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Chapter 9: Problem 70

Would Hess's law be valid if enthalpy were not a state function? Why or why not?

Short Answer

Expert verified
Explain your answer. Answer: No, Hess's law would not be valid if enthalpy were not a state function. This is because the independence of enthalpy change from the path taken is a crucial aspect of Hess's law. It allows us to add together enthalpy changes for individual steps to determine the overall enthalpy change of a process. If enthalpy were path-dependent, this simple summation would not be possible, and Hess's law could not be applied to predict enthalpy changes for reactions.

Step by step solution

01

Definition of a state function

A state function is a property that depends only on the current state of a system and not on the path taken to achieve that state. Enthalpy (H) is a state function because it depends only on the current temperature, pressure, and composition of a system, not on how the system arrived at those conditions.
02

Understanding Hess's Law

Hess's law states that the total enthalpy change (鈭咹) of a reaction is independent of the path taken and is the same, whether the reaction takes place in one step or several steps. This is because enthalpy is a state function, and the overall change in enthalpy depends only on the initial and final states of the system and not on how the reaction proceeds. This property of enthalpy allows us to add together the enthalpy changes for individual reactions to find the overall enthalpy change of a multi-step process, even if the process is not experimentally observable.
03

Consequences of Enthalpy not being a state function

If enthalpy were not a state function, the enthalpy change for each individual step of the reaction would depend on the path taken, and each step would have a unique enthalpy change depending on the specific conditions of the reaction. In this case, the overall enthalpy change of a reaction could vary depending on the specific sequence of steps taken and the conditions of each step. This would make it impossible to apply Hess's law, which assumes that the total enthalpy change of a reaction is independent of the path taken.
04

Conclusion

Hess's law would not be valid if enthalpy were not a state function. The independence of enthalpy change from the path taken is a crucial aspect of Hess's law, allowing us to add together enthalpy changes for individual steps to determine the overall enthalpy change of a process. If enthalpy were path-dependent, this simple summation would not be possible, and Hess's law could not be applied to predict enthalpy changes for reactions.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

State Function
In the realm of chemistry, a state function is a crucial concept. It refers to any property of a system that relies solely on the current state of the system. This means the value of a state function is independent of the path or process that the system has undergone to reach that state. It is like taking a snapshot of the system at a particular moment.

For example, properties like temperature, pressure, and volume are state functions. They depend only on the present condition. Imagine a mountain: the elevation is like a state function, it doesn't matter if you climbed from the north or south.
  • Properties are path-independent.
  • Relies only on initial and final states.
This characteristic makes state functions highly useful in thermodynamics, allowing predictions and calculations to be made without detailed knowledge of the process history.
Enthalpy
Enthalpy (H) is an essential state function in thermodynamics. It represents the total heat content of a system. Enthalpy is particularly important because it helps us understand how energy is transferred as heat during a chemical reaction.

The enthalpy of a system is influenced by its temperature, pressure, and composition. Yet, it remains independent of the path taken. Whether a reaction occurs in one fell swoop or through a series of steps, the total change in enthalpy \( \Delta H \) depends only on the initial and final states. This is key in making calculations for reactions using Hess's Law.
  • Key to energy transfer during reactions.
  • Path-independent relationship.
Understanding enthalpy allows chemists to predict if a reaction will release or absorb heat.
Reaction Enthalpy Change
When a chemical reaction occurs, the enthalpy change (\(\Delta H\)) tells us how much heat is absorbed or released. This change serves as a window into the energy shifts that occur within a reaction. It's like keeping track of your car's fuel gauge: the difference before and after a trip indicates your fuel consumption.

Reaction enthalpy changes allow us to compare the energy profiles of various reactions. Thanks to the nature of enthalpy as a state function, Hess's Law states that the total change in enthalpy for a reaction is the same no matter how the reaction unfolds.
  • Illustrates energy absorption or release.
  • Enables calculation using Hess鈥檚 Law.
This provides valuable insights into reaction feasibility and helps engineers and scientists design efficient chemical processes.
Thermodynamics
Thermodynamics is the branch of science focused on understanding energy transformations. It deals with how heat, work, and energy interact in a system. By studying these interactions, we can design more effective systems and predict how energy-related processes unfold.

Enthalpy, as a part of thermodynamics, allows us to look at energy exchanges involving heat. Through the principles of thermodynamics, such as Hess鈥檚 Law, we gain valuable tools to break down complex thermodynamic problems into manageable parts.
  • Analyzes energy interactions and transformations.
  • Guides the prediction of reaction behavior.
By deepening our understanding of these concepts, we enhance our ability to harness energy transformations for practical and industrial applications.

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Most popular questions from this chapter

Use standard enthalpies of formation from Appendix 4 to calculate the standard enthalpy of reaction for the following methane-generating reaction of methanogenic bacteria, given \(\Delta H_{f}^{\circ}\) of \(\mathrm{CH}_{3} \mathrm{NH}_{2}(g)=-22.97 \mathrm{kJ} / \mathrm{mol}:\) $$4 \mathrm{CH}_{3} \mathrm{NH}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow 3 \mathrm{CH}_{4}(g)+\mathrm{CO}_{2}(g)+4 \mathrm{NH}_{3}(g)$$

Why is the heat of vaporization of water so much greater than its heat of fusion?

Calculate the lattice energy of sodium oxide \(\left(\mathrm{Na}_{2} \mathrm{O}\right)\) from the following data: Ionization energy of \(\mathrm{Na}(g)=495 \mathrm{kJ} / \mathrm{mol}\) Electron affinity of \(\mathrm{O}(g)\) for 2 electrons \(=603 \mathrm{kJ} / \mathrm{mol}\) Energy to sublime \(\mathrm{Na}(s)=109 \mathrm{kJ} / \mathrm{mol}\) Bond energy of \(\mathrm{O}_{2}(g)=498 \mathrm{kJ} / \mathrm{mol}\) \(\Delta H_{\mathrm{rxn}}\) for \(2 \mathrm{Na}(s)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{Na}_{2} \mathrm{O}(s)=-416 \mathrm{kJ} / \mathrm{mol}\)

In a simple "kitchen chemistry" experiment, some vinegar is poured into an empty soda bottle. A deflated balloon containing baking soda is stretched over the mouth of the bottle. Holding up the balloon and shaking it allows the baking soda to fall into the vinegar, which starts the following reaction and inflates the balloon: $$\begin{aligned} \mathrm{NaHCO}_{3}(a q)+\mathrm{CH}_{3} \mathrm{COOH}(a q) \rightarrow & \\ & \mathrm{CH}_{3} \mathrm{COONa}(a q)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(\ell) \end{aligned}$$ If the contents of the bottle are the system, is work being done on the surroundings or on the system?

Use appropriate bond energies from Table A4.1 of Appendix 4 to predict whether the reaction in which ethylene forms polyethylene plastic is exothermic, endothermic, or involves no change in enthalpy. The reaction can be written: $$n \mathrm{CH}_{2}=\mathrm{CH}_{2} \rightarrow\left[-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\right]_{n}$$ where the structure in the brackets is the repeating unit of polyethylene and the value of \(n\) is typically in the thousands.
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