Problem 92 - Chemistry: An Atoms-Focused Approach

Question

Explosives called amatols are mixtures of ammonium nitrate and trinitrotoluene (TNT) introduced during World War I when TNT was in short supply. The mixtures can provide \(30 \%\) more explosive power than TNT alone. Above \(300^{\circ} \mathrm{C},\) ammonium nitrate decomposes to \(\mathrm{N}_{2}, \mathrm{O}_{2},\) and \(\mathrm{H}_{2} \mathrm{O} .\) Write a balanced chemical reaction describing the decomposition of ammonium nitrate, and calculate its \(\Delta H_{\mathrm{rxn}}^{\circ}\) using the appropriate \(\Delta H_{\mathrm{f}}^{\circ}\) values from Appendix 4.

Step-by-Step Solution

Answer

Answer: The balanced chemical equation for the decomposition of ammonium nitrate is NH4NO3 (s) → N2 (g) + 2 H2O (g) + 1/2 O2 (g). The standard enthalpy of reaction for this decomposition is -118 kJ/mol.

Step 1: Write the balanced chemical equation

The decomposition of ammonium nitrate, the process occurs above 300°C, can be represented by the following balanced chemical equation: NH4NO3 (s) → N2 (g) + 2 H2O (g) + 1/2 O2 (g)

Step 2: Identify the products and reactants

In this reaction, there is one reactant, ammonium nitrate (NH4NO3), and three products, nitrogen gas (N2), water vapor (H2O), and oxygen gas (O2).

Step 3: Find the standard heat of formation (∆Hf) values

Using Appendix 4, we can find the standard heat of formation values for each reactant and product involved in the reaction: ∆Hf(NH4NO3) = -365.6 kJ/mol ∆Hf(N2) = 0 kJ/mol (since N2 is in its standard state) ∆Hf(H2O) = -241.8 kJ/mol ∆Hf(O2) = 0 kJ/mol (since O2 is in its standard state)

Step 4: Calculate the standard enthalpy of reaction (∆Hrxn)

Using Hess's Law, we can calculate the standard enthalpy of reaction as follows: ∆Hrxn = [∆Hf(products) - ∆Hf(reactants)] ∆Hrxn = [(1 mol N2 × 0 kJ/mol) + (2 mol H2O × (-241.8 kJ/mol)) + (1/2 mol O2 × 0 kJ/mol)] - [1 mol NH4NO3 × (-365.6 kJ/mol)] ∆Hrxn = [(0 kJ) + (-483.6 kJ) + (0 kJ)] - (-365.6 kJ) ∆Hrxn = -118 kJ/mol The standard enthalpy of reaction for the decomposition of ammonium nitrate is -118 kJ/mol.

Key Concepts

Ammonium Nitrate

Ammonium nitrate is a chemical compound with the formula \( \text{NH}_4\text{NO}_3 \). It is a white crystalline solid that is highly soluble in water. Ammonium nitrate is widely used in agriculture as a high-nitrogen fertilizer. It is notable for its role in the composition of explosives, as it can be combined with other substances to enhance explosive power.

In the context of the provided exercise, ammonium nitrate decomposes when heated above \(300^{\circ} \text{C} \), forming nitrogen gas (\( \text{N}_2 \)), water vapor (\( \text{H}_2\text{O} \)), and oxygen gas (\( \text{O}_2 \)). This decomposition process is crucial for understanding its use and storage because it can be hazardous if improperly handled.

**Key Points:**

• Ammonium nitrate has the chemical formula \( \text{NH}_4\text{NO}_3 \).
• It is used as a fertilizer and in explosives.
• Decomposition into \( \text{N}_2 \), \( \text{O}_2 \), and \( \text{H}_2\text{O} \) occurs at high temperatures.

Explosives

Explosives are substances that undergo a rapid chemical transformation with the release of gas, heat, and pressure. They are known for their ability to cause significant destruction or movement. In the context of chemical reactions, ammonia nitrate plays a pivotal role when mixed with other substances like trinitrotoluene (TNT). This mixture is often called amatol.

Amatols were particularly useful during World War I owing to their increased explosive power compared to TNT alone. The mixture can enhance explosive potential by up to \( 30\% \). This is because ammonium nitrate acts as an oxidizing agent, facilitating the rapid combustion of TNT, releasing a significant amount of energy.

**Notable Aspects of Explosives:**

• Composed of reactive compounds that release energy rapidly.
• Amatols combine ammonium nitrate with other explosive materials like TNT.
• The decomposition of ammonium nitrate contributes to explosive reactions.

Balanced Chemical Equation

A balanced chemical equation accurately represents the conservation of mass in a chemical reaction. It ensures that the number of atoms for each element is the same on both sides of the equation. For ammonium nitrate's decomposition, the balanced equation is as follows:
\[\text{NH}_4\text{NO}_3 (s) \rightarrow \text{N}_2 (g) + 2 \text{H}_2\text{O} (g) + \frac{1}{2} \text{O}_2 (g) \]

Balancing a chemical equation involves adjusting coefficients to achieve the same quantity of each type of atom on both the reactant and product sides. For this particular equation:

• The nitrogen atoms are balanced with one molecule of \( \text{N}_2 \) and one of \( \text{NH}_4\text{NO}_3 \).
• The hydrogen atoms from \( \text{NH}_4\text{NO}_3 \) become two water molecules \( 2 \text{H}_2\text{O} \).
• Oxygen atoms balance as one and a half molecules: one from \( 2 \text{H}_2\text{O} \) and half from \( \frac{1}{2}\text{O}_2 \).

Balancing equations is essential for calculating reactions and enthalpy changes.

Enthalpy of Reaction

Enthalpy of reaction, denoted as \( \Delta H_{\text{rxn}} \), is the measure of heat change during a chemical reaction at constant pressure. It's indicative of whether a reaction is exothermic (releases heat) or endothermic (absorbs heat).

In the decomposition of ammonium nitrate, the enthalpy can be calculated using standard heats of formation values from a data table. By employing Hess's Law, which states that the total enthalpy change in a reaction is the same, regardless of the steps taken, you calculate \( \Delta H_{\text{rxn}} \) as:

\[\Delta H_{\text{rxn}} = [\Delta H_{\text{f}}(\text{products}) - \Delta H_{\text{f}}(\text{reactants})] \]

For ammonium nitrate:

• Products: \( \text{N}_2, \text{H}_2\text{O}, \text{O}_2 \)
• Reactants: \( \text{NH}_4\text{NO}_3 \)

Using provided \( \Delta H_{\text{f}} \) values, you find \( \Delta H_{\text{rxn}} \) is \(-118\) kJ/mol, indicating an exothermic reaction. This negative value signifies energy release, vital for understanding energetic dynamics in reactions involving explosives.