5.1 Spontaneous processes and entropy

The Second Law of Thermodynamics introduces spontaneous processes and entropy, key concepts in understanding energy flow and disorder in systems. Spontaneous processes occur without external intervention, increasing the universe's entropy, while non-spontaneous processes require energy input and decrease overall entropy.

Entropy, a measure of disorder, plays a crucial role in determining process spontaneity. The relationship between entropy, enthalpy, and Gibbs free energy helps predict whether a process will occur naturally or require external energy, shaping our understanding of chemical and physical changes.

Spontaneous vs Non-spontaneous Processes

Defining Spontaneous and Non-spontaneous Processes

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• A spontaneous process occurs without any external intervention or input of energy (rusting of iron, ice melting at room temperature)
• A non-spontaneous process requires an external source of energy to occur (water splitting into hydrogen and oxygen, water freezing at room temperature)
• Spontaneous processes are characterized by an increase in the entropy of the universe (system + surroundings)
• Non-spontaneous processes are characterized by a decrease in the entropy of the universe

Relationship between Spontaneity and Entropy Changes

• The spontaneity of a process depends on the change in entropy (ΔS) of the system and the surroundings
  • A process is spontaneous if ΔSuniverse > 0
  • A process is non-spontaneous if ΔSuniverse < 0
• The relationship between the change in Gibbs free energy (ΔG) and the spontaneity of a process at constant temperature and pressure is given by the equation: $ΔG = ΔH - TΔS$
  • ΔH is the change in enthalpy
  • T is the absolute temperature
  • ΔS is the change in entropy
• A process is spontaneous if ΔG < 0, non-spontaneous if ΔG > 0, and at equilibrium if ΔG = 0

Entropy: A Measure of Disorder

Defining Entropy

• Entropy (S) is a thermodynamic property that quantifies the degree of disorder or randomness in a system
• Entropy measures the number of possible microstates (arrangements of particles) in a system
• The second law of thermodynamics states that the entropy of the universe always increases for a spontaneous process, meaning the disorder or randomness of the universe increases over time

Calculating Entropy Changes

• The change in entropy (ΔS) for a system can be calculated using the equation: $ΔS = qrev/T$
  • qrev is the heat absorbed or released by the system during a reversible process
  • T is the absolute temperature
• For a phase transition (melting, vaporization), the change in entropy can be calculated using the equation: $ΔS = ΔH/T$
  • ΔH is the change in enthalpy (heat of fusion or heat of vaporization)
  • T is the absolute temperature at which the phase transition occurs
• The third law of thermodynamics states that the entropy of a perfect crystal at absolute zero (0 K) is zero, providing a reference point for calculating the absolute entropy of a substance at any temperature

Factors Affecting Spontaneity

Temperature and Pressure Effects

• Temperature affects spontaneity through its influence on the entropy change (ΔS) and the Gibbs free energy change (ΔG)
  • At higher temperatures, the TΔS term in the Gibbs free energy equation becomes more significant, favoring processes with a positive entropy change
• Pressure affects spontaneity through its influence on the enthalpy change (ΔH) and the Gibbs free energy change (ΔG)
  • For processes involving gases, an increase in pressure generally favors the side of the reaction with fewer moles of gas, reducing the volume and increasing the enthalpy of the system

Other Factors Influencing Spontaneity

• The presence of a catalyst does not affect the spontaneity of a process, as it does not change the thermodynamic properties (ΔH, ΔS, or ΔG) of the system
  • However, a catalyst can increase the rate of a spontaneous process by lowering the activation energy
• The concentration of reactants and products can influence spontaneity through its effect on the Gibbs free energy change (ΔG)
  • According to Le Chatelier's principle, increasing the concentration of reactants or decreasing the concentration of products will shift the equilibrium towards the products, making the forward reaction more spontaneous

Second Law of Thermodynamics and Spontaneity

Entropy and the Direction of Spontaneous Processes

• The second law of thermodynamics states that the entropy of the universe always increases for a spontaneous process, meaning the direction of a spontaneous process is always towards increasing entropy
• For a spontaneous process, the change in entropy of the universe (ΔSuniverse) must be greater than zero
  • This can be determined by calculating the change in entropy of the system (ΔSsystem) and the surroundings (ΔSsurroundings) separately, and then adding them together
• The change in entropy of the surroundings can be calculated using the equation: $ΔSsurroundings = -ΔHsystem/T$
  • ΔHsystem is the change in enthalpy of the system (heat absorbed or released by the system)
  • T is the absolute temperature of the surroundings

Reversible and Irreversible Processes

• In an isolated system (no exchange of energy or matter with the surroundings), a spontaneous process will always proceed in the direction of increasing entropy until equilibrium is reached, at which point the entropy of the system is at a maximum
• For a reversible process, the change in entropy of the universe is zero (ΔSuniverse = 0), as the entropy change in the system is exactly balanced by the entropy change in the surroundings
• For an irreversible process, the change in entropy of the universe is always greater than zero (ΔSuniverse > 0)