Entropy vs Enthalpy: A Comprehensive Guide for Science Students

Entropy (S) and enthalpy (H) are two fundamental thermodynamic properties that play a crucial role in understanding the spontaneity and direction of chemical reactions. Entropy is a measure of the randomness or disorder of a system, while enthalpy is a measure of the total energy of a system, including both the internal energy and the energy associated with the system’s interactions with its surroundings.

Understanding Entropy

Entropy is a quantitative measure of the disorder or randomness of a system. It can be calculated using the Boltzmann equation, which relates the entropy of a system to the number of possible microstates it can occupy:

S = k_B ln Ω

Where:
– S is the entropy of the system
– k_B is the Boltzmann constant (1.380 × 10^-23 J/K)
– Ω is the number of possible microstates of the system

The third law of thermodynamics states that the entropy of a pure, perfect crystal is zero at absolute zero (0 K). By measuring the heat required to raise the temperature of a substance from absolute zero to a given temperature, the entropy of the substance can be calculated.

For example, the standard molar entropy of water is 70.0 J/(mol·K) at 298 K, while the standard molar entropy of hydrogen gas is 130.7 J/(mol·K) at the same temperature. This means that hydrogen gas has a higher entropy than water at the same temperature, indicating that the hydrogen gas is more disordered or random.

Factors Affecting Entropy

Several factors can influence the entropy of a system:

1. Temperature: Increasing the temperature of a system generally increases its entropy, as the higher kinetic energy of the particles leads to a greater number of possible microstates.
2. Phase changes: Phase changes, such as melting or boiling, typically increase the entropy of a system due to the increased disorder of the particles in the new phase.
3. Mixing: Mixing two or more substances generally increases the entropy of the system, as the particles become more randomly distributed.
4. Chemical reactions: The entropy change in a chemical reaction depends on the number of reactant and product particles, as well as the degree of disorder in the system.

Understanding Enthalpy

Enthalpy (H) is a measure of the total energy of a system, including both the internal energy and the energy associated with the system’s interactions with its surroundings. Enthalpy can be quantified by measuring the heat required to change the state of a substance, such as from a solid to a liquid or from a liquid to a gas.

For example, the standard molar enthalpy of fusion of water is 6.007 kJ/mol at 273.15 K, while the standard molar enthalpy of vaporization is 40.65 kJ/mol at 373.15 K. These values represent the amount of heat required to change the state of one mole of water from a solid to a liquid or from a liquid to a gas, respectively.

Factors Affecting Enthalpy

Several factors can influence the enthalpy of a system:

1. Chemical bonds: The formation or breaking of chemical bonds during a reaction can either release or absorb energy, affecting the enthalpy of the system.
2. Phase changes: Phase changes, such as melting or boiling, typically involve a change in enthalpy due to the energy required to overcome the intermolecular forces between particles.
3. Pressure and volume: Changes in pressure and volume can affect the enthalpy of a system, as described by the first law of thermodynamics.
4. Temperature: Enthalpy is often temperature-dependent, as the internal energy of a system can change with temperature.

Relationship between Entropy and Enthalpy

The relationship between entropy and enthalpy is crucial in understanding the spontaneity and direction of chemical reactions. The Gibbs free energy equation, which is given by:

ΔG = ΔH – TΔS

Where:
– ΔG is the change in Gibbs free energy
– ΔH is the change in enthalpy
– ΔS is the change in entropy
– T is the absolute temperature

The Gibbs free energy change (ΔG) determines the spontaneity and direction of a chemical reaction. If ΔG is negative, the reaction is spontaneous; if ΔG is positive, the reaction is non-spontaneous.

For example, the synthesis of carbon dioxide from graphite and oxygen has a standard entropy change of ΔS° = -213.6 J/(mol·K) and a standard enthalpy change of ΔH° = -393.5 kJ/mol. Using the Gibbs free energy equation, the standard Gibbs free energy change for this reaction is ΔG° = -394.4 kJ/mol at 298 K, indicating that the reaction is spontaneous.

Numerical Examples and Problems

1. Calculating Entropy Change
2. Given: The standard molar entropy of water is 70.0 J/(mol·K) at 298 K, and the standard molar entropy of hydrogen gas is 130.7 J/(mol·K) at the same temperature.

3. Calculate the entropy change (ΔS) for the reaction: 2H2(g) + O2(g) → 2H2O(l)

4. Calculating Enthalpy Change

5. Given: The standard molar enthalpy of fusion of water is 6.007 kJ/mol at 273.15 K, and the standard molar enthalpy of vaporization is 40.65 kJ/mol at 373.15 K.

6. Calculate the enthalpy change (ΔH) for the reaction: H2O(s) → H2O(l) → H2O(g)

7. Calculating Gibbs Free Energy Change

8. Given: The synthesis of carbon dioxide from graphite and oxygen has a standard entropy change of ΔS° = -213.6 J/(mol·K) and a standard enthalpy change of ΔH° = -393.5 kJ/mol.
9. Calculate the standard Gibbs free energy change (ΔG°) for this reaction at 298 K.

Conclusion

Entropy and enthalpy are fundamental thermodynamic properties that play a crucial role in understanding the spontaneity and direction of chemical reactions. By understanding the factors that affect these properties and their relationship, as well as solving numerical examples and problems, science students can develop a deeper understanding of the underlying principles of thermodynamics and their applications in various fields of study.

References

1. Chem. LibreTexts. (2023-07-07). 19.4: Entropy Changes in Chemical Reactions – Chemistry LibreTexts. Retrieved from https://chem.libretexts.org/Bookshelves/General_Chemistry/Map:_Chemistry_-_The_Central_Science_%28Brown_et_al.%29/19:_Chemical_Thermodynamics/19.04:_Entropy_Changes_in_Chemical_Reactions
2. Open Text BC. (n.d.). Measuring Entropy and Entropy Changes – Introductory Chemistry. Retrieved from https://opentextbc.ca/introductorychemistry/chapter/measuring-entropy-and-entropy-changes/
3. NCBI. (2014, March 1). Entropy-enthalpy compensation: Role and ramifications in biomolecular ligand recognition and design. Retrieved from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4124006/