Problem 104 - Chemistry The Central Science In Si Units

Question

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?

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: 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.

Step 3: 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.

Step 4: 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.

Key Concepts

Enthalpy

Enthalpy is a measure of the total energy within a system. It combines the system’s 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°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’s reliance on state functions, allowing predictability and understanding of reactions regardless of their detailed pathways.