entropy

• Entropy


  A measure of the randomness or disorder of a system
• Free Energy


  A measure of the useful work that can be obtained from a thermodynamic system
• Spontaneous movement


  Heart
• Spontaneous


  Waterfalls
• Nonspontaneous


  Throwing ball upward
• Spontaneous


  Decomposition of water into hydrogen and oxygen
• Nonspontaneous


  Water pump
• Spontaneous and Nonspontaneous Processes


  • spontaneous
  • nonspontaneous
• Entropy (S)


  A measure of the randomness or disorder of a system
• Increase in randomness


  ΔS > 0
• For any substance, the solid state is more ordered than the liquid state and the liquid state is more ordered than gas state
• S(solid) < S(liquid) << S(gas)
• Processes that lead to an increase in entropy (ΔS > 0)
• How does the entropy of a system change for each of the following processes?

  1. Condensing water vapor: Randomness decreases, Entropy decreases (ΔS < 0)

  2. Forming sucrose crystals from a supersaturated solution: Randomness decreases, Entropy decreases (ΔS < 0)

  3. Heating hydrogen gas from 60°C to 80°C: Randomness increases, Entropy increases (ΔS > 0)

  4. Subliming dry ice: Randomness increases, Entropy increases (ΔS > 0)
• State functions


  Properties that are determined by the state of the system, regardless of how that condition was achieved
• A positive value of ΔS (ΔS>0) indicates that the final state is more random or disordered than the initial state
• A negative ΔS value (ΔS<0) indicates that the final state is more ordered than the initial state
• Δ S


  S final - S initial
• Factors that influence the amount of entropy present in a system at a particular state

  • Change in Phase
  • Change in Temperature
  • Number of particles
• Increase in the number of particles

  Increase in entropy
• A2B → 2A + B

  Entropy increases because there are more particles in the products compared to the reactants
• Sublimation of solid carbon dioxide (dry ice): CO2(s) → CO2(g)

  Entropy increases and ΔS is > 0 because the solid is converted to gas, the particles are more scattered and are no longer confined to a limited volume of space, thus leading to greater disorder
• Change in Entropy


  A numerical value for entropy can be possibly determined for any substance under a given set of conditions
• ΔS


  The change in entropy, related to heat transferred during the process
• This equation applies only to processes that are almost reversible
• First Law of Thermodynamics

  Energy can be converted from one form to another but energy cannot be created or destroyed
• Second Law of Thermodynamics

  The entropy of the universe increases in a spontaneous process and remains unchanged in an equilibrium process
• If a reaction produces more gas molecules than it consumes, ΔS° > 0
• If the total number of gas molecules diminishes, ΔS° < 0
• If there is no net change in the total number of gas molecules, then ΔS° may be positive or negative but will be a small number
• S0rxn


  Entropy change for a reaction carried out at 1 atm and 25°C
• Entropy change in the system (ΔSsys)

  • If a reaction produces more gas molecules than it consumes, ΔS0 > 0
  • If the total number of gas molecules diminishes, ΔS0 < 0
  • If there is no net change in the total number of gas molecules, then ΔS0 may be positive or negative but ΔS0 will be a small number
• Entropy change in the surroundings (ΔSsurr)

  • Exothermic process: ΔSsurr > 0
  • Endothermic process: ΔSsurr < 0
• The entropy of a perfect crystalline substance is zero at the absolute zero of temperature
• Gibbs free energy (G)


  A thermodynamic function that considers both enthalpy and entropy factors to assess the spontaneity of a process
• Gibbs free energy is defined as G = H - TS, where H is enthalpy, T is temperature in Kelvin, and S is entropy
• For a spontaneous process, ΔGuniv = ΔGsys + ΔGsurr < 0
• For a constant temperature and pressure process, ΔG = ΔHsys - TΔSsys
• Gibbs free energy (G)

  • ΔG < 0: The reaction is spontaneous in the forward direction
  • ΔG > 0: The reaction is nonspontaneous as written, but spontaneous in the reverse direction
  • ΔG = 0: The reaction is at equilibrium
• Standard free-energy of reaction (ΔG°rxn)


  The free-energy change for a reaction when it occurs under standard-state conditions