🧤Physical Chemistry I Unit 1 – Intro to Physical Chem & Thermodynamics

Key Concepts and Definitions

• Thermodynamics studies the relationships between heat, work, and energy in a system
• System refers to the specific part of the universe under study (can be open, closed, or isolated)
• Surroundings include everything outside the system
• State functions depend only on the current state of the system (pressure, temperature, volume)
  • Path independent
• Process functions depend on the path taken to reach the final state (heat, work)
  • Path dependent
• Extensive properties depend on the amount of matter in the system (volume, mass)
• Intensive properties are independent of the amount of matter (density, temperature)

Fundamental Laws of Thermodynamics

• Zeroth Law states that if two systems are in thermal equilibrium with a third system, they are in thermal equilibrium with each other
  • Allows for the definition of temperature
• First Law states that energy cannot be created or destroyed, only converted from one form to another
  • Expressed as $\Delta U = Q + W$
    • $\Delta U$ is the change in internal energy
    • $Q$ is the heat added to the system
    • $W$ is the work done on the system
• Second Law states that the entropy of the universe always increases in a spontaneous process
  • Expressed as $\Delta S_{universe} > 0$
• Third Law states that the entropy of a perfect crystal at absolute zero is zero
  • Provides a reference point for entropy calculations

States of Matter and Phase Transitions

• Matter exists in three main states solid, liquid, and gas
  • Plasma is sometimes considered a fourth state
• Solid has a fixed shape and volume due to strong intermolecular forces
• Liquid has a fixed volume but takes the shape of its container due to moderate intermolecular forces
• Gas has no fixed shape or volume due to weak intermolecular forces
• Phase transitions occur when a substance changes from one state to another
  • Melting solid to liquid
  • Vaporization liquid to gas
  • Sublimation solid to gas
  • Condensation gas to liquid
  • Freezing liquid to solid
  • Deposition gas to solid

Equations of State and Ideal Gas Law

• Equation of state relates the state variables (pressure, volume, temperature) of a system
• Ideal Gas Law is a specific equation of state for ideal gases
  • Expressed as $PV = nRT$
    • $P$ is the pressure
    • $V$ is the volume
    • $n$ is the number of moles
    • $R$ is the ideal gas constant
    • $T$ is the absolute temperature
• Real gases deviate from ideal behavior at high pressures and low temperatures
  • Van der Waals equation accounts for these deviations
• Dalton's Law states that the total pressure of a mixture of ideal gases is the sum of the partial pressures of each gas

Energy, Heat, and Work

• Energy is the capacity to do work or transfer heat
  • Kinetic energy is associated with motion
  • Potential energy is associated with position or configuration
• Heat is the transfer of energy due to a temperature difference
  • Measured in joules (J) or calories (cal)
• Work is the transfer of energy due to a force acting over a distance
  • Measured in joules (J)
• Work done by a gas during expansion is expressed as $W = -P\Delta V$
  • Negative sign indicates work is done by the system
• Heat capacity is the amount of heat required to raise the temperature of a substance by one degree
  • Specific heat capacity is the heat capacity per unit mass

Enthalpy and Heat Capacity

• Enthalpy is a state function that represents the total heat content of a system
  • Expressed as $H = U + PV$
    • $U$ is the internal energy
    • $P$ is the pressure
    • $V$ is the volume
• Change in enthalpy is equal to the heat absorbed or released at constant pressure
  • Expressed as $\Delta H = Q_p$
• Heat capacity at constant pressure ($C_p$) is greater than heat capacity at constant volume ($C_v$)
  • Difference is due to the work done during expansion
• Hess's Law states that the enthalpy change of a reaction is independent of the pathway
  • Allows for the calculation of enthalpy changes using standard enthalpies of formation

Entropy and Spontaneity

• Entropy is a measure of the disorder or randomness of a system
  • Expressed as $S = k \ln W$
    • $k$ is the Boltzmann constant
    • $W$ is the number of microstates
• Second Law of Thermodynamics states that the entropy of the universe always increases in a spontaneous process
• Spontaneous processes occur without external intervention
  • Gibbs free energy ($\Delta G$) determines the spontaneity of a process at constant temperature and pressure
    • $\Delta G < 0$ indicates a spontaneous process
    • $\Delta G > 0$ indicates a non-spontaneous process
    • $\Delta G = 0$ indicates a system at equilibrium
• Entropy of mixing always increases when two substances are combined

Free Energy and Chemical Equilibrium

• Gibbs free energy is a state function that combines enthalpy and entropy
  • Expressed as $G = H - TS$
    • $H$ is the enthalpy
    • $T$ is the absolute temperature
    • $S$ is the entropy
• Change in Gibbs free energy determines the spontaneity of a process
  • Expressed as $\Delta G = \Delta H - T\Delta S$
• Chemical equilibrium is reached when the forward and reverse reactions occur at the same rate
  • Equilibrium constant ($K$) is related to the standard Gibbs free energy change ($\Delta G^\circ$)
    • Expressed as $\Delta G^\circ = -RT \ln K$
• Le Chatelier's Principle states that a system at equilibrium will shift to counteract any external stress
  • Changes in concentration, pressure, volume, or temperature can shift the equilibrium position

Applications in Real-World Systems

• Thermodynamics plays a crucial role in understanding and optimizing real-world systems
• Heat engines convert heat into mechanical work (internal combustion engines, steam turbines)
  • Efficiency is limited by the Second Law of Thermodynamics
• Refrigerators and heat pumps transfer heat from a cold reservoir to a hot reservoir
  • Coefficient of performance (COP) measures the efficiency
• Phase diagrams show the conditions at which different phases of a substance are stable
  • Used in materials science and engineering (alloys, ceramics)
• Gibbs free energy is used to predict the feasibility of chemical reactions
  • Important in chemical synthesis and industrial processes (Haber-Bosch process for ammonia production)
• Biological systems rely on thermodynamic principles (energy transduction in cells, protein folding)
• Environmental science uses thermodynamics to study climate change and global energy balance