ap chemistry unit 9 study guides

Key Concepts and Definitions

• Thermodynamics studies the relationships between heat, work, and energy in a system
• A system is a specific portion of the universe that is being studied, while the surroundings include everything outside the system
• Open systems can exchange both matter and energy with their surroundings, while closed systems can only exchange energy
• Isolated systems do not exchange matter or energy with their surroundings
• State functions depend only on the current state of the system and not on the path taken to reach that state (include internal energy, enthalpy, and entropy)
• Extensive properties depend on the amount of matter in a system (volume and mass), while intensive properties are independent of the amount of matter (temperature and pressure)
• Thermal equilibrium occurs when two objects in contact with each other reach the same temperature and no net heat transfer occurs between them

Laws of Thermodynamics

• The first law of thermodynamics states that energy cannot be created or destroyed, only converted from one form to another
  • In a closed system, the change in internal energy ($\Delta U$) equals the heat added to the system ($q$) minus the work done by the system ($w$): $\Delta U = q - w$
• The second law of thermodynamics states that the entropy of the universe always increases in a spontaneous process
  • Entropy is a measure of the disorder or randomness of a system
  • In an isolated system, spontaneous processes always proceed in the direction of increasing entropy
• The third law of thermodynamics states that the entropy of a perfect crystal at absolute zero (0 K) is zero
  • As temperature approaches absolute zero, the entropy of a system approaches a constant minimum value
• The zeroth law of thermodynamics defines thermal equilibrium and provides the basis for temperature measurement
  • If two systems are in thermal equilibrium with a third system, they are also in thermal equilibrium with each other

Energy Transfer and Heat Flow

• Heat is the transfer of thermal energy from a hotter object to a cooler object
  • Heat always flows spontaneously from a higher temperature to a lower temperature
• Temperature is a measure of the average kinetic energy of the particles in a substance
• The specific heat capacity ($c$) of a substance is the amount of heat required to raise the temperature of 1 gram of the substance by 1 degree Celsius
  • The molar heat capacity ($C$) is the heat capacity per mole of a substance
• The heat transferred ($q$) is calculated using the equation $q = mc\Delta T$, where $m$ is the mass, $c$ is the specific heat capacity, and $\Delta T$ is the change in temperature
• Calorimetry is the measurement of heat transfer in chemical reactions or physical processes
  • A calorimeter is an insulated device used to measure heat transfer
• Phase changes (melting, freezing, vaporization, and condensation) involve heat transfer without a change in temperature
  • The heat of fusion ($\Delta H_{\text{fus}}$) is the heat required to melt one mole of a substance at its melting point
  • The heat of vaporization ($\Delta H_{\text{vap}}$) is the heat required to vaporize one mole of a substance at its boiling point

Enthalpy and Enthalpy Changes

• Enthalpy ($H$) is a state function that represents the total heat content of a system at constant pressure
  • Enthalpy is defined as $H = U + PV$, where $U$ is the internal energy, $P$ is the pressure, and $V$ is the volume
• The change in enthalpy ($\Delta H$) for a process is the heat absorbed or released by the system at constant pressure
  • For an endothermic process, $\Delta H$ is positive, and heat is absorbed by the system from the surroundings
  • For an exothermic process, $\Delta H$ is negative, and heat is released by the system to the surroundings
• Hess's law states that the overall enthalpy change for a reaction is independent of the pathway and is equal to the sum of the enthalpy changes for each step
  • This allows for the calculation of enthalpy changes for reactions that cannot be directly measured using standard enthalpies of formation ($\Delta H_f^\circ$)
• The standard enthalpy of formation ($\Delta H_f^\circ$) is the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states at 1 atm and 25°C
• The standard enthalpy of combustion ($\Delta H_c^\circ$) is the enthalpy change when one mole of a substance is completely burned in excess oxygen at 1 atm and 25°C
• Bond enthalpies can be used to estimate the enthalpy change of a reaction by considering the energy required to break and form chemical bonds

Entropy and Spontaneity

• Entropy ($S$) is a state function that measures the disorder or randomness of a system
  • A system with higher entropy has more disorder and a greater number of possible microstates
• The second law of thermodynamics states that the entropy of the universe always increases in a spontaneous process
• The change in entropy ($\Delta S$) for a system can be calculated using the equation $\Delta S = \frac{q_{\text{rev}}}{T}$, where $q_{\text{rev}}$ is the heat absorbed or released in a reversible process and $T$ is the absolute temperature
• The standard molar entropy ($S^\circ$) is the entropy of one mole of a substance in its standard state at 1 atm and 25°C
• The third law of thermodynamics states that the entropy of a perfect crystal at absolute zero (0 K) is zero
• The entropy change for a reaction ($\Delta S_{\text{rxn}}$) can be calculated using the standard molar entropies of the products and reactants: $\Delta S_{\text{rxn}} = \sum S^\circ_{\text{products}} - \sum S^\circ_{\text{reactants}}$
• A spontaneous process is one that occurs without external intervention and is characterized by an increase in the entropy of the universe ($\Delta S_{\text{univ}} > 0$)
  • The entropy change of the universe is the sum of the entropy changes of the system and surroundings: $\Delta S_{\text{univ}} = \Delta S_{\text{sys}} + \Delta S_{\text{surr}}$

Gibbs Free Energy

• Gibbs free energy ($G$) is a state function that combines the effects of enthalpy and entropy to determine the spontaneity of a process at constant temperature and pressure
  • Gibbs free energy is defined as $G = H - TS$, where $H$ is the enthalpy, $T$ is the absolute temperature, and $S$ is the entropy
• The change in Gibbs free energy ($\Delta G$) for a process determines its spontaneity:
  • If $\Delta G < 0$, the process is spontaneous and will occur naturally
  • If $\Delta G > 0$, the process is non-spontaneous and will not occur naturally
  • If $\Delta G = 0$, the process is at equilibrium and has no net change
• The standard Gibbs free energy change ($\Delta G^\circ$) for a reaction can be calculated using the standard Gibbs free energies of formation ($\Delta G_f^\circ$) of the products and reactants: $\Delta G^\circ = \sum \Delta G_f^\circ(\text{products}) - \sum \Delta G_f^\circ(\text{reactants})$
• The relationship between $\Delta G$, $\Delta H$, and $\Delta S$ is given by the equation $\Delta G = \Delta H - T\Delta S$
  • This equation shows that the spontaneity of a process depends on the balance between the enthalpy and entropy changes
• The equilibrium constant ($K$) for a reaction is related to the standard Gibbs free energy change by the equation $\Delta G^\circ = -RT \ln K$, where $R$ is the gas constant and $T$ is the absolute temperature
  • This relationship allows for the calculation of equilibrium constants from thermodynamic data and vice versa

Real-World Applications

• Thermodynamics plays a crucial role in understanding and optimizing chemical reactions and processes in various fields, such as chemical engineering, materials science, and biochemistry
• Hess's law is used to calculate the enthalpy changes of complex reactions by combining the known enthalpy changes of simpler reactions (formation or combustion of compounds)
• The spontaneity of chemical reactions is essential in predicting the feasibility and direction of processes, such as the synthesis of new materials, drug design, and metabolic pathways in living organisms
• Gibbs free energy is used to determine the stability and solubility of compounds, which is important in fields like pharmaceuticals and environmental chemistry
  • The solubility product constant ($K_{\text{sp}}$) is related to the standard Gibbs free energy change of dissolution
• Thermodynamic principles are applied in the design and optimization of industrial processes, such as the Haber-Bosch process for ammonia synthesis and the production of sulfuric acid
• Energy storage and conversion devices, such as batteries and fuel cells, rely on thermodynamic concepts to maximize efficiency and performance
• Biochemical processes, such as enzyme-catalyzed reactions and ATP synthesis, are governed by thermodynamic principles and can be analyzed using Gibbs free energy and equilibrium constants

Problem-Solving Strategies

• Identify the system and surroundings, and determine whether the process occurs at constant pressure or constant volume
• Write balanced chemical equations for the reactions involved, and ensure that the stoichiometry is correct
• Determine the appropriate thermodynamic quantities (enthalpy, entropy, or Gibbs free energy) needed to solve the problem
• Use the given data, such as standard enthalpies of formation, standard entropies, or standard Gibbs free energies of formation, to calculate the desired thermodynamic quantities
  • Be careful with units and convert values to the appropriate units if necessary
• Apply the relevant thermodynamic equations, such as $\Delta H = \sum \Delta H_f^\circ(\text{products}) - \sum \Delta H_f^\circ(\text{reactants})$ or $\Delta G = \Delta H - T\Delta S$, to solve for the unknown variables
• For problems involving Hess's law, combine the known enthalpy changes of reactions to determine the overall enthalpy change for the desired reaction
• When using the relationship between Gibbs free energy and the equilibrium constant ($\Delta G^\circ = -RT \ln K$), make sure to use the appropriate units for the gas constant $R$ and the absolute temperature $T$
• Double-check your calculations and ensure that the final answer is reasonable and consistent with the problem's context