Thermodynamics and Chemical Energetics – Comprehensive Notes

Thermodynamics is a fundamental branch of science that deals with energy changes accompanying physical and chemical transformations. Chemical energetics, a subset of thermodynamics, specifically focuses on the heat changes involved in chemical reactions. This chapter is highly quantitative and conceptual, making it crucial for NEET and JEE Main.

1. Introduction to Thermodynamics

• Thermodynamics Defined: The study of the relationships between heat, work, temperature, and energy. It describes how thermal energy is converted into other forms of energy and how energy affects matter.
• Chemical Energetics: The study of energy changes (primarily heat changes) during chemical reactions.
• Key Idea: Thermodynamics deals with macroscopic properties of matter and provides insights into the feasibility (spontaneity) of a process, but not its rate.

2. Basic Thermodynamic Terms

• System: The part of the universe chosen for thermodynamic consideration. It is separated from the rest of the universe by a boundary.
  • Types of Systems:
    • Open System: Can exchange both energy (heat and work) and matter with its surroundings. (e.g., Water in an open beaker, living organisms).
    • Closed System: Can exchange energy (heat and work) but NOT matter with its surroundings. (e.g., Water in a sealed flask, but not insulated).
    • Isolated System: Cannot exchange either energy or matter with its surroundings. (e.g., Water in an insulated closed thermos flask, universe).
• Surroundings: The rest of the universe outside the system that can interact with the system.
• Boundary: The real or imaginary surface separating the system from its surroundings.
• State of a System: Defined by its measurable macroscopic properties like temperature (T), pressure (P), volume (V), and composition (n).
• State Functions: Properties that depend only on the initial and final states of the system, irrespective of the path taken.
  • Examples: Internal Energy (U or E), Enthalpy (H), Entropy (S), Gibbs Free Energy (G), Temperature (T), Pressure (P), Volume (V).
  • ΔX=Xfinal​−Xinitial​ (change in state function).
• Path Functions: Properties that depend on the path taken to go from the initial state to the final state.
  • Examples: Heat (q), Work (w).
• Extensive Properties: Properties that depend on the amount of matter present in the system. They are additive.
  • Examples: Mass, Volume, Internal Energy, Enthalpy, Entropy, Gibbs Free Energy, Heat Capacity.
• Intensive Properties: Properties that do NOT depend on the amount of matter present in the system.
  • Examples: Temperature, Pressure, Density, Viscosity, Surface Tension, Refractive Index, Molar Heat Capacity, Specific Heat.
• Thermodynamic Processes:
  • Isothermal Process: Temperature (T) remains constant (ΔT=0). For ideal gases, ΔU=0.
  • Isobaric Process: Pressure (P) remains constant (ΔP=0). Most chemical reactions in open containers are isobaric.
  • Isochoric Process: Volume (V) remains constant (ΔV=0). No PV work done (w = 0).
  • Adiabatic Process: No heat exchange between system and surroundings (q = 0). System is thermally insulated.
  • Cyclic Process: A process in which the system returns to its initial state after a series of changes. For a cyclic process, ΔU=0, ΔH=0, ΔS=0, ΔG=0.
  • Reversible Process: An idealized process that takes place in infinitely small steps, such that the system and surroundings are always in equilibrium at every stage. It can be reversed by an infinitesimal change. Maximum work is obtained.
  • Irreversible Process: A real, spontaneous process that occurs rapidly and cannot be reversed by an infinitesimal change. It takes place in a finite time. Work obtained is less than maximum. All natural processes are irreversible.

3. First Law of Thermodynamics (Law of Conservation of Energy)

• Statement: Energy can neither be created nor destroyed, but it can be converted from one form to another. The total energy of the universe (system + surroundings) remains constant.
• Mathematical Form: ΔU=q+w
  • ΔU = Change in Internal Energy of the system.
  • q = Heat absorbed by the system from the surroundings.
  • w = Work done on the system by the surroundings.
• Sign Conventions for q and w (IUPAC Convention):
  • q = positive (+) if heat is absorbed by the system (endothermic).
  • q = negative (-) if heat is released by the system (exothermic).
  • w = positive (+) if work is done ON the system (compression).
  • w = negative (-) if work is done BY the system (expansion).
• Internal Energy (U or E): The sum of all forms of energy associated with the molecules (kinetic, potential, vibrational, rotational, translational, electronic, nuclear). It is a state function.
  • ΔU depends only on initial and final states.
• Work (w):
  • PV Work (Pressure-Volume Work): Work done during expansion or compression of gases.
  • Formula: w=−Pext​ΔV (for irreversible process)
    • Pext​ = external pressure (constant for irreversible).
    • ΔV=Vfinal​−Vinitial​.
  • For expansion (gas expands): ΔV>0, so w is negative (work done by the system).
  • For compression (gas compressed): ΔV<0, so w is positive (work done on the system).
  • For reversible isothermal expansion of an ideal gas: w=−2.303nRTlog(V2​/V1​)=−2.303nRTlog(P1​/P2​).
  • For isochoric process (ΔV=0): w=0. In this case, ΔU=qV​ (heat at constant volume).
• Enthalpy (H): A thermodynamic state function representing the total heat content of a system at constant pressure.
  • Definition: H=U+PV
  • Change in Enthalpy (ΔH): ΔH=ΔU+PΔV (at constant pressure).
  • Relationship between ΔH and ΔU for chemical reactions: ΔH=ΔU+Δng​RT
    • Δng​ = (moles of gaseous products) – (moles of gaseous reactants).
    • R = Universal gas constant.
    • T = Absolute temperature.
  • Significance: ΔH=qP​ (heat at constant pressure). Most chemical reactions are carried out at constant pressure (atmospheric pressure), so ΔH is a very useful quantity in chemistry.

4. Thermochemistry

The study of heat changes during chemical reactions.

• Exothermic Reactions: Reactions that release heat to the surroundings. ΔH is negative (-).
  • Example: Combustion reactions, Neutralization of strong acid/base. CH4(g)+2O2(g)→CO2(g)+2H2O(l), ΔH=−890 kJ/mol
• Endothermic Reactions: Reactions that absorb heat from the surroundings. ΔH is positive (+).
  • Example: Photosynthesis, Decomposition of CaCO3. N2(g)+O2(g)→2NO(g), ΔH=+180.7 kJ/mol
• Standard Enthalpy of Reaction (ΔH∘): The enthalpy change for a reaction when all reactants and products are in their standard states (298 K and 1 bar pressure for gases, 1 M concentration for solutions).
• Standard Enthalpy of Formation (ΔHf∘​): The enthalpy change when one mole of a compound is formed from its constituent elements in their most stable elemental forms under standard conditions.
  • By convention, ΔHf∘​ of an element in its most stable form is zero (e.g., ΔHf∘​(O2(g))=0, ΔHf∘​(C(graphite))=0).
  • ΔHreaction∘​=∑ΔHf∘​(products)−∑ΔHf∘​(reactants)
• Standard Enthalpy of Combustion (ΔHc∘​): The enthalpy change when one mole of a substance is completely burnt in oxygen under standard conditions. Always negative (exothermic).
• Standard Enthalpy of Neutralization (ΔHneut∘​): The enthalpy change when one gram equivalent of an acid is completely neutralized by one gram equivalent of a base in dilute solution. For strong acid-strong base, it is approximately constant (around -57.3 kJ/mol) due to the formation of one mole of water from H+ and OH- ions.
• Standard Enthalpy of Atomization (ΔHatom∘​): The enthalpy change required to break all bonds in one mole of a substance to obtain free gaseous atoms. Always positive (endothermic).
• Bond Enthalpy (Bond Energy): The energy required to break one mole of a specific type of bond in the gaseous state. Always positive.
  • Average bond enthalpy is used for polyatomic molecules.
  • ΔHreaction∘​=∑Bond Enthalpies(reactants)−∑Bond Enthalpies(products) (Breaking bonds is endothermic, forming bonds is exothermic).
• Hess’s Law of Constant Heat Summation:
  • Statement: If a chemical reaction can be expressed as a series of steps (individual reactions), then the overall enthalpy change for the reaction is the sum of the enthalpy changes for each step, regardless of the number of steps or the path taken.
  • Significance: Allows calculation of ΔH for reactions that are difficult or impossible to measure directly.
• Born-Haber Cycle: A thermochemical cycle used to calculate the lattice energy of an ionic compound. It is based on Hess’s Law and relates the lattice energy to other measurable enthalpy changes (formation, atomization, ionization, electron gain enthalpy).

5. Second Law of Thermodynamics

• Spontaneous Processes: Processes that have a natural tendency to occur without any external aid. They proceed in one direction until equilibrium is reached.
  • Examples: Heat flows from hot to cold, a gas expands into a vacuum, a ball rolls downhill, rusting of iron.
  • These processes may or may not be fast.
• Entropy (S): A measure of the randomness or disorder of a system. It is a state function.
  • Units: J K-1 mol-1.
  • Trends in Entropy:
    • Solid < Liquid < Gas: Gases have the highest entropy (most disordered).
    • Increasing Temperature: Entropy increases with increasing temperature.
    • Increasing Volume (for gases): Entropy increases with increasing volume.
    • Increasing Number of Moles of Gas: Entropy increases as the number of gaseous moles increases in a reaction.
    • Dissolution: Generally increases entropy (e.g., solid dissolving in liquid).
  • Second Law Statement: “The entropy of the universe (system + surroundings) always increases for a spontaneous process and remains constant for a reversible process.”
    • ΔSuniverse​=ΔSsystem​+ΔSsurroundings​
    • For spontaneous process: ΔSuniverse​>0
    • For reversible process (equilibrium): ΔSuniverse​=0
  • Limitations of ΔH and ΔS alone: ΔH predicts spontaneity only for exothermic reactions (favored by negative ΔH). ΔS predicts spontaneity only for processes increasing disorder (favored by positive ΔS). To predict spontaneity under all conditions, we use Gibbs Free Energy.
• Gibbs Free Energy (G): A thermodynamic state function that combines enthalpy and entropy, providing a criterion for spontaneity of a process at constant temperature and pressure.
  • Definition: G=H−TS
  • Change in Gibbs Free Energy (ΔG): ΔG=ΔH−TΔS (Gibbs-Helmholtz Equation)
  • Criteria for Spontaneity (at constant T, P):
    • If ΔG<0: The process is spontaneous (feasible) in the forward direction.
    • If ΔG>0: The process is non-spontaneous (feasible in the reverse direction).
    • If ΔG=0: The system is at equilibrium.
• Relationship between ΔG∘ and Equilibrium Constant (K):
  • ΔG∘=−RTlnK
  • Where ΔG∘ is standard Gibbs free energy change, R is the gas constant, T is absolute temperature, and K is the equilibrium constant (Kp or Kc).
  • If ΔG∘<0, K > 1 (reaction is product-favored at equilibrium).
  • If ΔG∘>0, K < 1 (reaction is reactant-favored at equilibrium).
  • If ΔG∘=0, K = 1.
• Effect of Temperature on Spontaneity (ΔG=ΔH−TΔS):

ΔH	ΔS	ΔG Sign	Spontaneity
– (Exo)	+ (Inc)	Always –	Spontaneous at all temperatures
+ (Endo)	– (Dec)	Always +	Non-spontaneous at all temperatures
– (Exo)	– (Dec)	– at low T, + at high T	Spontaneous at low temperatures
+ (Endo)	+ (Inc)	+ at low T, – at high T	Spontaneous at high temperatures

* The crossover temperature where $\Delta G = 0$ is approximately $T = \Delta H / \Delta S$.

6. Third Law of Thermodynamics

• Statement: “The entropy of a perfectly crystalline substance (perfectly ordered crystal) is zero at absolute zero temperature (0 K).”
• Significance: Provides a reference point for determining absolute entropy values of substances. It implies that a perfect crystal at 0 K has maximum order and no residual disorder.

7. Key Formulas and Concepts Summary

• First Law: ΔU=q+w
• Work: w=−Pext​ΔV (irreversible), w=−2.303nRTlog(V2​/V1​) (reversible isothermal)
• Enthalpy: ΔH=ΔU+Δng​RT
• Hess’s Law: ΔHreaction​=∑ΔHf​(products)−∑ΔHf​(reactants)
• Bond Enthalpy: ΔHreaction​=∑Bond Enthalpies(reactants)−∑Bond Enthalpies(products)
• Gibbs Free Energy: ΔG=ΔH−TΔS
• Spontaneity: ΔG<0 (spontaneous), ΔG>0 (non-spontaneous), ΔG=0 (equilibrium)
• Equilibrium Constant: ΔG∘=−RTlnK

This detailed guide should provide a strong foundation for understanding Thermodynamics and Chemical Energetics for your NEET and JEE Main exams. Focus on derivations, numerical problems, and conceptual clarity regarding spontaneity and energy changes.