Problem 88 - Chemistry The Science in Context

Question

Explosives called amatols are mixtures of ammonium nitrate and 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 determine the standard enthalpy of reaction by using the appropriate standard enthalpies of formation from Appendix 4.

Step-by-Step Solution

Answer

Answer: The standard enthalpy of the decomposition reaction for ammonium nitrate (NH4NO3) is -119 kJ/mol.

Step 1: 1. Write the chemical formula for ammonium nitrate

The chemical formula for ammonium nitrate is NH4NO3.

Step 2: 2. Write the balanced chemical reaction for the decomposition of ammonium nitrate

When ammonium nitrate decomposes, it forms nitrogen (N2), oxygen (O2), and water (H2O). The balanced chemical reaction is: NH4NO3 (s) -> N2 (g) + 2 O2 (g) + 2 H2O (g)

Step 3: 3. Find the standard enthalpies of formation for the reactants and products

From Appendix 4, we can find the standard enthalpies of formation (∆Hf) for the reactants and products: ∆Hf (NH4NO3) = -365 kJ/mol ∆Hf (N2) = 0 kJ/mol (since it is an element in its standard state) ∆Hf (O2) = 0 kJ/mol (since it is an element in its standard state) ∆Hf (H2O) = -242 kJ/mol

Step 4: 4. Calculate the standard enthalpy of the reaction

To calculate the standard enthalpy of the reaction, (∆Hr), we use the equation: ∆Hr = Σn∆Hf(products) - Σm∆Hf(reactants) where n and m are the stoichiometric coefficients of the products and reactants, respectively. Substituting the values for the standard enthalpies of formation: ∆Hr = [(1)(0) + (2)(0) + (2)(-242)] - [(1)(-365)] ∆Hr = (-484) - (-365) ∆Hr = -119 kJ/mol

Step 5: 5. Conclusion

The standard enthalpy of the decomposition reaction for ammonium nitrate (NH4NO3) is -119 kJ/mol.

Key Concepts

Enthalpy of Reaction

The enthalpy of reaction, often represented as \( \Delta H_r \), refers to the heat change that occurs during a chemical reaction. It is a crucial concept in thermodynamics. When a reaction occurs, bonds between atoms break and form, which involves energy changes. If a reaction releases heat into its surroundings, it is called exothermic, and \( \Delta H_r \) is negative. If it absorbs heat, it is endothermic, and \( \Delta H_r \) is positive. In practical terms:

• \( \Delta H_r \) tells us how much energy is involved in a reaction.
• For engineers and scientists, understanding the enthalpy of reaction is essential as it helps in energy calculations for processes like combustion and explosion.
• In our exercise, the decomposition of ammonium nitrate is considered. The enthalpy change reveals that the reaction is exothermic with \( \Delta H_r = -119 \) kJ/mol.

Overall, the enthalpy of reaction helps predict how a substance behaves under certain conditions and is important for safety and efficiency in industrial applications.

Balanced Chemical Equation

A balanced chemical equation is essential for correctly describing a chemical reaction. It ensures that the number of each type of atom is conserved from reactants to products. This follows the law of conservation of mass which states that matter cannot be created or destroyed in a chemical reaction.Consider our example of ammonium nitrate decomposition:

• The unbalanced reaction might not necessarily reflect the same number of atoms on either side of the equation.
• By balancing, we have \( \text{NH}_4\text{NO}_3 \) decomposing to produce \( \text{N}_2, \text{O}_2, \) and \( \text{H}_2\text{O} \) with coefficients ensuring the same number of nitrogen, oxygen, and hydrogen atoms on both sides: \( \text{NH}_4\text{NO}_3 (s) \rightarrow \text{N}_2 (g) + 2 \text{O}_2 (g) + 2 \text{H}_2\text{O} (g). \)

Balancing allows chemists to predict amounts of products formed from given reactants and ensures that reactions are understood in terms of mole ratios and real-world applications like this explosive decomposition.

Standard Enthalpy of Formation

The standard enthalpy of formation, denoted as \( \Delta H_f^\circ \), is an important concept when calculating reaction enthalpies. It refers to the heat change when one mole of a substance is formed from its elements under standard conditions (1 atm, 25°C).Key points include:

• \( \Delta H_f^\circ \) values for elements in their standard states, like \( \text{N}_2 \) and \( \text{O}_2 \), are zero because no energy is required to form an element from itself.
• The values for compounds like \( \text{NH}_4\text{NO}_3 \) are determined experimentally and tabulated for various substances.
• For water, \( \Delta H_f^\circ = -242 \) kJ/mol, reflecting its formation from hydrogen and oxygen.

By using these values, we can calculate the overall reaction enthalpy. In our example, the decomposing ammonium nitrate utilized these standard enthalpies to find \( \Delta H_r = -119 \) kJ/mol, illustrating the exothermic nature of the decomposition.