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Chapter 5: Problem 104

Both oxyhydrogen torches and fuel cells use the following reaction to produce energy: $$ 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) $$ Both processes occur at constant pressure. In both cases the change in state of the system is the same: the reactant is oxyhydrogen ("Knallgas") and the product is water. Yet, with an oxyhydrogen torch, the heat evolved is large and with a fuel cell it is small. If heat at constant pressure is considered to be a state function, why does it depend on path?

Short Answer

Expert verified
Heat appears path-dependent due to the energy form conversion difference between pathways despite having the same enthalpy change.

Step by step solution

01

Understanding the Reaction and Processes

First, recognize that the reaction given, \( 2 \mathrm{H}_{2}(g) + \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{H}_{2}O(l) \), is the same for both an oxyhydrogen torch and a fuel cell. The reactants and products are identical in both cases; hydrogen gas and oxygen gas react to form liquid water.
02

Heat at Constant Pressure as a State Function

Enthalpy change (\(\Delta H\)) measures heat at constant pressure and is considered a state function because it depends only on the initial and final states, not on the path taken. For both the torch and the fuel cell, \(\Delta H\) is the same since the start and end states are the same.
03

Paths of the Reactions

An oxyhydrogen torch combusts hydrogen rapidly, releasing energy as heat and light. This is an exothermic process where energy is mainly released as heat. In a fuel cell, the reaction occurs through a controlled electrochemical process, converting energy directly into electrical energy, with less heat being produced.
04

Path Dependence of the Perceived Heat

Although \(\Delta H\) is the same, the pathway defines how energy is split between different forms - thermal (heat), electrical, and light energy. The torch mainly produces heat and light, while the fuel cell produces electrical energy with minimal heat. This difference in the form of produced energy gives the impression that heat differs, highlighting perceived path dependence.

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Key Concepts

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

Enthalpy
Enthalpy is a measure of the total energy within a system. It combines the system鈥檚 internal energy with the energy needed to make room for it by displacing its environment. The change in enthalpy, denoted as \(\Delta H\), is crucial because it reflects the heat change at constant pressure. This makes it extremely useful in the study of thermochemistry. In thermochemical equations, like the combustion of hydrogen in the reaction, \ 2 \mathrm{H}_{2}(g) + \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{H}_{2}O(l) \, \(\Delta H\) is a state function.
  • State Function: It only depends on the initial and final states, not the path taken to get there.
  • Unit of Measurement: Joules (J) or kilojoules (kJ).
  • Sign Convention: Exothermic reactions (releasing heat) have a negative \(\Delta H,\) while endothermic reactions (absorbing heat) have a positive \(\Delta H.\)
Oxyhydrogen Torch
An oxyhydrogen torch is a device that combines hydrogen and oxygen gases to produce a high-temperature flame. This flame can reach temperatures exceeding 2,000掳C, making it suitable for metal cutting and welding.
  • Combustion Reaction: The hydrogen fuel combusts with oxygen, rapidly releasing energy.
  • Outputs: Produces energy mainly as heat and some light.
  • Exothermic Process: A significant amount of heat is evolved quickly due to the rapid reaction.
Despite having the same chemical reaction as a fuel cell, the process results in different energy outputs. This occurs because of its quick, direct conversion of reactants to products, predominantly in the form of thermal energy.
Fuel Cell
Fuel cells use similar reactions to an oxyhydrogen torch but differ significantly in their operation and the type of energy produced. A fuel cell converts chemical energy directly into electrical energy through an electrochemical process.
  • Controlled Reaction: The process is slower and aims to harness electrical energy rather than heat.
  • Components: Typically includes an anode, cathode, and an electrolyte.
  • Advantages: Efficient and clean energy conversion with water as a byproduct.
The key feature of a fuel cell is its pathway, which conserves more of the energy as electricity rather than losing it as heat. This is why, despite similar \(\Delta H\), the perceived heat is lower compared to an oxyhydrogen torch.
State Function
Understanding state functions helps demystify why enthalpy, despite being the same, results in varied energy outputs in different processes. A state function depends solely on the state of the system, characterized by properties like temperature, pressure, and volume. It does not care how the state was reached.
  • Examples: Enthalpy, internal energy, and entropy are state functions.
  • Path Independence: The intrinsic properties do not change based on how the process unfolds.
  • Implication: In both an oxyhydrogen torch and a fuel cell, while the \(\Delta H\) is the same, the difference comes in the path, not the endpoint.
This principle highlights thermochemistry鈥檚 reliance on state functions, allowing predictability and understanding of reactions regardless of their detailed pathways.

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Most popular questions from this chapter

Under constant-volume conditions, the heat of combustion of naphthalene \(\left(\mathrm{C}_{10} \mathrm{H}_{8}\right)\) is \(40.18 \mathrm{~kJ} / \mathrm{g}\). A \(2.50-\mathrm{g}\) sample of naphthalene is burned in a bomb calorimeter. The temperature of the calorimeter increases from 21.50 to \(28.83^{\circ} \mathrm{C}\). (a) What is the total heat capacity of the calorimeter? (b) A 1.50-g sample of a new organic substance is combusted in the same calorimeter. The temperature of the calorimeter increases from 21.14 to \(25.08^{\circ} \mathrm{C}\). What is the heat of combustion per gram of the new substance? (c) Suppose that in changing samples, a portion of the water in the calorimeter were lost. In what way, if any, would this change the heat capacity of the calorimeter?

Assume that 2 moles of water are formed according to the following reaction at constant pressure (101.3 kPa) and constant temperature \((298 \mathrm{~K}):\) $$ 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) $$ (a) Calculate the pressure-volume work for this reaction. (b) Calculate \(\Delta E\) for the reaction using your answer to (a).

At the end of \(2012,\) global population was about 7.0 billion people. What mass of glucose in \(\mathrm{kg}\) would be needed to provide 1500 Cal/person/day of nourishment to the global population for one year? Assume that glucose is metabolized entirely to \(\mathrm{CO}_{2}(\mathrm{~g})\) and \(\mathrm{H}_{2} \mathrm{O}(I)\) according to the following thermochemical equation: $$ \begin{aligned} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) \longrightarrow 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(I) \\ \Delta H^{\circ} &=-2803 \mathrm{~kJ} \end{aligned} $$

(a) Derive an equation to convert the specific heat of a pure substance to its molar heat capacity. (b) The specific heat of aluminum is \(0.9 \mathrm{~J} /(\mathrm{g} \cdot \mathrm{K}) .\) Calculate its molar heat capacity. (c) If you know the specific heat of aluminum, what additional information do you need to calculate the heat capacity of a particular piece of an aluminum component?

Suppose an Olympic diver who weighs \(52.0 \mathrm{~kg}\) executes a straight dive from a \(10-\mathrm{m}\) platform. At the apex of the dive, the diver is \(10.8 \mathrm{~m}\) above the surface of the water. (a) What is the potential energy of the diver at the apex of the dive, relative to the surface of the water? (b) Assuming that all the potential energy of the diver is converted into kinetic energy at the surface of the water, at what speed, in \(\mathrm{m} / \mathrm{s}\), will the diver enter the water? (c) Does the diver do work on entering the water? Explain.
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