chm 12901 general chemistry with a biological focus unit 7 study guides

Key Concepts and Definitions

• Thermodynamics studies the relationships between heat, work, and energy in a system
• System refers to the part of the universe being studied, while surroundings encompass everything outside the system
• State functions depend only on the current state of the system (pressure, temperature, volume) and not on the path taken to reach that state
• Extensive properties depend on the amount of matter present (volume, mass), while intensive properties are independent of the amount of matter (density, temperature)
• Thermal equilibrium occurs when two objects in contact have the same temperature and no net heat flow between them
• Exothermic processes release heat to the surroundings (combustion reactions), while endothermic processes absorb heat from the surroundings (melting ice)
  • Exothermic processes have a negative enthalpy change ($\Delta H < 0$)
  • Endothermic processes have a positive enthalpy change ($\Delta H > 0$)

Laws of Thermodynamics

• The first law of thermodynamics states that energy cannot be created or destroyed, only converted from one form to another
  • Mathematically expressed as $\Delta U = Q + W$, where $\Delta U$ is the change in internal energy, $Q$ is heat, and $W$ is work
• The second law of thermodynamics states that the entropy of the universe always increases in a spontaneous process
  • Entropy is a measure of disorder or randomness in a system
• The third law of thermodynamics states that the entropy of a perfect crystal at absolute zero (0 K) is zero
• The zeroth law of thermodynamics defines thermal equilibrium and allows for the measurement of temperature
• Thermodynamic processes can be reversible (system remains infinitesimally close to equilibrium) or irreversible (system deviates significantly from equilibrium)
• Adiabatic processes occur without heat exchange between the system and surroundings (insulated container), while isothermal processes occur at constant temperature

Energy Transfer and Types

• Energy can be transferred between a system and its surroundings through heat, work, or matter exchange
• Heat is the transfer of thermal energy due to a temperature difference between the system and surroundings
  • Heat flows from a higher temperature object to a lower temperature object
• Work is the energy transfer that occurs when a force moves an object over a distance
  • Examples include mechanical work (lifting a weight), electrical work (moving charges), and chemical work (battery producing current)
• Internal energy is the sum of all kinetic and potential energies of the particles within a system
  • Kinetic energy is associated with the motion of particles, while potential energy is associated with the position or configuration of particles
• Enthalpy is a state function that combines internal energy and the product of pressure and volume ($H = U + PV$)
  • Enthalpy change ($\Delta H$) is the heat absorbed or released by a system at constant pressure

Enthalpy and Heat Capacity

• Heat capacity is the amount of heat required to raise the temperature of a substance by one degree Celsius or Kelvin
  • Specific heat capacity ($c$) is the heat capacity per unit mass (J/g·°C or J/g·K)
  • Molar heat capacity ($C$) is the heat capacity per mole of a substance (J/mol·°C or J/mol·K)
• The heat absorbed or released by a substance is calculated using $q = mc\Delta T$ or $q = nC\Delta T$, where $m$ is mass, $n$ is the number of moles, and $\Delta T$ is the change in temperature
• Hess's law states that the enthalpy change of a reaction is independent of the pathway and depends only on the initial and final states
  • Allows for the calculation of enthalpy changes using standard enthalpies of formation ($\Delta H_f^\circ$) or standard enthalpies of combustion ($\Delta H_c^\circ$)
• Calorimetry measures the heat absorbed or released during a chemical or physical process
  • Bomb calorimeters measure the heat of combustion at constant volume, while coffee cup calorimeters measure the heat of reaction at constant pressure

Entropy and Spontaneity

• Entropy ($S$) is a measure of the disorder or randomness of a system
  • Spontaneous processes always result in an increase in the entropy of the universe ($\Delta S_\text{universe} > 0$)
• The second law of thermodynamics states that the entropy of the universe always increases in a spontaneous process
• Entropy changes can be calculated using $\Delta S = \frac{q_\text{rev}}{T}$, where $q_\text{rev}$ is the heat absorbed or released in a reversible process and $T$ is the absolute temperature
• Standard molar entropies ($S^\circ$) can be used to calculate the entropy change of a reaction using $\Delta S_\text{rxn}^\circ = \sum S_\text{products}^\circ - \sum S_\text{reactants}^\circ$
• The third law of thermodynamics allows for the determination of absolute entropies and states that the entropy of a perfect crystal at 0 K is zero

Gibbs Free Energy

• Gibbs free energy ($G$) combines enthalpy and entropy to determine the spontaneity of a process at constant temperature and pressure
  • Defined as $G = H - TS$, where $H$ is enthalpy, $T$ is absolute temperature, and $S$ is entropy
• The change in Gibbs free energy ($\Delta G$) determines the spontaneity of a process
  • If $\Delta G < 0$, the process is spontaneous; if $\Delta G > 0$, the process is non-spontaneous; if $\Delta G = 0$, the system is at equilibrium
• Standard Gibbs free energy changes ($\Delta G^\circ$) can be calculated using standard enthalpies of formation ($\Delta H_f^\circ$) and standard molar entropies ($S^\circ$)
  • $\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ$
• The relationship between $\Delta G^\circ$ and the equilibrium constant ($K$) is given by $\Delta G^\circ = -RT \ln K$, 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

Biological Applications

• Thermodynamics plays a crucial role in understanding biological systems and processes
• ATP (adenosine triphosphate) is the primary energy currency in living organisms
  • Hydrolysis of ATP to ADP (adenosine diphosphate) and inorganic phosphate releases energy for cellular processes
• Metabolism involves a series of coupled reactions, where exergonic reactions (release energy) drive endergonic reactions (require energy)
• Enzymes lower the activation energy of reactions, increasing the reaction rate without affecting the overall equilibrium
• Membrane transport processes, such as diffusion and active transport, are driven by concentration gradients and energy input
• Protein folding and stability are influenced by thermodynamic factors, such as enthalpy and entropy
  • Hydrophobic interactions, hydrogen bonding, and van der Waals forces contribute to the stability of protein structures
• Thermodynamics also plays a role in the regulation of gene expression, cell signaling, and other cellular processes

Problem-Solving Strategies

• Identify the system and surroundings, and determine the type of process (isothermal, adiabatic, reversible, or irreversible)
• Determine the state functions involved (internal energy, enthalpy, entropy, or Gibbs free energy) and the appropriate equations to use
• Gather the necessary data, such as heat capacities, standard enthalpies of formation, or standard molar entropies
• Apply the relevant equations and solve for the desired quantity, paying attention to units and sign conventions
• For problems involving Hess's law, break down the overall reaction into steps with known enthalpy changes and sum them to find the overall enthalpy change
• In calorimetry problems, use the heat absorbed or released by the calorimeter and the heat capacity of the calorimeter to determine the heat of the process
• For problems involving Gibbs free energy and equilibrium, use the relationship between $\Delta G^\circ$ and $K$ to calculate the desired quantity
• Always check the reasonableness of the answer and ensure that it is consistent with the principles of thermodynamics