At $298 \, K$, $\Delta H^0 = -314 \, \text{kJ/mol}$ And $\Delta S^0 = -0.372 \, \text{kJ/(K \cdot Mol)}$. What Is The Gibbs Free Energy Of The Reaction?A. $34,900 \, \text{kJ}$ B. $0.393 \, \text{kJ}$ C.

by ADMIN 206 views

Calculating Gibbs Free Energy: A Key Concept in Chemistry

The Gibbs free energy, denoted by the symbol ΔG, is a crucial thermodynamic property that helps us understand the spontaneity of a chemical reaction. It is defined as the maximum amount of work that can be extracted from a system at constant temperature and pressure. In this article, we will delve into the concept of Gibbs free energy and learn how to calculate it using the given values of enthalpy (ΔH) and entropy (ΔS).

Understanding the Relationship Between ΔG, ΔH, and ΔS

The Gibbs free energy is related to the enthalpy and entropy of a reaction through the following equation:

ΔG = ΔH - TΔS

where ΔG is the Gibbs free energy, ΔH is the enthalpy change, T is the temperature in Kelvin, and ΔS is the entropy change.

Given Values and Their Significance

We are given the following values:

  • ΔH^0 = -314 kJ/mol (the standard enthalpy change)
  • ΔS^0 = -0.372 kJ/(K·mol) (the standard entropy change)
  • T = 298 K (the temperature at which the reaction occurs)

Calculating the Gibbs Free Energy

Now, let's substitute the given values into the equation for ΔG:

ΔG = ΔH - TΔS ΔG = -314 kJ/mol - (298 K) × (-0.372 kJ/(K·mol)) ΔG = -314 kJ/mol + 110.76 kJ/mol ΔG = -203.24 kJ/mol

Interpreting the Result

The calculated value of ΔG indicates that the reaction is non-spontaneous at the given temperature. A negative value of ΔG would have indicated a spontaneous reaction.

Comparison with the Given Options

Let's compare our calculated value of ΔG with the given options:

A. 34,900 kJ34,900 \, \text{kJ} - This value is incorrect. B. 0.393 kJ0.393 \, \text{kJ} - This value is also incorrect. C. -203.24 kJ/mol - This is the correct answer.

Conclusion

In conclusion, we have successfully calculated the Gibbs free energy of a reaction using the given values of enthalpy and entropy. The calculated value of ΔG indicates that the reaction is non-spontaneous at the given temperature. This calculation is essential in understanding the thermodynamics of a reaction and predicting its spontaneity.

Key Takeaways

  • The Gibbs free energy is a crucial thermodynamic property that helps us understand the spontaneity of a chemical reaction.
  • The Gibbs free energy is related to the enthalpy and entropy of a reaction through the equation ΔG = ΔH - TΔS.
  • A negative value of ΔG indicates a spontaneous reaction, while a positive value indicates a non-spontaneous reaction.
  • The calculated value of ΔG can be used to predict the spontaneity of a reaction at a given temperature.

Frequently Asked Questions

  • What is the Gibbs free energy? The Gibbs free energy is a thermodynamic property that helps us understand the spontaneity of a chemical reaction.
  • How is the Gibbs free energy related to the enthalpy and entropy of a reaction? The Gibbs free energy is related to the enthalpy and entropy of a reaction through the equation ΔG = ΔH - TΔS.
  • What does a negative value of ΔG indicate? A negative value of ΔG indicates a spontaneous reaction.
  • What does a positive value of ΔG indicate? A positive value of ΔG indicates a non-spontaneous reaction.
    Gibbs Free Energy Q&A: Understanding the Spontaneity of Chemical Reactions

In our previous article, we explored the concept of Gibbs free energy and learned how to calculate it using the given values of enthalpy and entropy. In this article, we will delve into the world of frequently asked questions and provide answers to some of the most common queries related to Gibbs free energy.

Q1: What is the Gibbs free energy?

A1: The Gibbs free energy, denoted by the symbol ΔG, is a thermodynamic property that helps us understand the spontaneity of a chemical reaction. It is defined as the maximum amount of work that can be extracted from a system at constant temperature and pressure.

Q2: How is the Gibbs free energy related to the enthalpy and entropy of a reaction?

A2: The Gibbs free energy is related to the enthalpy and entropy of a reaction through the equation ΔG = ΔH - TΔS, where ΔG is the Gibbs free energy, ΔH is the enthalpy change, T is the temperature in Kelvin, and ΔS is the entropy change.

Q3: What does a negative value of ΔG indicate?

A3: A negative value of ΔG indicates a spontaneous reaction. This means that the reaction will occur on its own without any external influence.

Q4: What does a positive value of ΔG indicate?

A4: A positive value of ΔG indicates a non-spontaneous reaction. This means that the reaction will not occur on its own and requires an external influence to proceed.

Q5: How can I calculate the Gibbs free energy of a reaction?

A5: To calculate the Gibbs free energy of a reaction, you need to know the values of enthalpy (ΔH) and entropy (ΔS) at the given temperature (T). You can then use the equation ΔG = ΔH - TΔS to calculate the Gibbs free energy.

Q6: What is the significance of the Gibbs free energy in chemistry?

A6: The Gibbs free energy is a crucial concept in chemistry as it helps us understand the spontaneity of chemical reactions. It is used to predict whether a reaction will occur on its own or require an external influence.

Q7: Can the Gibbs free energy be used to predict the direction of a reaction?

A7: Yes, the Gibbs free energy can be used to predict the direction of a reaction. If ΔG is negative, the reaction will proceed in the forward direction. If ΔG is positive, the reaction will proceed in the reverse direction.

Q8: How does the temperature affect the Gibbs free energy?

A8: The temperature affects the Gibbs free energy through the term TΔS in the equation ΔG = ΔH - TΔS. As the temperature increases, the term TΔS also increases, which can change the sign of ΔG.

Q9: Can the Gibbs free energy be used to predict the equilibrium constant of a reaction?

A9: Yes, the Gibbs free energy can be used to predict the equilibrium constant of a reaction. The equation ΔG = -RT ln(K) relates the Gibbs free energy to the equilibrium constant.

Q10: What are some common applications of the Gibbs free energy in chemistry?

A10: The Gibbs free energy has numerous applications in chemistry, including:

  • Predicting the spontaneity of chemical reactions
  • Determining the direction of a reaction
  • Calculating the equilibrium constant of a reaction
  • Understanding the thermodynamics of chemical reactions

Conclusion

In conclusion, the Gibbs free energy is a fundamental concept in chemistry that helps us understand the spontaneity of chemical reactions. By answering some of the most common questions related to Gibbs free energy, we hope to have provided a better understanding of this important thermodynamic property.

Key Takeaways

  • The Gibbs free energy is a thermodynamic property that helps us understand the spontaneity of chemical reactions.
  • The Gibbs free energy is related to the enthalpy and entropy of a reaction through the equation ΔG = ΔH - TΔS.
  • A negative value of ΔG indicates a spontaneous reaction, while a positive value indicates a non-spontaneous reaction.
  • The Gibbs free energy can be used to predict the direction of a reaction and the equilibrium constant of a reaction.

Frequently Asked Questions

  • What is the Gibbs free energy?
  • How is the Gibbs free energy related to the enthalpy and entropy of a reaction?
  • What does a negative value of ΔG indicate?
  • What does a positive value of ΔG indicate?
  • How can I calculate the Gibbs free energy of a reaction?
  • What is the significance of the Gibbs free energy in chemistry?
  • Can the Gibbs free energy be used to predict the direction of a reaction?
  • How does the temperature affect the Gibbs free energy?
  • Can the Gibbs free energy be used to predict the equilibrium constant of a reaction?
  • What are some common applications of the Gibbs free energy in chemistry?