Given The Values: { \Delta H^{\circ} {rxn} = -60 \text{ KJ}$}$, { S^{\circ} {rxn} = -105.5 \text{ J/K}$}$, And Temperature { T = 327.4 \text{ K}$}$, Determine { \Delta G^{\circ}_{rxn}$}$.Provide The Answer To

Introduction

In chemistry, the standard free energy change (${\Delta G^{\circ}_{rxn}}$) is a crucial thermodynamic property that helps predict the spontaneity of a reaction. Given the values of the standard enthalpy change (${\Delta H^{\circ}_{rxn}}$), the standard entropy change (${S^{\circ}_{rxn}}$), and the temperature (${T}$), we can calculate ${\Delta G^{\circ}_{rxn}}$ using the Gibbs free energy equation. In this article, we will walk you through the step-by-step process of calculating ${\Delta G^{\circ}_{rxn}}$ using the given values.

The Gibbs Free Energy Equation

The Gibbs free energy equation is given by:

${\Delta G^{\circ}_{rxn} = \Delta H^{\circ}_{rxn} - T \Delta S^{\circ}_{rxn}}$

where ${\Delta G^{\circ}_{rxn}}$ is the standard free energy change, ${\Delta H^{\circ}_{rxn}}$ is the standard enthalpy change, ${T}$ is the temperature in Kelvin, and ${\Delta S^{\circ}_{rxn}}$ is the standard entropy change.

Given Values

We are given the following values:

• ${\Delta H^{\circ}_{rxn} = -60 \text{ kJ}}$
• ${S^{\circ}_{rxn} = -105.5 \text{ J/K}}$
• ${T = 327.4 \text{ K}}$

Converting Units

Before we can plug in the values into the Gibbs free energy equation, we need to convert the units of ${\Delta H^{\circ}_{rxn}}$ and ${S^{\circ}_{rxn}}$ to the same units. We will convert ${\Delta H^{\circ}_{rxn}}$ from kJ to J.

${\Delta H^{\circ}_{rxn} = -60 \text{ kJ} \times 1000 \text{ J/kJ} = -60000 \text{ J}}$

Calculating ${\Delta G^{\circ}_{rxn}}$

Now that we have the values in the same units, we can plug them into the Gibbs free energy equation:

${\Delta G^{\circ}_{rxn} = \Delta H^{\circ}_{rxn} - T \Delta S^{\circ}_{rxn}}$

${\Delta G^{\circ}_{rxn} = -60000 \text{ J} - (327.4 \text{ K}) (-105.5 \text{ J/K})}$

${\Delta G^{\circ}_{rxn} = -60000 \text{ J} + 34651.3 \text{ J}}$

${\Delta G^{\circ}_{rxn} = -25348.7 \text{ J}}$

Conclusion

In this article, we calculated the standard free energy change (${\Delta G^{\circ}_{rxn}}$) using the Gibbs free energy equation. We were given the values of the standard enthalpy change (${\Delta H^{\circ}_{rxn}}$), the standard entropy change (${S^{\circ}_{rxn}}$), and the temperature (${T}$). We converted the units of ${\Delta H^{\circ}_{rxn}}$ and ${S^{\circ}_{rxn}}$ to the same units and then plugged them into the Gibbs free energy equation. The result is a negative value, indicating that the reaction is spontaneous.

Importance of ${\Delta G^{\circ}_{rxn}}$

The standard free energy change (${\Delta G^{\circ}_{rxn}}$) is a crucial thermodynamic property that helps predict the spontaneity of a reaction. It is used in various fields, including chemistry, biochemistry, and materials science. Understanding the concept of ${\Delta G^{\circ}_{rxn}}$ is essential for designing and optimizing chemical reactions, as well as predicting the behavior of complex systems.

Real-World Applications

The concept of ${\Delta G^{\circ}_{rxn}}$ has numerous real-world applications. For example:

• Biochemistry: Understanding the standard free energy change of biochemical reactions is essential for designing new enzymes and understanding the mechanisms of biological processes.
• Materials Science: The standard free energy change of materials is used to predict their stability and reactivity.
• Chemical Engineering: The standard free energy change of chemical reactions is used to design and optimize chemical processes.

Limitations of ${\Delta G^{\circ}_{rxn}}$

While the standard free energy change (${\Delta G^{\circ}_{rxn}}$) is a powerful tool for predicting the spontaneity of reactions, it has some limitations. For example:

• Assumes Ideal Conditions: The standard free energy change assumes ideal conditions, such as constant temperature and pressure.
• Does Not Account for Non-Ideal Behavior: The standard free energy change does not account for non-ideal behavior, such as non-ideal gas behavior or non-ideal solution behavior.

Conclusion

$$$$ $$

Frequently Asked Questions

Q: What is the standard free energy change (${\Delta G^{\circ}_{rxn}}$)?

A: The standard free energy change (${\Delta G^{\circ}_{rxn}}$) is a thermodynamic property that helps predict the spontaneity of a reaction. It is defined as the change in Gibbs free energy of a reaction at standard conditions.

Q: How is the standard free energy change (${\Delta G^{\circ}_{rxn}}$) calculated?

A: The standard free energy change (${\Delta G^{\circ}_{rxn}}$) is calculated using the Gibbs free energy equation:

${\Delta G^{\circ}_{rxn} = \Delta H^{\circ}_{rxn} - T \Delta S^{\circ}_{rxn}}$

where ${\Delta H^{\circ}_{rxn}}$ is the standard enthalpy change, ${T}$ is the temperature in Kelvin, and ${\Delta S^{\circ}_{rxn}}$ is the standard entropy change.

Q: What is the significance of the standard free energy change (${\Delta G^{\circ}_{rxn}}$)?

A: The standard free energy change (${\Delta G^{\circ}_{rxn}}$) is a crucial thermodynamic property that helps predict the spontaneity of a reaction. It is used in various fields, including chemistry, biochemistry, and materials science.

Q: What are the limitations of the standard free energy change (${\Delta G^{\circ}_{rxn}}$)?

A: The standard free energy change (${\Delta G^{\circ}_{rxn}}$) assumes ideal conditions, such as constant temperature and pressure. It also does not account for non-ideal behavior, such as non-ideal gas behavior or non-ideal solution behavior.

Q: Can the standard free energy change (${\Delta G^{\circ}_{rxn}}$) be used to predict the spontaneity of a reaction?

A: Yes, the standard free energy change (${\Delta G^{\circ}_{rxn}}$) can be used to predict the spontaneity of a reaction. If ${\Delta G^{\circ}_{rxn}}$ is negative, the reaction is spontaneous. If ${\Delta G^{\circ}_{rxn}}$ is positive, the reaction is non-spontaneous.

Q: How is the standard free energy change (${\Delta G^{\circ}_{rxn}}$) related to the equilibrium constant (${K}$)?

A: The standard free energy change (${\Delta G^{\circ}_{rxn}}$) is related to the equilibrium constant (${K}$) by the equation:

${\Delta G^{\circ}_{rxn} = -RT \ln K}$

where ${R}$ is the gas constant and ${T}$ is the temperature in Kelvin.

Q: Can the standard free energy change (${\Delta G^{\circ}_{rxn}}$) be used to predict the direction of a reaction?

A: Yes, the standard free energy change (${\Delta G^{\circ}_{rxn}}$) can be used to predict the direction of a reaction. If ${\Delta G^{\circ}_{rxn}}$ is negative, the reaction will proceed in the forward direction. If ${\Delta G^{\circ}_{rxn}}$ is positive, the reaction will proceed in the reverse direction.

Q: What are some real-world applications of the standard free energy change (${\Delta G^{\circ}_{rxn}}$)?

A: The standard free energy change (${\Delta G^{\circ}_{rxn}}$) has numerous real-world applications, including:

• Biochemistry: Understanding the standard free energy change of biochemical reactions is essential for designing new enzymes and understanding the mechanisms of biological processes.
• Materials Science: The standard free energy change of materials is used to predict their stability and reactivity.
• Chemical Engineering: The standard free energy change of chemical reactions is used to design and optimize chemical processes.

Conclusion

In conclusion, the standard free energy change (${\Delta G^{\circ}_{rxn}}$) is a crucial thermodynamic property that helps predict the spontaneity of reactions. It is used in various fields, including chemistry, biochemistry, and materials science. Understanding the concept of ${\Delta G^{\circ}_{rxn}}$ is essential for designing and optimizing chemical reactions, as well as predicting the behavior of complex systems.