17.6
Gibbs Free Energy
One of the challenges of using the second law of thermodynamics to determine if a process is spontaneous is that it requires measurements of the entro…
The second law of thermodynamics states that for all spontaneous processes, the entropy of the universe—the sum of the entropy of the system and the entropy of the surroundings—increases.
While the entropy of the system can be calculated from standard molar entropies, the entropy of the surroundings is more difficult to calculate or measure.
Therefore, J. Willard Gibbs defined a new thermodynamic function, which allows spontaneity to be determined solely through the entropy and enthalpy of the system and not the surroundings.
Recall that under constant pressure and temperature conditions, the ΔS of the surroundings is equal to the negative ΔH of the system divided by the temperature, T. This term can be substituted into the equation representing the second law.
When both sides are multiplied by negative T, the equation now becomes: −TΔSuniv = ΔHsys − TΔSsys. The thermodynamic functions on the right side of the equation—enthalpy and entropy—are both solely dependent on the system.
Because both enthalpy and entropy are state functions, a new state function can be defined as −TΔSuniv. This new term is called Gibbs free energy and is denoted by the letter G.
The equation for ΔG leads to a new criterion for spontaneous reactions. The difference between the enthalpy change and the temperature or entropy change must be less than zero.
ΔG is also known as chemical potential because it is similar to the mechanical potential energy of a system.
Just as a ball will always roll downhill to lower its potential energy, a chemical reaction proceeds to lower its chemical potential.
Thus, at constant temperature and pressure, if the free energy of the system decreases (that is, ΔG < 0), the reaction is spontaneous.
Conversely, if the free energy of the system increases, ΔG > 0, and the reaction is not spontaneous.
If ΔG = 0, then the reactants and products are in equilibrium.
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Q1: Why did J. Willard Gibbs introduce a new thermodynamic function?
Gibbs created this function to simplify determining spontaneity. The second law of thermodynamics requires measuring entropy changes for both the system and surroundings, which is difficult. Gibbs's function allows spontaneity to be determined using only the system's enthalpy and entropy, eliminating the need to measure surroundings' entropy.
Q2: How does Gibbs free energy relate to the second law of thermodynamics?
Gibbs free energy (ΔG) is mathematically derived from the second law of thermodynamics direction spontaneous changes. When ΔG is negative, the reaction is spontaneous and the universe's entropy increases. When ΔG is positive, the reaction is nonspontaneous. This relationship makes ΔG a reliable indicator of spontaneity based solely on system properties.
Q3: What does it mean when ΔG equals zero?
When ΔG = 0, the system is at equilibrium. The reactants and products are present in amounts where no net change occurs. At this point, the free energy of the system is neither increasing nor decreasing, indicating the reaction has reached its equilibrium state.
Q4: How is Gibbs free energy similar to mechanical potential energy?
Gibbs free energy is also called chemical potential because it functions like mechanical potential energy. Just as a ball rolls downhill to lower its potential energy, a chemical reaction proceeds spontaneously to lower its chemical potential. Systems naturally move toward states of lower free energy, driving reactions forward.
Q5: What equation defines Gibbs free energy at constant temperature and pressure?
At constant temperature and pressure, Gibbs free energy is defined as ΔG = ΔH − TΔS, where ΔH is enthalpy change, T is absolute temperature, and ΔS is entropy change of the system. This equation shows that spontaneity depends on both the enthalpy and entropy contributions, weighted by temperature.
Q6: Why is Gibbs free energy considered a state function?
Gibbs free energy is a state function because it depends only on the current state of the system, not on the path taken to reach that state. Since both enthalpy and entropy are state functions, and ΔG is defined mathematically from these properties, ΔG is also a state function.
Q7: How does temperature affect the spontaneity of a reaction according to Gibbs free energy?
Temperature directly influences ΔG through the equation ΔG = ΔH − TΔS. The temperature term multiplies entropy change, so increasing temperature amplifies the entropy contribution to spontaneity. This means some reactions that are nonspontaneous at low temperatures may become spontaneous at higher temperatures.