Chemical Thermodynamics

• 1. Basic Concepts & System Types

  • System & Surroundings: Universe = System + Surroundings
  • Types of Systems:
    • Open System: Exchanges both energy and matter
    • Closed System: Exchanges energy, but not matter
    • Isolated System: No exchange of energy or matter
  • State of System: Defined by measurable properties (P, V, T, n)
  • State Functions: Dependent only on current state (U, H, S, G)
  • Path Functions: Dependent on path taken (q, w)
  • System Properties:
    • Extensive: Depends on mass/amount (Mass, Volume, Enthalpy)
    • Intensive: Independent of mass/amount (Temperature, Pressure, Density)
  • Thermodynamic Processes:
    • Isothermal: Constant temperature ($\Delta T = 0$)
    • Adiabatic: No heat exchange ($q = 0$)
    • Isobaric: Constant pressure ($\Delta P = 0$)
    • Isochoric: Constant volume ($\Delta V = 0$)
    • Reversible: Infinitely slow, always in equilibrium
    • Irreversible: Spontaneous, real-world processes

• 2. First Law of Thermodynamics

  • Statement: Energy can neither be created nor destroyed (Conservation of Energy)
  • Mathematical Form: $\Delta U = q + w$
  • Internal Energy ($\mathbf{U}$): Total energy contained within a system
  • Work ($\mathbf{w}$):
    • Pressure-Volume Work: $w = -P_{ext} \Delta V$
    • Reversible Isothermal Work: $w_{rev} = -2.303 nRT \log \left(\frac{V_2}{V_1}\right)$
  • Heat ($\mathbf{q}$): Energy transferred due to temperature difference
  • Enthalpy ($\mathbf{H}$): Heat content at constant pressure ($H = U + PV$)
    • Relation: $\Delta H = \Delta U + \Delta n_g RT$
  • Heat Capacity:
    • Molar Heat Capacity ($C$): Heat required to raise temperature of 1 mole by 1 K
    • Constant Volume ($C_v$): $\left(\frac{\partial U}{\partial T}\right)_v$
    • Constant Pressure ($C_p$): $\left(\frac{\partial H}{\partial T}\right)_p$
    • Mayer's Relation: $C_p - C_v = R$

• 3. Thermochemistry

  • Enthalpy of Reaction ($\mathbf{\Delta_r H}$): Heat change during a chemical reaction
  • Standard State: Pure substance at 1 bar pressure and specified temperature (298 K)
  • Key Enthalpies:
    • Enthalpy of Formation ($\mathbf{\Delta_f H^\circ}$): Formation of 1 mole compound from standard elements
    • Enthalpy of Combustion ($\mathbf{\Delta_c H^\circ}$): Heat released on complete burning of 1 mole
    • Enthalpy of Atomization ($\mathbf{\Delta_a H^\circ}$): Breaking 1 mole of bonds completely into atoms
    • Bond Enthalpy: Energy required to break 1 mole of specific bonds in gas phase
    • Phase Transitions: Enthalpy of Fusion, Vaporization, and Sublimation
  • Hess's Law: Total enthalpy change is identical regardless of multi-step reaction path

• 4. Second Law & Entropy

  • Spontaneous Process: Occurs naturally without external assistance
  • Entropy ($\mathbf{S}$): Measure of degree of randomness or disorder
    • Formula: $\Delta S = \frac{q_{rev}}{T}$
    • Units: $J \cdot K^{-1} \cdot mol^{-1}$
  • Second Law Statement: Entropy of the universe increases for any spontaneous process
    • Spontaneity Condition: $\Delta S_{total} = \Delta S_{sys} + \Delta S_{surr} > 0$

• 5. Gibbs Energy & Equilibrium

  • Gibbs Energy ($\mathbf{G}$): Thermodynamic potential to measure process spontaneity
  • Gibbs-Helmholtz Equation: $\Delta G = \Delta H - T\Delta S$
  • Criteria for Spontaneity:
    • $\Delta G < 0$: Spontaneous process
    • $\Delta G > 0$: Non-spontaneous process
    • $\Delta G = 0$: System at equilibrium
  • Effect of Temperature on Spontaneity:
    • $\Delta H < 0, \Delta S > 0$: Spontaneous at all temperatures
    • $\Delta H > 0, \Delta S < 0$: Non-spontaneous at all temperatures
    • $\Delta H < 0, \Delta S < 0$: Spontaneous at low temperatures
    • $\Delta H > 0, \Delta S > 0$: Spontaneous at high temperatures
  • Gibbs Energy & Equilibrium Constant:
    • $\Delta G^\circ = -RT \ln K = -2.303 RT \log K$

• 6. Third Law of Thermodynamics

  • Statement: Entropy of a perfectly crystalline substance approaches zero as temperature approaches absolute zero ($0\text{ K}$)
  • Significance: Enables determination of absolute entropy values of pure substances