For The Following Reactions, The { \Delta H_ Rxn}^{\circ}$}$ Is Not Equal To { \Delta H^{\circ}_f$}$ For The Product, Except For A. { H_2(g) + O_2(g) \rightarrow H_2O_2$ $ B. [$\frac{1}{2}N_2(g) + O_2(g) \rightarrow

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For the following reactions, the {\Delta H_{rxn}^{\circ}$}$ is not equal to {\Delta H^{\circ}_f$}$ for the product, except for

Understanding the Relationship Between {\Delta H_{rxn}^{\circ}$}$ and {\Delta H^{\circ}_f$}$

In chemistry, the relationship between the standard enthalpy change of a reaction ({\Delta H_{rxn}^{\circ}$})andthestandardenthalpyofformation() and the standard enthalpy of formation ({\Delta H^{\circ}_f\$}) of the product is a crucial concept. The standard enthalpy change of a reaction is the change in enthalpy that occurs when a reaction is carried out under standard conditions, while the standard enthalpy of formation is the change in enthalpy that occurs when a compound is formed from its constituent elements in their standard states.

The Relationship Between {\Delta H_{rxn}^{\circ}$}$ and {\Delta H^{\circ}_f$}$

The relationship between {\Delta H_{rxn}^{\circ}$}$ and {\Delta H^{\circ}_f$}$ can be expressed as follows:

{\Delta H_{rxn}^{\circ} = \sum \Delta H^{\circ}_f(\text{products}) - \sum \Delta H^{\circ}_f(\text{reactants})$}$

This equation indicates that the standard enthalpy change of a reaction is equal to the sum of the standard enthalpies of formation of the products minus the sum of the standard enthalpies of formation of the reactants.

When {\Delta H_{rxn}^{\circ}$}$ is Not Equal to {\Delta H^{\circ}_f$}$

However, there are certain cases where the standard enthalpy change of a reaction is not equal to the standard enthalpy of formation of the product. This occurs when the reaction involves the formation of a new bond or the breaking of an existing bond, which can result in a change in the enthalpy of the system.

Case A: {H_2(g) + O_2(g) \rightarrow H_2O_2$}$

In the case of the reaction {H_2(g) + O_2(g) \rightarrow H_2O_2$}$, the standard enthalpy change of the reaction is not equal to the standard enthalpy of formation of hydrogen peroxide. This is because the reaction involves the formation of a new bond between the hydrogen and oxygen atoms, which results in a change in the enthalpy of the system.

Case B: {\frac{1}{2}N_2(g) + O_2(g) \rightarrow NO$}$

In the case of the reaction {\frac{1}{2}N_2(g) + O_2(g) \rightarrow NO$}$, the standard enthalpy change of the reaction is not equal to the standard enthalpy of formation of nitrogen monoxide. This is because the reaction involves the breaking of a nitrogen-nitrogen bond and the formation of a nitrogen-oxygen bond, which results in a change in the enthalpy of the system.

Case C: {H_2(g) + O_2(g) \rightarrow H_2O$}$

In the case of the reaction {H_2(g) + O_2(g) \rightarrow H_2O$}$, the standard enthalpy change of the reaction is equal to the standard enthalpy of formation of water. This is because the reaction involves the formation of a new bond between the hydrogen and oxygen atoms, which results in a change in the enthalpy of the system.

Conclusion

In conclusion, the relationship between the standard enthalpy change of a reaction and the standard enthalpy of formation of the product is a crucial concept in chemistry. While the standard enthalpy change of a reaction is equal to the sum of the standard enthalpies of formation of the products minus the sum of the standard enthalpies of formation of the reactants, there are certain cases where the standard enthalpy change of a reaction is not equal to the standard enthalpy of formation of the product. These cases involve the formation of a new bond or the breaking of an existing bond, which results in a change in the enthalpy of the system.

References

  • Atkins, P. W., & De Paula, J. (2010). Physical chemistry. Oxford University Press.
  • Chang, R. (2010). Chemistry. McGraw-Hill.
  • Levine, I. N. (2012). Physical chemistry. McGraw-Hill.

Note

The above article is for educational purposes only and is not intended to be used as a reference for any scientific or academic work. The information provided is based on general knowledge and may not be accurate or up-to-date.
Q&A: Understanding the Relationship Between {\Delta H_{rxn}^{\circ}$}$ and {\Delta H^{\circ}_f$}$

Frequently Asked Questions

Q1: What is the difference between {\Delta H_{rxn}^{\circ}$}$ and {\Delta H^{\circ}_f$}$?

A1: The standard enthalpy change of a reaction ({\Delta H_{rxn}^{\circ}$})isthechangeinenthalpythatoccurswhenareactioniscarriedoutunderstandardconditions,whilethestandardenthalpyofformation() is the change in enthalpy that occurs when a reaction is carried out under standard conditions, while the standard enthalpy of formation ({\Delta H^{\circ}_f\$}) is the change in enthalpy that occurs when a compound is formed from its constituent elements in their standard states.

Q2: When is {\Delta H_{rxn}^{\circ}$}$ not equal to {\Delta H^{\circ}_f$}$?

A2: {\Delta H_{rxn}^{\circ}$}$ is not equal to {\Delta H^{\circ}_f$}$ when the reaction involves the formation of a new bond or the breaking of an existing bond, which results in a change in the enthalpy of the system.

Q3: Can you give an example of a reaction where {\Delta H_{rxn}^{\circ}$}$ is not equal to {\Delta H^{\circ}_f$}$?

A3: Yes, an example of a reaction where {\Delta H_{rxn}^{\circ}$}$ is not equal to {\Delta H^{\circ}_f$}$ is the reaction {H_2(g) + O_2(g) \rightarrow H_2O_2$}$. In this reaction, the standard enthalpy change of the reaction is not equal to the standard enthalpy of formation of hydrogen peroxide.

Q4: How can I determine if {\Delta H_{rxn}^{\circ}$}$ is equal to {\Delta H^{\circ}_f$}$ for a given reaction?

A4: To determine if {\Delta H_{rxn}^{\circ}$}$ is equal to {\Delta H^{\circ}f$}$ for a given reaction, you can use the equation {\Delta H{rxn}^{\circ} = \sum \Delta H^{\circ}_f(\text{products}) - \sum \Delta H^{\circ}f(\text{reactants})$}$. If the equation is true, then {\Delta H{rxn}^{\circ}$}$ is equal to {\Delta H^{\circ}_f$}$.

Q5: What are some common mistakes to avoid when working with {\Delta H_{rxn}^{\circ}$}$ and {\Delta H^{\circ}_f$}$?

A5: Some common mistakes to avoid when working with {\Delta H_{rxn}^{\circ}$}$ and {\Delta H^{\circ}_f$}$ include:

  • Not considering the formation of new bonds or the breaking of existing bonds
  • Not using the correct values for {\Delta H^{\circ}_f$}$
  • Not using the correct equation to calculate {\Delta H_{rxn}^{\circ}$}$

Conclusion

In conclusion, the relationship between the standard enthalpy change of a reaction and the standard enthalpy of formation of the product is a crucial concept in chemistry. By understanding the difference between {\Delta H_{rxn}^{\circ}$}$ and {\Delta H^{\circ}f$}$ and how to determine if {\Delta H{rxn}^{\circ}$}$ is equal to {\Delta H^{\circ}_f$}$ for a given reaction, you can avoid common mistakes and accurately calculate the standard enthalpy change of a reaction.

References

  • Atkins, P. W., & De Paula, J. (2010). Physical chemistry. Oxford University Press.
  • Chang, R. (2010). Chemistry. McGraw-Hill.
  • Levine, I. N. (2012). Physical chemistry. McGraw-Hill.

Note

The above article is for educational purposes only and is not intended to be used as a reference for any scientific or academic work. The information provided is based on general knowledge and may not be accurate or up-to-date.