How to Find Delta H in Gibbs Free Energy: A Comprehensive Guide

Summary

Calculating the enthalpy change (ΔH) in Gibbs free energy is a crucial step in understanding the thermodynamics of chemical reactions. This comprehensive guide will walk you through the step-by-step process of determining ΔH, using the formula ΔG = ΔH – TΔS, and provide you with the necessary tools and examples to master this concept.

Identifying Reactants and Products

The first step in finding ΔH is to identify the reactants and products involved in the chemical reaction. This can be done by writing down the balanced chemical equation, including the physical states of the reactants and products.

For example, consider the reaction:
2H2(g) + O2(g) → 2H2O(l)

In this reaction, the reactants are hydrogen gas (H2) and oxygen gas (O2), and the product is liquid water (H2O).

Finding Enthalpy of Formation

The next step is to find the enthalpy of formation (ΔHf) for each reactant and product. The enthalpy of formation is the enthalpy change when one mole of a substance in its standard state is formed from the component elements in their standard states.

You can look up the enthalpy of formation values in reference tables, such as the NIST Chemistry WebBook. For the example reaction, the enthalpy of formation values are:
– ΔHf(H2(g)) = 0 kJ/mol (since the formation of H2 from H atoms does not involve a chemical reaction)
– ΔHf(O2(g)) = 0 kJ/mol (since the formation of O2 from O atoms does not involve a chemical reaction)
– ΔHf(H2O(l)) = -285.8 kJ/mol

Calculating Enthalpy Change (ΔH)

To calculate the enthalpy change (ΔH) for the reaction, you can use the formula:

ΔH = Σ(n × ΔHf(products)) – Σ(m × ΔHf(reactants))

Where:
– n is the stoichiometric coefficient of the product
– m is the stoichiometric coefficient of the reactant

Applying this formula to the example reaction:
ΔH = [2 × (-285.8 kJ/mol)] – [2 × 0 + 1 × 0] = -571.6 kJ/mol

Therefore, the enthalpy change for this reaction is -571.6 kJ/mol, indicating that the reaction is exothermic (releases heat).

Calculating Entropy Change (ΔS)

To find the entropy change (ΔS) for the reaction, you can use the formula:

ΔS = (ΔH – ΔG) / T

Where:
– ΔG is the Gibbs free energy change
– T is the absolute temperature in Kelvin

For example, if the temperature is 298 K, ΔH = -571.6 kJ/mol, and ΔG = -522.9 kJ/mol, then:

ΔS = (-571.6 kJ/mol – (-522.9 kJ/mol)) / 298 K = -163.4 J/mol·K

Calculating Gibbs Free Energy (ΔG)

Once you have calculated ΔH and ΔS, you can use the formula ΔG = ΔH – TΔS to find the Gibbs free energy change (ΔG) for the reaction.

Continuing the example, if T = 298 K, ΔH = -571.6 kJ/mol, and ΔS = -163.4 J/mol·K, then:

ΔG = -571.6 kJ/mol – (298 K × -0.1634 kJ/mol·K) = -571.6 kJ/mol + 48.7 kJ/mol = -522.9 kJ/mol

Therefore, the Gibbs free energy change for this reaction at 298 K is -522.9 kJ/mol, indicating that the reaction is spontaneous under standard conditions.

Factors Affecting ΔH, ΔS, and ΔG

It is important to note that the values of ΔH, ΔS, and ΔG can vary depending on the conditions of the reaction, such as temperature, pressure, and concentration. Therefore, it is crucial to specify the conditions under which the reaction takes place when reporting these thermodynamic properties.

Additionally, while a negative ΔG value indicates that a reaction is spontaneous, it does not necessarily mean that the reaction will occur at a significant rate. Other factors, such as activation energy and reaction cross section, can affect the rate of a reaction.

Conclusion

Calculating the enthalpy change (ΔH) in Gibbs free energy is a fundamental step in understanding the thermodynamics of chemical reactions. By following the step-by-step process outlined in this guide, you can determine ΔH, ΔS, and ΔG for any given reaction, and gain a deeper understanding of the driving forces behind chemical processes.

References

• NIST Chemistry WebBook: https://webbook.nist.gov/chemistry/