Problem 61 - Chemical Principles: The Quest for Insight

Question

Using standard enthalpies of formation from Appendix \(2 \mathrm{~A}\), calculate the standard reaction enthalpy for each of the following reactions: (a) the final stage in the production of nitric acid, when nitrogen dioxide dissolves in and reacts with water: \(3 \mathrm{NO}_{2}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow 2 \mathrm{HNO}_{3}(\mathrm{aq})+\mathrm{NO}(\mathrm{g})\) (b) the formation of boron trifluoride, which is widely used in the chemical industry: \(\mathrm{B}_{2} \mathrm{O}_{3}(\mathrm{~s})+3 \mathrm{CaF}_{2}(\mathrm{~s}) \rightarrow 2 \mathrm{BF}_{3}(\mathrm{~g})+3 \mathrm{CaO}(\mathrm{s})\) (c) the formation of a sulfide by the action of hydrogen sulfide on an aqueous solution of a base: \(\mathrm{H}_{2} \mathrm{~S}(\mathrm{aq})+2 \mathrm{KOH}(\mathrm{aq}) \rightarrow \mathrm{K}_{2} \mathrm{~S}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})\)

Step-by-Step Solution

Answer

To find the standard reaction enthalpies, use the standard enthalpies of formation for each reactant and product, then apply Hess's Law to calculate the net change in enthalpy for each reaction.

Step 1: Find the standard enthalpies of formation

Look up the standard enthalpies of formation (\f\(\fDelta H_^\fo\f\)) for all reactants and products involved in the given reactions from Appendix 2A or relevant data sources.

Step 2: Apply Hess's Law for reaction (a)

For the reaction \f\(3NO_2(g) + H_2O(l) \rightarrow 2HNO_3(aq) + NO(g)\f\), use the enthalpy of formation values and apply Hess's Law: \f\(\fDelta H_{reaction} = \f(\fsum \fDelta H_^\fo\f_{products}) - \f(\fsum \fDelta H_^\fo\f_{reactants})\f\). Insert the corresponding values for each substance to calculate the reaction enthalpy.

Step 3: Calculate the standard reaction enthalpy for (a)

Perform the arithmetic operation using the values from Step 2 to obtain the standard reaction enthalpy for the reaction (a).

Step 4: Apply Hess's Law for reaction (b)

For the reaction \f\(B_2O_3(s) + 3CaF_2(s) \rightarrow 2BF_3(g) + 3CaO(s)\f\), apply Hess's Law in the same manner as in Step 2.

Step 5: Calculate the standard reaction enthalpy for (b)

Calculate the standard reaction enthalpy for reaction (b) using the values from Step 4.

Step 6: Apply Hess's Law for reaction (c)

For the reaction \f\(H_2S(aq) + 2KOH(aq) \rightarrow K_2S(aq) + 2H_2O(l)\f\), apply Hess's Law as done previously.

Step 7: Calculate the standard reaction enthalpy for (c)

Use the calculated enthalpies of formation to derive the standard reaction enthalpy for reaction (c).

Key Concepts

Enthalpies of Formation

The enthalpy of formation refers to the change in enthalpy when one mole of a compound is formed from its elements in their standard states. It provides a measure of the energy changes involved during the formation of a substance from its constituent elements. To understand this concept, visualize creating a compound in a process that takes each element from nature — such as hydrogen gas or solid carbon — to form a singular compound, for instance, water or carbon dioxide.

These enthalpy changes are so fundamental in chemistry that they are tabulated in reference books and used as benchmarks. The standard enthalpy of formation of an element in its most stable form is zero because there is no change involved in creating the element from itself. When these values are given for compounds, they enable us to calculate the overall energy changes, like reaction enthalpies, simply by combining these standard benchmarks.

Hess's Law

Hess's Law is grounded in the principle that the total enthalpy change for a chemical reaction is the same, no matter how the reaction occurs, provided it happens under constant pressure. This law allows us to use known enthalpies of formation to determine unknown reaction enthalpies. Essentially, it's like a budget sheet for energy changes: you can add and subtract enthalpy changes from various steps of a reaction to find the total energy change.

Through Hess's Law, complex reactions that may be difficult to study directly can be broken down into simpler steps whose enthalpies are known or can be more easily determined. The power of Hess's Law lies in the fact that it transforms the calculation of enthalpies for complex chemical changes into an exercise of bookkeeping, carefully balancing the energy inputs and outputs.

Chemical Thermodynamics

Chemical thermodynamics involves the study of energy transformations and the accompanying changes in enthalpy and entropy within chemical reactions. Enthalpy is a measure of the total heat content in a system, while entropy expresses the degree of disorder or randomness.

The study of chemical thermodynamics provides deep insights into the balance of energy that occurs during chemical processes. For any given reaction, energy can be absorbed from or released into the surroundings, hinting at its endothermic or exothermic nature. The laws of thermodynamics set the stage for understanding these energy transformations and allow us to predict the feasibility and spontaneity of chemical reactions. An overarching theme in thermodynamics is the pursuit of states that present a lower energy and higher disorder, guiding the direction of natural processes.

Enthalpy Calculation

Calculating enthalpy, specifically reaction enthalpy, involves using the standard enthalpies of formation for the reactants and products involved in a chemical process. The general formula to determine the standard reaction enthalpy is:
\[\fDelta H_{\text{rxn}}^{\text{o}} = \f(\fsum \fDelta H_f^\text{o}_{\text{products}}) - \f(\fsum \fDelta H_f^\text{o}_{\text{reactants}})\].
In this calculation, the enthalpies of formation for each product are multiplied by their respective stoichiometric coefficients and summed; the same is done for the reactants. Subtraction of the total reactants' enthalpy from the total products' enthalpy gives the reaction enthalpy. The precision of these calculations can be pivotal, for example, in predicting product yields or assessing safety in industrial settings, where the heat released or absorbed needs careful monitoring.