At Which Temperature Would A Reaction With Δ H = − 92 KJ/mol , Δ S = − 0.199 KJ/(mol \cdot K) \Delta H = -92 \, \text{kJ/mol}, \Delta S = -0.199 \, \text{kJ/(mol \cdot K)} Δ H = − 92 KJ/mol , Δ S = − 0.199 KJ/(mol \cdot K) Be Spontaneous?A. 600 K B. 700 K C. 500 K D. 400 K

At which temperature would a reaction with $\Delta H = -92 \, \text{kJ/mol}, \Delta S = -0.199 \, \text{kJ/(mol \cdot K)}$ be spontaneous?

Understanding the Basics of Spontaneity

In chemistry, the spontaneity of a reaction is determined by the change in Gibbs free energy ($\Delta G$). A reaction is considered spontaneous if $\Delta G$ is negative. The Gibbs free energy equation is given by:

$$\Delta G = \Delta H - T\Delta S$$

where $\Delta H$ is the change in enthalpy, $T$ is the temperature in Kelvin, and $\Delta S$ is the change in entropy.

The Role of Enthalpy and Entropy

Enthalpy ($H$) is a measure of the total energy of a system, including the internal energy and the energy associated with the pressure and volume of a system. A negative $\Delta H$ indicates that the reaction is exothermic, releasing heat energy.

Entropy ($S$) is a measure of the disorder or randomness of a system. A negative $\Delta S$ indicates that the reaction is decreasing the disorder of the system.

Determining the Temperature for Spontaneity

To determine the temperature at which the reaction would be spontaneous, we need to set $\Delta G$ to be less than zero and solve for $T$.

$$\Delta G = \Delta H - T\Delta S < 0$$

Rearranging the equation to solve for $T$, we get:

$$T > \frac{\Delta H}{\Delta S}$$

Substituting the Given Values

We are given that $\Delta H = -92 \, \text{kJ/mol}$ and $\Delta S = -0.199 \, \text{kJ/(mol \cdot K)}$. Substituting these values into the equation, we get:

$$T > \frac{-92 \, \text{kJ/mol}}{-0.199 \, \text{kJ/(mol \cdot K)}}$$

Simplifying the equation, we get:

$$T > 462.23 \, \text{K}$$

Comparing the Temperature with the Options

The calculated temperature is approximately 462.23 K. Comparing this value with the given options, we can see that:

• Option A: 600 K is greater than the calculated temperature.
• Option B: 700 K is greater than the calculated temperature.
• Option C: 500 K is less than the calculated temperature.
• Option D: 400 K is less than the calculated temperature.

Conclusion

Based on the calculation, the reaction would be spontaneous at a temperature greater than 462.23 K. Therefore, the correct answer is:

The final answer is: A. 600 K
At which temperature would a reaction with $\Delta H = -92 \, \text{kJ/mol}, \Delta S = -0.199 \, \text{kJ/(mol \cdot K)}$ be spontaneous?

Q&A: Understanding the Basics of Spontaneity

Q: What is the Gibbs free energy equation?

A: The Gibbs free energy equation is given by:

$$\Delta G = \Delta H - T\Delta S$$

where $\Delta H$ is the change in enthalpy, $T$ is the temperature in Kelvin, and $\Delta S$ is the change in entropy.

Q: What is the role of enthalpy in the Gibbs free energy equation?

A: Enthalpy ($H$) is a measure of the total energy of a system, including the internal energy and the energy associated with the pressure and volume of a system. A negative $\Delta H$ indicates that the reaction is exothermic, releasing heat energy.

Q: What is the role of entropy in the Gibbs free energy equation?

A: Entropy ($S$) is a measure of the disorder or randomness of a system. A negative $\Delta S$ indicates that the reaction is decreasing the disorder of the system.

Q: How do we determine the temperature for spontaneity?

A: To determine the temperature at which the reaction would be spontaneous, we need to set $\Delta G$ to be less than zero and solve for $T$.

$$\Delta G = \Delta H - T\Delta S < 0$$

Rearranging the equation to solve for $T$, we get:

$$T > \frac{\Delta H}{\Delta S}$$

Q: What is the significance of the temperature in the spontaneity equation?

A: The temperature ($T$) is a critical factor in determining the spontaneity of a reaction. A higher temperature can increase the disorder of the system, making the reaction more spontaneous.

Q: How do we calculate the temperature for spontaneity?

A: We can calculate the temperature for spontaneity by substituting the given values of $\Delta H$ and $\Delta S$ into the equation:

$$T > \frac{\Delta H}{\Delta S}$$

Q: What is the calculated temperature for spontaneity?

A: Substituting the given values of $\Delta H = -92 \, \text{kJ/mol}$ and $\Delta S = -0.199 \, \text{kJ/(mol \cdot K)}$ into the equation, we get:

$$T > \frac{-92 \, \text{kJ/mol}}{-0.199 \, \text{kJ/(mol \cdot K)}}$$

Simplifying the equation, we get:

$$T > 462.23 \, \text{K}$$

Q: Which option is the correct answer?

A: Based on the calculation, the reaction would be spontaneous at a temperature greater than 462.23 K. Therefore, the correct answer is:

The final answer is: A. 600 K

Additional Tips and Resources

• To determine the spontaneity of a reaction, you need to calculate the Gibbs free energy ($\Delta G$) using the equation: $\Delta G = \Delta H - T\Delta S$.
• A negative $\Delta G$ indicates that the reaction is spontaneous.
• A higher temperature can increase the disorder of the system, making the reaction more spontaneous.
• You can use online calculators or software to calculate the Gibbs free energy and determine the spontaneity of a reaction.

Conclusion

In conclusion, the Gibbs free energy equation is a powerful tool for determining the spontaneity of a reaction. By understanding the role of enthalpy and entropy in the equation, you can calculate the temperature for spontaneity and determine whether a reaction is likely to occur.