Both oxyhydrogen torches and fuel cells use the following reaction to produce energy: 2 H2(g) + O2(g) → 2 H2O(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?

Verified step by step guidance

Step 1: Understand the concept of a state function. A state function is a property whose value does not depend on the path taken to reach that specific value. Examples include enthalpy, internal energy, and entropy.

Step 2: Recognize that enthalpy (H) is a state function. In the given reaction, the change in enthalpy (ΔH) is the same regardless of the process (oxyhydrogen torch or fuel cell) because it depends only on the initial and final states of the system.

Step 3: Differentiate between the terms 'heat' and 'enthalpy'. While enthalpy is a state function, the heat (q) exchanged in a process can vary depending on the path, especially in terms of how the reaction is carried out (e.g., fast combustion in a torch vs. controlled reaction in a fuel cell).

Step 4: Consider the role of reaction kinetics and mechanism. In an oxyhydrogen torch, the reaction occurs rapidly, releasing a large amount of heat quickly, whereas in a fuel cell, the reaction is controlled and slower, resulting in a smaller, more gradual release of heat.

Step 5: Conclude that while the total enthalpy change (ΔH) is the same for both processes, the rate and manner in which heat is released (the path) can affect the perceived amount of heat evolved, even though the overall energy change is consistent.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

State Functions vs. Path Functions

In thermodynamics, state functions are properties that depend only on the state of the system, such as temperature, pressure, and enthalpy, while path functions depend on the specific process taken to reach that state. Heat and work are considered path functions because their values can vary based on the process used to transfer energy. This distinction is crucial for understanding why the heat evolved in different processes, despite having the same initial and final states, can differ.

Enthalpy Change (ΔH)

Enthalpy change, represented as ΔH, is the heat content of a system at constant pressure. It reflects the energy absorbed or released during a chemical reaction. In the case of the oxyhydrogen torch and fuel cell, although both reactions produce water, the rate and manner in which energy is released differ, leading to varying enthalpy changes. This concept helps explain why the heat evolved can be large in one process and small in another.

Reaction Mechanism and Energy Transfer

The reaction mechanism refers to the step-by-step sequence of elementary reactions by which overall chemical change occurs. Different mechanisms can lead to different energy transfer profiles, affecting how heat is released or absorbed. In an oxyhydrogen torch, the rapid combustion releases energy quickly, while in a fuel cell, the energy is released more gradually through electrochemical reactions, resulting in different heat outputs despite the same overall reaction.

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Textbook Question

Consider a system consisting of the following apparatus, in which gas is confined in one flask and there is a vacuum in the other flask. The flasks are separated by a valve. Assume that the flasks are perfectly insulated and will not allow the flow of heat into or out of the flasks to the surroundings. When the valve is opened, gas flows from the filled flask to the evacuated one. (a) Is work performed during the expansion of the gas? (b) Why or why not?

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Textbook Question

A sample of gas is contained in a cylinder-and-piston arrangement. There is an external pressure of 100 kPa. The gas undergoes the change in state shown in the drawing. (b) Now assume that the cylinder and piston are made up of a thermal conductor such as a metal. During the state change, the cylinder gets colder to the touch. What is the sign of q for the state change in this case? Describe the difference in the state of the system at the end of the process in the two cases. What can you say about the relative values of E?

Textbook Question

A house is designed to have passive solar energy features. Brickwork incorporated into the interior of the house acts as a heat absorber. Each brick weighs approximately 1.8 kg. The specific heat of the brick is 0.85 J/g•K. How many bricks must be incorporated into the interior of the house to provide the same total heat capacity as 1.7⨉10³ gal of water?

Textbook Question

A coffee-cup calorimeter of the type shown in Figure 5.18 contains 150.0 g of water at 25.1°C A 121.0-g block of copper metal is heated to 100.4°C by putting it in a beaker of boiling water. The specific heat of Cu(s) is 0.385 J/g-K The Cu is added to the calorimeter, and after a time the contents of the cup reach a constant temperature of 30.1°C. (a) Determine the amount of heat, in J, lost by the copper block.

Textbook Question

A coffee-cup calorimeter of the type shown in Figure 5.18 contains 150.0 g of water at 25.1°C A 121.0-g block of copper metal is heated to 100.4°C by putting it in a beaker of boiling water. The specific heat of Cu(s) is 0.385 J/g-K The Cu is added to the calorimeter, and after a time the contents of the cup reach a constant temperature of 30.1°C (b) Determine the amount of heat gained by the water. The specific heat of water is 4.184 J/1gK.