In an irreversible process, the force which drives the reactants towards products is greater than the opposing force, which is to carry out the reverse process.

8. Heat of Reaction:

The change in heat that accompanies a chemical reaction, represented by a balanced chemical equation, is called the heat of reaction.

• C(s) + O₂(g) → CO₂(g) ΔH = -393.5 kJ

• CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(g) ΔH = -890.3 kJ

Exothermic & Endothermic Reactions

1. Exothermic Reaction:

• If heat is released during a chemical reaction, it is called an exothermic reaction. In exothermic reactions, the change in heat (ΔH) is negative.

  • C(s) + O₂(g) → CO₂(g) ΔH = -393.5 kJ

  • H₂ (g) + 1/2 O₂ (g) → H₂O (g) ΔH = -286.0 kJ

2. Endothermic Reaction:

• If heat is absorbed during a chemical reaction, the reaction is called an endothermic reaction.

• In an endothermic reaction, the change in heat (ΔH) is positive.

• C(s) + H₂O(g) → CO(g) + H₂(g) ΔH = +131.2 kJ

• N₂ (g) + O₂ (g) → 2NO (g) ΔH = +180.0 kJ

Different Types of Heat of Reactions

1. Heat of Formation:

The heat change during the formation of one mole of a compound from its constituent elements at a given temperature and pressure is called the heat of formation.

• C(s) + 2H₂ (g) → CH₄ (g) ΔHf = -74.8 kJ/mol

• C(s) + O2(g) → CO2(g) ΔHf = -393.5 kJ/mol

2. Heat of Combustion:

The heat change during combustion of one mole of a substance in excess of air or oxygen is called the heat of combustion.

• CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(g) ΔHc = -890.3 kJ/mol

• C6H6(l) + 15/2 O2(g) → 6CO2(g) + 3H2O(l) ΔHc = -3268 kJ/mol

3. Heat of Neutralisation:

The change in heat when one gram equivalent of an acid and one gram equivalent of a base present in their aqueous solution neutralise each other is called the heat of neutralisation.

The heat of neutralisation of a strong acid and a strong base is always constant (-57.1 kJ), but for a weak acid or a weak base, the heat of neutralisation is less than -57.1 kJ because some heat is used to ionise the weak acid/base.

• NaOH(aq) + HCl(aq) → NaCl(aq) + H₂O(l) ΔH = -57.1 kJ

• NaOH(aq) + CH₃COOH(aq) → CH₃COONa(aq) + H₂O(l) ΔH = -55.2 kJ

4. Heat of Solution:

The change in heat when one mole of a substance is dissolved in such a large excess of solvent at a given temperature that the further addition of solvent does not produce any more heat is called the heat of solution.

• NaCl(s) + aq → NaCl(aq) ΔH = +5.35 kJ/mol

• KCl(s) + aq → KCl(aq) ΔH = +18.56 kJ/mol

5. Enthalpy of Hydration:

The change in heat when one mole of the anhydrous salt changes to a hydrated salt by combining with a specified number of moles of water is called the enthalpy of hydration.

• CuSO₄(s) + 5H₂O(l) → CuSO₄·5H₂O(s)
  ΔH = -78.2 kJ/mol

• BaCl2(s) + 2H2O(l) → BaCl2·2H2O(s)
  ΔH = -29.4 kJ/mol

Hess's Law of Constant Heat Summation

When a chemical reaction is carried out in one step or in more than one step, the change in heat will be identical. This statement is called Hess's law of constant heat summation.

• ΔH (directly) = ΔH1 + ΔH2

According to Hess’s law, ΔH = ΔH1 + ΔH2

• Latent Heat of Vaporisation: The heat energy required to change 1 kg of liquid to gas at atmospheric pressure at its boiling point.

• Latent Heat of Fusion: The amount of heat energy required to change 1 kg of solid into liquid at its melting point.

Final Thoughts

The behaviour of gases follows several key principles, including Boyle’s, Charles’s, and Gay-Lussac’s laws, each describing how volume, pressure, and temperature interact under different conditions. The ideal gas equation (pV = nRT) ties together pressure, volume, temperature, and the number of moles, showing how gases behave under various states.

Thermodynamics, the study of energy changes, explains how systems exchange energy, distinguishing between open, closed, and isolated systems. In chemical reactions, heat exchange plays a major role.

Exothermic reactions release energy, while endothermic reactions absorb it. Heat of formation, combustion, neutralisation, and solution are crucial concepts that help quantify the energy changes in different processes.