If ΔG Is Positive For A Chemical Reaction, Then The Following Is Expected To Be True Of The Change In Entropy And Enthalpy.

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Understanding the Relationship Between ΔG, ΔH, and ΔS: A Comprehensive Analysis

Chemical reactions are governed by the principles of thermodynamics, which describe the relationships between energy, entropy, and the spontaneity of a reaction. One of the most fundamental concepts in thermodynamics is the Gibbs free energy (ΔG), which is a measure of the energy available to do work in a system. In this article, we will explore the relationship between ΔG, ΔH (enthalpy change), and ΔS (entropy change) for a chemical reaction, with a focus on what is expected to be true when ΔG is positive.

What is ΔG?

ΔG, or the Gibbs free energy change, is a measure of the energy available to do work in a system. It is defined as the difference between the enthalpy (H) and the product of the temperature (T) and entropy (S) of a system:

ΔG = ΔH - TΔS

The Significance of a Positive ΔG

When ΔG is positive, it indicates that the reaction is non-spontaneous, meaning that it will not occur on its own under standard conditions. In other words, the reaction requires an input of energy to proceed. This is because the energy required to overcome the activation energy barrier is greater than the energy released by the reaction.

The Relationship Between ΔG, ΔH, and ΔS

When ΔG is positive, we can expect the following to be true of the change in entropy (ΔS) and enthalpy (ΔH):

  • ΔH is positive: When ΔG is positive, it is likely that ΔH is also positive. This is because the enthalpy change is a measure of the energy released or absorbed during the reaction. If the reaction is non-spontaneous, it is likely that the energy required to overcome the activation energy barrier is greater than the energy released by the reaction, resulting in a positive ΔH.
  • ΔS is negative: When ΔG is positive, it is likely that ΔS is also negative. This is because the entropy change is a measure of the disorder or randomness of the system. If the reaction is non-spontaneous, it is likely that the system becomes more ordered or less random, resulting in a negative ΔS.

Why is ΔS Negative When ΔG is Positive?

When ΔG is positive, it is likely that the reaction involves the formation of a more ordered or structured product. This is because the entropy change is a measure of the disorder or randomness of the system. If the reaction is non-spontaneous, it is likely that the system becomes more ordered or less random, resulting in a negative ΔS.

For example, consider the reaction between hydrogen gas (H2) and oxygen gas (O2) to form water (H2O):

2H2(g) + O2(g) → 2H2O(l)

In this reaction, the reactants are gases, which are highly disordered and random. The product, water, is a liquid, which is more ordered and structured. Therefore, the entropy change (ΔS) is negative, indicating that the system becomes more ordered or less random during the reaction.

Why is ΔH Positive When ΔG is Positive?

When ΔG is positive, it is likely that the reaction involves the absorption of energy. This is because the enthalpy change is a measure of the energy released or absorbed during the reaction. If the reaction is non-spontaneous, it is likely that the energy required to overcome the activation energy barrier is greater than the energy released by the reaction, resulting in a positive ΔH.

For example, consider the reaction between calcium carbonate (CaCO3) and water (H2O) to form calcium hydroxide (Ca(OH)2) and carbon dioxide (CO2):

CaCO3(s) + H2O(l) → Ca(OH)2(aq) + CO2(g)

In this reaction, the reactants are a solid and a liquid, which are relatively ordered and structured. The products are a liquid and a gas, which are more disordered and random. Therefore, the enthalpy change (ΔH) is positive, indicating that the reaction absorbs energy.

Conclusion

In conclusion, when ΔG is positive for a chemical reaction, it is expected to be true that ΔH is positive and ΔS is negative. This is because the reaction is non-spontaneous, requiring an input of energy to proceed. The positive ΔH indicates that the reaction absorbs energy, while the negative ΔS indicates that the system becomes more ordered or less random during the reaction.

Understanding the Relationship Between ΔG, ΔH, and ΔS: A Comprehensive Analysis

Chemical reactions are governed by the principles of thermodynamics, which describe the relationships between energy, entropy, and the spontaneity of a reaction. One of the most fundamental concepts in thermodynamics is the Gibbs free energy (ΔG), which is a measure of the energy available to do work in a system. In this article, we have explored the relationship between ΔG, ΔH (enthalpy change), and ΔS (entropy change) for a chemical reaction, with a focus on what is expected to be true when ΔG is positive.

Key Takeaways

  • When ΔG is positive, it is likely that ΔH is also positive.
  • When ΔG is positive, it is likely that ΔS is also negative.
  • The positive ΔH indicates that the reaction absorbs energy.
  • The negative ΔS indicates that the system becomes more ordered or less random during the reaction.

References

  • Atkins, P. W., & De Paula, J. (2010). Physical chemistry (9th ed.). Oxford University Press.
  • Chang, R. (2010). Chemistry: The central science (11th ed.). McGraw-Hill.
  • Levine, I. N. (2014). Physical chemistry (6th ed.). McGraw-Hill.

Further Reading

  • For a more in-depth discussion of the relationship between ΔG, ΔH, and ΔS, see:
  • Atkins, P. W., & De Paula, J. (2010). Physical chemistry (9th ed.). Oxford University Press.
  • Chang, R. (2010). Chemistry: The central science (11th ed.). McGraw-Hill.
  • For a more detailed explanation of the thermodynamic principles governing chemical reactions, see:
  • Levine, I. N. (2014). Physical chemistry (6th ed.). McGraw-Hill.