Problem 87 - Chemistry The Science in Context

Question

Ammonium nitrate decomposes to \(\mathrm{N}_{2} \mathrm{O}\) and water vapor at temperatures between \(250^{\circ} \mathrm{C}\) and \(300^{\circ} \mathrm{C} .\) Write a balanced chemical reaction describing the decomposition of ammonium nitrate, and calculate the enthalpy of reaction by using the appropriate enthalpies of formation from Appendix 4.

Step-by-Step Solution

Answer

Answer: The enthalpy of reaction for the decomposition of ammonium nitrate is -242.55 kJ/mol.

Step 1: Write the balanced chemical equation for the decomposition of ammonium nitrate

The decomposition reaction of ammonium nitrate can be expressed as: \(\mathrm{NH}_{4} \mathrm{NO}_{3} (s) \rightarrow \mathrm{N}_{2} \mathrm{O} (g) + 2 \mathrm{H}_{2} \mathrm{O} (g)\) The equation is already balanced.

Step 2: Identify the enthalpies of formation for the compounds in the reaction

From Appendix 4, we have the enthalpies of formation for each compound. These values are: \(\Delta H^\circ_\mathrm{f} [\mathrm{NH}_{4} \mathrm{NO}_{3} (s)] = -365.6 \,\mathrm{kJ/mol}\) \(\Delta H^\circ_\mathrm{f} [\mathrm{N}_{2} \mathrm{O} (g)] = +82.05 \,\mathrm{kJ/mol}\) \(\Delta H^\circ_\mathrm{f} [\mathrm{H}_{2} \mathrm{O} (g)] = -241.8\, \mathrm{kJ/mol}\)

Step 3: Calculate the enthalpy of reaction using the enthalpies of formation

Now we will apply Hess's law to calculate the enthalpy of reaction. The enthalpy of reaction (\(\Delta H^\circ_\mathrm{rxn}\)) can be defined as: \(\Delta H^\circ_\mathrm{rxn} = \sum [\Delta H^\circ_\mathrm{f}(\mathrm{products})] - \sum[\Delta H^\circ_\mathrm{f}(\mathrm{reactants})]\) In our case, the reaction involves the decomposition of ammonium nitrate to form N2O and water. \(\Delta H^\circ_\mathrm{rxn} = 1 \times \Delta H^\circ_\mathrm{f} (\mathrm{N}_{2} \mathrm{O}) + 2 \times \Delta H^\circ_\mathrm{f} (\mathrm{H}_{2} \mathrm{O}) - 1 \times \Delta H^\circ_\mathrm{f} (\mathrm{NH}_{4} \mathrm{NO}_{3})\) Now, substitute the values of the enthalpies of formation from Step 2: \(\Delta H^\circ_\mathrm{rxn} = 1 \times (+82.05\, \mathrm{kJ/mol}) + 2 \times (-241.8\, \mathrm{kJ/mol}) - 1 \times (-365.6 \, \mathrm{kJ/mol})\) \(\Delta H^\circ_\mathrm{rxn} = -242.55\, \mathrm{kJ/mol}\) The enthalpy of reaction for the decomposition of ammonium nitrate is -242.55 kJ/mol.

Key Concepts

Balanced Chemical Equation

A balanced chemical equation is akin to a recipe for a chemical reaction; it shows the exact quantities of reactants and products involved. In the case of ammonium nitrate decomposition, the equation is

\(\mathrm{NH}_{4}\mathrm{NO}_{3}(s) \rightarrow \mathrm{N}_{2}\mathrm{O}(g) + 2\mathrm{H}_{2}\mathrm{O}(g)\).
Each element on the left side (reactants) is accounted for on the right side (products) in the precise ratios dictated by the law of conservation of mass. This is important for predicting the amounts of products and for calculating the reaction's energetics.

Enthalpy of Formation

The enthalpy of formation, represented as \(\Delta H^\circ_\mathrm{f}\), is the heat change that results when one mole of a compound is formed from its elements in their standard states. For ammonium nitrate decomposition, we consider the enthalpy of formation for reactants and products. With known values, such as \(\Delta H^\circ_\mathrm{f} [\mathrm{NH}_{4}\mathrm{NO}_{3}(s)] = -365.6\,\mathrm{kJ/mol}\), we can predict the heat released or absorbed during the reaction. These values are fundamental for calculating the overall energy of a chemical process.

Hess's Law

Hess's Law is a powerful tool in chemistry used for determining the overall change in enthalpy for a reaction. It states that the total enthalpy change for a reaction is the same, regardless of the number of steps taken. This allows us to utilize known enthalpies of formation to calculate the enthalpy of a reaction. The equation

\(\Delta H^\circ_\mathrm{rxn} = \sum [\Delta H^\circ_\mathrm{f}(\mathrm{products})] - \sum[\Delta H^\circ_\mathrm{f}(\mathrm{reactants})]\)
is an application of Hess's Law. The calculated value of -242.55 kJ/mol for the decomposition of ammonium nitrate indicates the reaction is exothermic, releasing heat into the surroundings.

Chemical Thermodynamics

Chemical thermodynamics deals with the study of energy and work of chemical reactions and how energy is interchanged with the surroundings. It encompasses concepts like enthalpy and entropy and laws like Hess's Law. Understanding the energetics of a reaction, such as the decomposition of ammonium nitrate, requires a grasp of thermodynamic principles. By analyzing the enthalpies of formation and applying Hess's Law, we determine whether a reaction is likely to occur spontaneously and the thermal effect it would have on the environment. Chemical thermodynamics helps predict the feasibility of reactions and the management of energy resources in industrial processes.