A-Level Chemistry 9701

Physical Chemistry

Chemical Energetics II: Entropy, Gibbs Free Energy, Feasibility of Reactions

This section delves deeper into the concepts of entropy and Gibbs free energy, crucial for understanding the spontaneity and feasibility of chemical reactions. We will explore how these thermodynamic properties dictate whether a reaction will occur under specific conditions.

Entropy (ΔS)

Entropy is a measure of the disorder or randomness of a system. The higher the disorder, the higher the entropy. It is a state function, meaning its change depends only on the initial and final states of the system, not the path taken.

Factors affecting entropy:

• Physical state: Gases have higher entropy than liquids, which have higher entropy than solids.
• Number of moles: Increasing the number of moles of a gas increases entropy.
• Temperature: Increasing the temperature increases entropy.
• Volume: Increasing the volume of a gas increases entropy (assuming constant pressure).
• Mixing: Mixing different substances generally increases entropy.

Calculating Entropy Change (ΔS):

The change in entropy for a process can be calculated using the following equation:

$$ \Delta S = \frac{q_{rev}}{T} $$

where:

• $q_{rev}$ is the heat transferred in a reversible process.
• $T$ is the absolute temperature (in Kelvin).

Entropy and Phase Changes:

Phase changes (e.g., melting, boiling, sublimation) are accompanied by significant changes in entropy. For example, the transition from solid to liquid involves an increase in disorder, hence a positive ΔS.

Gibbs Free Energy (ΔG)

Gibbs Free Energy is a thermodynamic potential that can be used to predict the spontaneity of a process occurring at constant temperature and pressure. It combines enthalpy (ΔH) and entropy (ΔS) changes.

Equation for Gibbs Free Energy Change:

$$ \Delta G = \Delta H - T\Delta S $$

where:

• $\Delta G$ is the change in Gibbs free energy.
• $\Delta H$ is the change in enthalpy.
• $T$ is the absolute temperature (in Kelvin).
• $\Delta S$ is the change in entropy.

Spontaneity and ΔG:

1. ΔG < 0: The process is spontaneous (favored) under the given conditions.
2. ΔG > 0: The process is non-spontaneous (requires energy input) under the given conditions. The reverse process is spontaneous.
3. ΔG = 0: The process is at equilibrium.

Relationship between ΔG, ΔH, and T:

The sign of ΔG at a given temperature tells us whether the reaction is spontaneous. The magnitude of ΔG tells us the extent to which the reaction will proceed.

Feasibility of Reactions

The spontaneity of a reaction is determined by the change in Gibbs free energy (ΔG). We can use ΔG to predict whether a reaction will occur without external energy input.

Factors affecting ΔG:

• Enthalpy Change (ΔH):
• Exothermic reactions (ΔH < 0): These reactions tend to be spontaneous.
• Endothermic reactions (ΔH > 0): These reactions are non-spontaneous and require a continuous input of heat to proceed.
• Entropy Change (ΔS):
• Positive ΔS: Favors spontaneity.
• Negative ΔS: Disfavors spontaneity.
• Temperature (T):
• At high temperatures, the TΔS term becomes more significant. Even if ΔH is positive (endothermic), a positive ΔS can make ΔG negative and the reaction spontaneous.
• At low temperatures, the ΔH term becomes more significant. Even if ΔS is positive, a large positive ΔH can make ΔG positive and the reaction non-spontaneous.

Example: Haber Process

The Haber process (nitrogen fixation) is an exothermic reaction: N₂(g) + 3H₂(g) ⇌ 2NH₃(g) ΔH = -92 kJ/mol. It is also an exothermic reaction, so a negative ΔH favors spontaneity. However, it is still not spontaneous at room temperature. A high pressure and a low temperature are used to increase the rate of the reaction. This is because the reaction is exothermic, so a low temperature favors the forward reaction (product formation), and high pressure favors the forward reaction (fewer moles of gas on the product side).

Summary Table

Property	Symbol	Meaning
Entropy	ΔS	Measure of disorder or randomness
Gibbs Free Energy	ΔG	Measure of spontaneity at constant T and P
Enthalpy	ΔH	Change in heat energy
Temperature	T	Absolute temperature (K)
Spontaneous Reaction	ΔG < 0	Reaction occurs without external energy input
Non-Spontaneous Reaction	ΔG > 0	Reaction requires external energy input
Equilibrium	ΔG = 0	Forward and reverse reaction rates are equal