Thermodynamics governs energy changes in chemical reactions. The laws of thermodynamics explain how energy behaves, from conservation to entropy increase. These principles are crucial for understanding spontaneous processes and predicting chemical reactions.

State functions like internal energy and enthalpy depend only on initial and final states. Path functions like heat and work depend on the process. Understanding these concepts helps chemists analyze and optimize reactions in various systems.

Laws of Thermodynamics

Laws of thermodynamics

• First Law of Thermodynamics
  • States energy cannot be created or destroyed, only converted from one form to another (kinetic, potential, thermal, electrical)
  • Defines the change in internal energy ($\Delta U$) of a system as equal to the heat ($q$) added to the system minus the work ($w$) done by the system: $\Delta U = q - w$
  • Implies the total energy of the universe (system + surroundings) remains constant during any process
• Second Law of Thermodynamics
  • Asserts the entropy of the universe always increases in a spontaneous process (irreversible process)
  • Describes how heat flows spontaneously from a hot object (coffee) to a cold object (ice cube), never the reverse
  • Implies the universe tends towards disorder (messy room) and that not all energy can be converted into useful work (heat engine efficiency)
• Third Law of Thermodynamics
  • States the entropy of a perfect crystal (diamond) at absolute zero (0 K or -273.15 ℃) is zero
  • Asserts it is impossible to reach absolute zero in a finite number of steps (cooling process)
  • Implies there is a limit to how much heat can be extracted from a system (refrigerator)

State vs path functions

• State functions
  • Depend only on the initial and final states of a system (pressure, volume, temperature), not on the path taken (isothermal, adiabatic)
  • Include internal energy ($U$), enthalpy ($H$), entropy ($S$), Gibbs free energy ($G$)
  • Exhibit changes ($\Delta U$, $\Delta H$, $\Delta S$, $\Delta G$) that are independent of the path (route) taken between states
• Path functions
  • Depend on the specific path taken between the initial and final states (hiking trail)
  • Include heat ($q$) and work ($w$)
  • Exhibit values that depend on the process or path followed (integration)

Thermodynamic Processes and State Functions

Internal energy in thermodynamic processes

• Internal energy ($U$)
  • Represents the sum of the kinetic (translational, rotational, vibrational) and potential (intermolecular forces) energies of all particles in a system
  • Relates the change in internal energy ($\Delta U$) to the heat ($q$) added to the system minus the work ($w$) done by the system: $\Delta U = q - w$
• Heat ($q$)
  • Refers to energy transferred between a system and its surroundings due to a temperature difference (hot plate)
  • Defines positive $q$ when heat is absorbed by the system (melting), negative $q$ when heat is released by the system (freezing)
• Work ($w$)
  • Represents energy transferred between a system and its surroundings due to a force acting over a distance (piston)
  • Defines positive $w$ when work is done on the system (compression), negative $w$ when work is done by the system (expansion)
• Solving problems
  1. Identify the system (gas in a cylinder) and surroundings (atmosphere)
  2. Determine the initial (1 atm, 300 K) and final (2 atm, 400 K) states of the system
  3. Use the equation $\Delta U = q - w$ to calculate the change in internal energy, heat, or work, depending on the given information (heat capacity, pressure-volume work)

Relationships of thermodynamic state functions

• Enthalpy ($H$)
  • Measures the total heat content of a system (energy required to create a system)
  • Relates the change in enthalpy ($\Delta H$) to the heat absorbed or released by a system at constant pressure: $\Delta H = q_p$
  • Classifies exothermic processes as having negative $\Delta H$ (combustion), endothermic processes as having positive $\Delta H$ (photosynthesis)
• Entropy ($S$)
  • Quantifies the disorder or randomness of a system (number of microstates)
  • Defines the change in entropy ($\Delta S$) as the heat absorbed or released by a system divided by the temperature: $\Delta S = q_{rev}/T$
  • Asserts spontaneous processes always result in an increase in the entropy of the universe (mixing)
• Gibbs free energy ($G$)
  • Represents the maximum useful work that can be obtained from a system (electrical work)
  • Relates the change in Gibbs free energy ($\Delta G$) to the change in enthalpy ($\Delta H$) and the change in entropy ($\Delta S$) by the equation: $\Delta G = \Delta H - T\Delta S$
  • Determines spontaneous processes have negative $\Delta G$ (rusting), non-spontaneous processes have positive $\Delta G$ (electrolysis), and processes at equilibrium have $\Delta G = 0$ (saturated solution)
• Relationship between $H$, $S$, and $G$
  • Describes how the spontaneity of a process depends on the balance between the change in enthalpy and the change in entropy, as determined by the Gibbs free energy equation: $\Delta G = \Delta H - T\Delta S$
  • Asserts processes with a negative $\Delta H$ (exothermic) and a positive $\Delta S$ (increasing disorder) are always spontaneous (neutralization)
  • States processes with a positive $\Delta H$ (endothermic) and a negative $\Delta S$ (decreasing disorder) are never spontaneous (freezing)
  • Explains the spontaneity of processes with a positive $\Delta H$ and a positive $\Delta S$ (evaporation), or a negative $\Delta H$ and a negative $\Delta S$ (crystallization), depends on the temperature and the relative magnitudes of $\Delta H$ and $T\Delta S$