entropy

Examples of entropy in the following topics:

• Standard Entropy

  • The standard entropy of a substance (its entropy at 1 atmospheric pressure) helps determine if a reaction will take place spontaneously.
  • The standard entropy of a substance is its entropy at 1 atm pressure.
  • Some typical standard entropy values for gaseous substances include:
  • It is apparent that entropies generally increase with molecular weight.
  • There is an inverse correlation between the hardness of a solid and its entropy.

• Changes in Energy

  • For isolated systems, entropy never decreases.
  • Increases in entropy correspond to irreversible changes in a system.
  • The entropy of a system is defined only if it is in thermodynamic equilibrium.
  • However, the entropy of the system of ice and water has increased more than the entropy of the surrounding room has decreased.
  • Ice melting in a warm room is a common example of increasing entropy.

• Microstates and Entropy

  • With more available microstates, the entropy of a system increases.
  • As a result, entropy (denoted by S) is an expression of disorder or randomness.
  • With more available microstates, the entropy of a system increases.
  • This is the basis of an alternative (and more fundamental) definition of entropy:
  • Therefore, the entropy of a solid is less than the entropy of a liquid, which is much less than the entropy of a gas:

• The Third Law of Thermodynamics and Absolute Energy

  • Specifically, the entropy of a pure crystalline substance at absolute zero temperature is zero.
  • Entropy is related to the number of possible microstates according to $S = k_Bln(\Omega)$, where S is the entropy of the system, kB is Boltzmann's constant, and Ω is the number of microstates (e.g. possible configurations of atoms).
  • The constant value (not necessarily zero) is called the residual entropy of the system.
  • The entropy determined relative to this point (absolute zero) is the absolute entropy.
  • The entropy (S) of a substance (compound or element) as a function of temperature (T).

• Solutions and Entropy Changes

  • Chemists use the term "entropy" to denote this aspect of molecular randomness.
  • Entropy is indeed a fascinating, but somewhat confusing, topic.
  • In a similar manner entropy plays an important role in solution formation.
  • All these factors increase the entropy of the solute.
  • This is the same as saying that the entropy of the solute increases.

• Changes in the Entropy of Surroundings

  • Irreversible reactions result in a change in entropy to the surroundings.
  • The heat from the surroundings (entropy) goes into the ice water and the ice melts.
  • The entropy of the ice water increases while the entropy of the surroundings decreases.
  • Distinguish whether or not entropy of surroundings changes in various reactions

• Vapor Pressure of Nonelectrolyte Solutions

  • When molecules transition from the liquid phase to the gas phase, entropy of the system increases.
  • Entropy of the gaseous state is greater than the entropy of the liquid state because the gaseous molecules occupy a larger volume.
  • If the liquid solvent becomes "diluted" with solute, the entropy of the liquid state increases.
  • Therefore, even though the gaseous state has a higher entropy, the difference in entropy between the two systems decreases.
  • The decrease in entropy difference lowers the vapor pressure.

• The Three Laws of Thermodynamics

  • The second law of thermodynamics says that the entropy of any isolated system always increases.
  • Isolated systems spontaneously evolve towards thermal equilibrium—the state of maximum entropy of the system.
  • More simply put: the entropy of the universe (the ultimate isolated system) only increases and never decreases.
  • When the room is cleaned, its entropy decreases, but the effort to clean it has resulted in an increase in entropy outside the room that exceeds the entropy lost.
  • Specifically, the entropy of a pure crystalline substance (perfect order) at absolute zero temperature is zero.

• Free Energy Changes in Chemical Reactions

  • Water below zero degrees Celsius undergoes a decrease in its entropy, but the heat released into the surroundings more than compensates for this so the entropy of the world increases, the free energy of the H2O diminishes, and the process proceeds spontaneously.
  • where ΔG = change in Gibbs free energy, ΔH = change in enthalpy, T = absolute temperature, and ΔS = change in entropy
  • It is apparent that the temperature dependence of ΔG depends almost entirely on the entropy change associated with the process.
  • An exothermic reaction whose entropy increases will be spontaneous at all temperatures.
  • This is the reverse of the previous case; the entropy increase must overcome the handicap of an endothermic process so that TΔS > ΔH.

• Spontaneous and Nonspontaneous Processes

  • The laws of thermodynamics govern the direction of a spontaneous process, ensuring that if a sufficiently large number of individual interactions (like atoms colliding) are involved, then the direction will always be in the direction of increased entropy.
  • The second law of thermodynamics states that for any spontaneous process, the overall ΔS must be greater than or equal to zero; yet, spontaneous chemical reactions can result in a negative change in entropy.
  • The increase in temperature of the reaction surroundings results in a sufficiently large increase in entropy, such that the overall change in entropy is positive.
  • Since the overall ΔS = ΔSsurroundings + ΔSsystem, the overall change in entropy is still positive.