Question

When ammonium perchlorate decomposes thermally, the products of the reaction are \(\mathrm{N}_{2}(g), \mathrm{O}_{2}(g), \mathrm{H}_{2} \mathrm{O}(g),\) and \(\mathrm{HCl}(g)\) (a) Write a balanced equation for the reaction. [Hint: You might find it easier to use fractional coefficients for the products.] (b) Calculate the enthalpy change in the reaction per mole of \(\mathrm{NH}_{4} \mathrm{ClO}_{4}\). The standard enthalpy of formation of \(\mathrm{NH}_{4} \mathrm{ClO}_{4}(s)\) is \(-295.8 \mathrm{~kJ}\) (c) When \(\mathrm{NH}_{4} \mathrm{ClO}_{4}(s)\) is employed in solid-fuel booster rockets, it is packed with powdered aluminum. Given the high temperature needed for \(\mathrm{NH}_{4} \mathrm{ClO}_{4}(s)\) decomposition and what the products of the reaction are, what role does the aluminum play? (d) Calculate the volume of all the gases that would be produced at STP, assuming complete reaction of one pound of ammonium perchlorate.

Short answer

(a) The balanced equation for the decomposition of ammonium perchlorate is: \(NH_{4}ClO_{4}(s) \rightarrow \frac{1}{2} N_{2}(g) + \frac{5}{4} O_{2}(g) + 2 H_{2}O(g) + HCl(g)\). (b) The enthalpy change for the reaction per mole of \(NH_{4}ClO_{4}\) is -1013.1 kJ/mol. (c) Aluminum reacts with the oxygen gas produced during ammonium perchlorate decomposition, creating an exothermic reaction that generates additional heat and increases the energy output, providing a more powerful and efficient fuel source for rocket's propulsion. (d) The total volume of gases produced at STP when one pound of ammonium perchlorate reacts completely is 410.8 L.

Step-by-step solution

Write the unbalanced equation

Start by writing the unbalanced equation for the decomposition of ammonium perchlorate. NH₄ClO₄(s) → N₂(g) + O₂(g) + H₂O(g) + HCl(g) #a) Balancing the equation#

Balance the chemical equation

Balance the chemical equation for the decomposition of ammonium perchlorate. You can start by balancing the elements individually. Since there are 4 H atoms in NH₄ClO₄, we need 2 moles of H₂O and 1 mole of HCl to balance the H atoms. Then, balance the Cl and O atoms accordingly. To balance the equation, we can use the following coefficients: NH₄ClO₄(s) → 1/2 N₂(g) + 5/4 O₂(g) + 2 H₂O(g) + HCl(g) #b) Enthalpy change per mole of NH₄ClO₄#

Calculate the enthalpy change per mole of NH₄ClO₄

To find the enthalpy change of the reaction, we will use the following formula: ΔH_r = Σ ΔH_f (products) - Σ ΔH_f (reactants) where ΔH_r is the enthalpy change of the reaction, and ΔH_f represents the enthalpy of formation of each species involved. Given that the standard enthalpy of formation of NH₄ClO₄(s) is -295.8 kJ, we can find the enthalpy change per mole of NH₄ClO₄ using the known standard enthalpies of formation for the other substances involved (N₂, O₂, H₂O and HCl) as follows: ΔH_r = [1/2(0) + 5/4(0) + 2(-241.8) + (-92.3)] - (-295.8) ΔH_r = -1013.1 kJ/mol Therefore, the enthalpy change for the reaction per mole of NH₄ClO₄ is -1013.1 kJ/mol. #c) Role of aluminum#

Explain the role of aluminum in solid-fuel booster rockets

Aluminum is included in solid-fuel booster rockets containing ammonium perchlorate because, under the high temperature conditions needed for NH₄ClO₄ decomposition, aluminum can react with the oxygen gas produced, creating an exothermic reaction that generates additional heat and increases the overall energy output. This intensifies the combustion process, providing a more powerful and efficient fuel source for the rocket's propulsion. #d) Volume of gases produced at STP#

Convert one pound of NH₄ClO₄ to moles

To find the volume of gases produced at STP when one pound of ammonium perchlorate reacts completely, we first need to convert one pound of NH₄ClO₄ to moles. The molecular weight of NH₄ClO₄ is 117.49 g/mol, and 1 pound = 453.59 grams. Moles of NH₄ClO₄ = (453.59 g) / (117.49 g/mol) = 3.86 mol #d) Volume of gases produced at STP#

Calculate the volume of gases produced at STP

For each mole of NH₄ClO₄, we get 1/2 mole of N₂, 2 moles of H₂O, and 1 mole of HCl. The volume of gas at STP for 1 mole of any gas is 22.4 L. Calculate the total volume of gases produced for 3.86 moles of NH₄ClO₄. Volume of N₂ = 3.86 * 1/2 * 22.4 = 43.3 L Volume of O₂ = 3.86 * 5/4 * 22.4 = 108.3 L Volume of H₂O = 3.86 * 2 * 22.4 = 172.8 L Volume of HCl = 3.86 * 22.4 = 86.4 L Total volume of all gases at STP = 43.3 + 108.3 + 172.8 + 86.4 = 410.8 L Thus, the total volume of gases produced at STP when one pound of ammonium perchlorate reacts completely is 410.8 L.

Key concepts

Chemical Reactions

Ammonium perchlorate decomposition is an example of a chemical reaction where a solid compound breaks down into several gaseous products. In any chemical reaction, it's essential to write a balanced chemical equation. A balanced equation ensures that the same number of each type of atom appears on both the reactant and the product sides. This keeps the law of conservation of mass intact, which states that mass cannot be created or destroyed in a chemical reaction.
When ammonium perchlorate decomposes, the balanced equation is:

• \( ext{NH}_4 ext{ClO}_4(s) \rightarrow \frac{1}{2} ext{N}_2(g) + \frac{5}{4} ext{O}_2(g) + 2 ext{H}_2 ext{O}(g) + ext{HCl}(g) \)

This equation includes fractional coefficients for the products, which are unique but valid in stoichiometry. Each coefficient corresponds to the stoichiometric requirement to balance the number of atoms of each element. Balancing chemical equations aids in predicting the outcomes of chemical reactions and is fundamental in chemical studies.

Enthalpy Change

Enthalpy change, represented as \( \Delta H \), in a reaction indicates the heat absorbed or released during the process. For the decomposition of ammonium perchlorate, the enthalpy change can be calculated using the standard enthalpies of formation of the reactants and the products. The formula is:

• \( \Delta H_r = \Sigma \Delta H_f \text{(products)} - \Sigma \Delta H_f \text{(reactants)} \)

Given that the standard enthalpy of formation for ammonium perchlorate is -295.8 kJ/mol, and considering the known values for N₂, O₂, H₂O, and HCl, we find \( \Delta H_r = -1013.1 \text{ kJ/mol} \). This negative value signifies that the reaction is exothermic, releasing heat into the surroundings. Understanding enthalpy changes is crucial for designing reactions that maximize energy efficiency, especially in industrial applications.

Solid-Fuel Rocket Propellants

Solid-fuel rocket propellants, such as those using ammonium perchlorate, often include additional components like powdered aluminum. The aluminum plays a critical role by reacting with oxygen produced during the decomposition of ammonium perchlorate. This reaction is highly exothermic, meaning it further releases heat.
By generating additional heat, the aluminum-oxygen reaction significantly increases the energy available for propulsion. This leads to more efficient fuel consumption and greater thrust in rocket engines. The combination of thermal decomposition and reactive metals in solid-fuel rockets exemplifies strategic chemistry applications to achieve desired outcomes in aerospace technology.

Gas Volume Calculation at STP

Calculating the gas volume at Standard Temperature and Pressure (STP) is a standard practice in chemistry to understand the behavior of gases in a reaction. At STP, which is defined as 0°C (273.15 K) and 1 atm pressure, one mole of any ideal gas occupies 22.4 liters. For the reaction of ammonium perchlorate, calculating the total gas volume involves several steps.

• First, convert the mass of ammonium perchlorate to moles: 1 pound equals 453.59 grams, which is about 3.86 moles for NH₄ClO₄.
• Each mole of ammonium perchlorate produces:
  • \( \frac{1}{2} \) mole of N₂
  • \( \frac{5}{4} \) mole of O₂
  • 2 moles of H₂O
  • 1 mole of HCl
• Multiply the moles of each gas by 22.4 L to find their respective volumes.

In total, 3.86 moles of ammonium perchlorate produce 410.8 liters of gas at STP. This volume calculation is essential for predicting the behavior of gases in practical scenarios, like those involving rocket propulsion.