Question

The reusable booster rockets of the U.S. space shuttle employ a mixture of aluminum and ammonium perchlorate for fuel. A possible equation for this reaction is $$\begin{aligned}3 \mathrm{Al}(s)+3 \mathrm{NH}_{4} \mathrm{ClO}_{4}(s) & \longrightarrow \\ \mathrm{Al}_{2} \mathrm{O}_{3}(s)+& \mathrm{AlCl}_{3}(s)+3 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\end{aligned}$$ What mass of \(\mathrm{NH}_{4} \mathrm{ClO}_{4}\) should be used in the fuel mixture for every kilogram of Al?

Short answer

For every kilogram of aluminum, 4350.26 g of ammonium perchlorate should be used in the fuel mixture.

Step-by-step solution

1. Write down the balanced chemical equation.

The balanced chemical equation for the reaction of aluminum with ammonium perchlorate is: \(3 \mathrm{Al}(s) + 3 \mathrm{NH}_{4}\mathrm{ClO}_{4}(s) \rightarrow \mathrm{Al}_{2}\mathrm{O}_{3}(s) + \mathrm{AlCl}_{3}(s) + 3 \mathrm{NO}(g) + 6 \mathrm{H}_{2}\mathrm{O}(g) \)

2. Calculate the molar mass of aluminum and ammonium perchlorate.

First, we need to calculate the molar masses of aluminum (Al) and ammonium perchlorate (NH4ClO4). - Molar mass of Al: \(26.98 \,g/mol\) - Molar mass of NH4ClO4: \((1 × 14.01) + (4 × 1.01) + (1 × 35.45) + (4 × 16.00) = 117.49 \, g/mol\)

3. Use the stoichiometry of the balanced equation to find the mass ratio of NH4ClO4 to Al.

From the balanced equation, we see that 3 moles of Al react with 3 moles of NH4ClO4. Therefore, the mole ratio of NH4ClO4 to Al is 1:1. To find the mass ratio, we'll use the molar masses we calculated in the previous step: Mass ratio: \(\frac{117.49 \, g/mol(NH_{4}ClO_{4})}{26.98 \, g/mol(Al)}= \frac{mass \, of \, NH_{4}ClO_{4}}{mass \, of \, Al} \)

4. Calculate the mass of NH4ClO4 needed for every kilogram of Al.

Let's plug the mass of Al (1 kg, or 1000 g) into the mass ratio equation and solve for the mass of NH4ClO4: \(\frac{117.49 \, g/mol(NH_{4}ClO_{4})}{26.98 \, g/mol(Al)}= \frac{mass \, of \, NH_{4}ClO_{4}}{1000 \, g(Al)} \) Now, solve for the mass of NH4ClO4: \(mass \, of \, NH_{4}ClO_{4} = \frac{117.49 \, g/mol(NH_{4}ClO_{4})}{26.98 \, g/mol(Al)} × 1000 \, g(Al)\) \(mass \, of \, NH_{4}ClO_{4} = 4350.26 \, g\) For every kilogram of aluminum, 4350.26 g of ammonium perchlorate should be used in the fuel mixture.

Key concepts

Balanced Chemical Equation

In chemistry, a balanced chemical equation is crucial for describing the transformation that occurs during a chemical reaction. It shows us which substances are consumed and which substances are produced. This ensures that the number of atoms for each element is conserved. In the case of the reaction between aluminum and ammonium perchlorate, the equation is:
3Al(s) + 3NH₄ClO₄(s) → Al₂O₃(s) + AlCl₃(s) + 3NO(g) + 6H₂O(g).
Here, the coefficients in front of each molecule indicate the number of moles of each substance that participate in the reaction. Therefore, three moles of aluminum react with three moles of ammonium perchlorate, creating several products, including aluminum oxide, aluminum chloride, nitrogen monoxide, and water vapor. Each of these chemicals reflects the conservation of mass, which means every atom that enters on one side of the equation must exit on the other side, just rearranged into new compounds.
Understanding how to balance a chemical equation is the first step towards mastering chemical stoichiometry, as it allows you to predict the amounts of reactants required and products formed in a chemical reaction.

Molar Mass Calculation

Molar mass is a vital concept in chemical stoichiometry, used to convert between the mass of a substance and the amount in moles. It is expressed in grams per mole (g/mol) and is calculated by summing the atomic masses of all the atoms in a molecule.
To figure out how much ammonium perchlorate needs to be used with aluminum, we calculate each of their molar masses first.

• The molar mass of aluminum (Al) is simply 26.98 g/mol, as it contains only one type of atom.
• For ammonium perchlorate (NH₄ClO₄), the calculation is: (1 × Nitrogen's atomic mass) + (4 × Hydrogen's atomic mass) + (1 × Chlorine's atomic mass) + (4 × Oxygen's atomic mass). Adding these gives a molar mass of 117.49 g/mol.

With these values, we can perform further stoichiometric calculations to find the mass of reactants needed in a reaction.

Mass Ratio

After finding the molar masses of reactants, the next step in stoichiometry is determining the mass ratio. This ratio demonstrates how much of each substance is required to meet the balanced equation.
In this example, because aluminum and ammonium perchlorate react in a 1:1 mole ratio according to the balanced chemical equation, the mass ratio is determined from their respective molar masses: 117.49 g/mol for NH₄ClO₄ and 26.98 g/mol for Al.
To calculate the mass ratio:

• Divide the molar mass of NH₄ClO₄ by the molar mass of Al, resulting in approximately 4.35.

This means that 4.35 grams of ammonium perchlorate are required for each gram of aluminum to fuel this reaction effectively. Hence, to maintain the stoichiometric balance, understanding mass ratios ensures that you have the correct proportions of reactants.

Rocket Propellant Chemistry

Rocket propellants, like the aluminum and ammonium perchlorate mixture used in U.S. space shuttles, are fascinating examples of applied chemistry. These combinations are specially designed to produce large amounts of energy to propel rockets into space.
The reaction of aluminum powder with ammonium perchlorate not only produces an intense burst of energy but also forms gaseous products like NO and H₂O, which expand rapidly. This rapid expansion of gases provides the necessary thrust force due to Newton's third law of motion: for every action, there's an equal and opposite reaction.
In refining this chemistry, precise stoichiometric calculations ensure the optimal amount of aluminum and ammonium perchlorate are combined. This combination must be cost-effective, maximize energy production, and minimize the production of harmful by-products.

• Understanding how to balance chemical equations and calculate molar masses is not just theoretical but is crucial in optimizing these fuel mixtures for the utmost efficiency and safety in space exploration.