Problem 60 - Chemical Principles: The Quest for Insight

Question

Use the enthalpies of formation in Appendix \(2 \mathrm{~A}\) to calculate the standard enthalpy of the following reactions: (a) the replacement of deuterium by ordinary hydrogen in heavy water: \(\mathrm{H}_{2}(\mathrm{~g})+\mathrm{D}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{l})+\mathrm{D}_{2}(\mathrm{~g})\) (b) the removal of sulfur from the hydrogen sulfide and sulfur dioxide in natural gas: \(2 \mathrm{H}_{2} \mathrm{~S}(\mathrm{~g})+\mathrm{SO}_{2}(\mathrm{~g}) \rightarrow 3 \mathrm{~S}(\mathrm{~s})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) (c) the oxidation of ammonia: \(4 \mathrm{NH}_{3}(\mathrm{~g})+5 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow 4 \mathrm{NO}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\)

Step-by-Step Solution

Answer

To calculate the standard enthalpies of reactions (a), (b), and (c), you need to find the sum of the standard enthalpies of formation of the products and subtract the sum of the standard enthalpies of formation of the reactants. Specific values from Appendix 2A will be required to find the exact values for \(\Delta H^\circ_{rxn}\).

Step 1 - Understand Reaction (a)

Recognize that the enthalpy change of a reaction can be found using the enthalpies of formation for each compound involved. The standard enthalpy for reaction (a) \(\mathrm{H}_{2}(\mathrm{~g})+\mathrm{D}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{l})+\mathrm{D}_{2}(\mathrm{~g})\) can be calculated using the enthalpy of formation for each species.

Step 2 - Calculate the Standard Enthalpy for Reaction (a)

Use the formula \(\Delta H^\circ_{rxn} = \sum \Delta H^\circ_{f, products} - \sum \Delta H^\circ_{f, reactants} \) where \(\Delta H^\circ_{f}\) is the standard enthalpy of formation. Locate the standard enthalpies of formation for each species in Appendix 2A.

Step 3 - Understand Reaction (b)

Identify that the reaction describes the removal of sulfur from hydrogen sulfide and sulfur dioxide. Apply the formula for enthalpy change using the enthalpies of formation for the reactants and products of reaction (b) \(2 \mathrm{H}_{2} \mathrm{~S}(\mathrm{~g})+\mathrm{SO}_{2}(\mathrm{~g}) \rightarrow 3 \mathrm{~S}(\mathrm{~s})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})\).

Step 4 - Calculate the Standard Enthalpy for Reaction (b)

Utilize the enthalpy change formula again to find \(\Delta H^\circ_{rxn} \) for reaction (b), referencing the necessary enthalpy of formation values.

Step 5 - Understand Reaction (c)

Note that the reaction represents the oxidation of ammonia. The same enthalpy change formula will be used for reaction (c) \(4 \mathrm{NH}_{3}(\mathrm{~g})+5 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow 4 \mathrm{NO}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\).

Step 6 - Calculate the Standard Enthalpy for Reaction (c)

Apply the enthalpy change formula to determine \(\Delta H^\circ_{rxn} \) for reaction (c) based on the enthalpies of formation provided.

Key Concepts

Enthalpy Change Calculation

In the realm of chemistry, the calculation of enthalpy change, denoted as \(\Delta H\), is a fundamental concept that allows scientists and students alike to gain insight into the heat energy involved in chemical reactions. Enthalpy change helps us understand whether a particular reaction is exothermic (releases heat) or endothermic (absorbs heat). The key to calculating the enthalpy change of a reaction lies in the standard enthalpy of formation values, represented as \(\Delta H^\text{{\textcircled{{\tiny{f}}}}}\), for each reactant and product.

For a given chemical reaction, the enthalpy change can be expressed using the equation:
\[\Delta H^\text{{\textcircled{{\tiny{rxn}}}}} = \sum \Delta H^\text{{\textcircled{{\tiny{f}}}}}_{, products} - \sum \Delta H^\text{{\textcircled{{\tiny{f}}}}}_{, reactants}\]
Where:\[\sum \Delta H^\text{{\textcircled{{\tiny{f}}}}}_{, products}\] is the sum of the standard enthalpies of formation for all products, and \[\sum \Delta H^\text{{\textcircled{{\tiny{f}}}}}_{, reactants}\] is the sum for all reactants. By convention, the formation of elements in their natural state (such as O\text{{\textsubscript{{2}}}}(g) or S(s)) has an enthalpy of formation value of zero. Thus, they do not contribute to the \(\Delta H\) calculation in their elemental form.

Please note, it is crucial in these calculations to ensure that coefficients from the balanced reaction are properly accounted for, as they directly affect the sum of the enthalpy values. When practicing enthalpy change calculations, keep in mind the importance of precision and attention to detail in both the determination of standard enthalpy values from references such as Appendix 2A and the arithmetic operations involved.

Chemical Reaction Enthalpy

The chemical reaction enthalpy is a measure of the total heat content change during a chemical reaction. It encompasses all the bonds broken and formed during the transformation from reactants to products. Each chemical bond has an associated energy cost to break it and energy release upon forming it. These individual contributions add up to determine the overall enthalpy change of the reaction.

Visualization Through Bond Enthalpies

One helpful way to understand reaction enthalpy is by visualizing the breaking and forming of bonds. When bonds in reactants are broken, energy is absorbed; when new bonds in products are formed, energy is released. If the energy required to break bonds is greater than that released upon forming new bonds, the outcome is an endothermic reaction. Conversely, if more energy is released than absorbed, the reaction is exothermic.

Implications of Enthalpy Changes

Understanding the enthalpy change of a chemical reaction has significant implications in fields such as thermodynamics, chemical engineering, and environmental science. It guides us in predicting reaction feasibility, designing energy-efficient processes, and assessing the impact of various chemical processes on the environment.

An example provided in the exercise illustrates the removal of sulfur from natural gas, a process crucial for reducing pollution and improving the energy content of the fuel. By determining the enthalpy of such a reaction, engineers can tailor processes to maximize efficiency and minimize undesirable by-products.

Thermochemistry

At the heart of energy exchange in chemical reactions lies thermochemistry, the study of heat changes that accompany chemical processes. Thermochemistry applies the principles of thermodynamics to chemical reactions, providing a quantitative bridge connecting the microscopic world of atoms and molecules to the macroscopic observations of heat and work.

The Laws of Thermodynamics

The first law of thermodynamics, often termed the law of conservation of energy, asserts that energy cannot be created or destroyed, only transformed. This fundamental principle underpins thermochemistry as it implies that during a chemical reaction, the energy lost or gained must be accounted for either in the form of heat, work, or a combination of both.

Measures of Heat Change

Two primary measures help determine the heat change during a reaction: calorimetry and Hess's Law. Calorimetry directly measures the heat exchanged with the surroundings using a calorimeter, while Hess's Law offers a path-independent tool to calculate reaction enthalpies based on the enthalpy changes of multiple related reactions.

The accurate quantification of energy changes via thermochemistry is essential in a myriad of applications. It is integral in predicting the outcome of reactions, assessing safety parameters for chemical processes, optimizing industrial chemical production, and even understanding the energy flow in biological systems. A solid grasp of thermochemistry equips students with the knowledge to assess energy changes critically and apply this information in a practical, problem-solving context.