Question

The rocket boosters of the space shuttle Discovery, launched on July \(26,2005,\) used a fuel mixture containing primarily solid ammonium perchlorate, \(\mathrm{NH}_{4} \mathrm{ClO}_{4}(\mathrm{s}),\) and aluminum metal. The unbalanced chemical equation for the reaction is given below. \(\mathrm{Al}(\mathrm{s})+\mathrm{NH}_{4} \mathrm{ClO}_{4}(\mathrm{s}) \longrightarrow\) $$ \mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{s})+\mathrm{AlCl}_{3}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l})+\mathrm{N}_{2}(\mathrm{g}) $$ What is the minimum mass of \(\mathrm{NH}_{4} \mathrm{ClO}_{4}\) consumed, per kilogram of \(\mathrm{Al}\), by the reaction of \(\mathrm{NH}_{4} \mathrm{ClO}_{4}\) and Al?[Hint: Balance the elements in the order \(\mathrm{Cl}, \mathrm{H},\) \(\mathrm{O}, \mathrm{Al}, \mathrm{N} .\)]

Short answer

The minimum mass of \(NH_{4}ClO_{4}\) consumed per kilogram of \(Al\) by the reaction of \(NH_{4}ClO_{4}\) and \(Al\), as calculated is approximately 7255.7 grams or 7.256 kg/kilogram of \(Al\).

Step-by-step solution

Balancing The Chemical Equation

The unbalanced equation is: \[Al(s) + NH_{4}ClO_{4}(s) \rightarrow Al_{2}O_{3}(s) + AlCl_{3}(s) + H_{2}O(l) + N_{2}(g)\] Balance the elements in the order: \(Cl, H, O, Al, N\) \[6Al(s) + 10NH_{4}ClO_{4}(s) \rightarrow 5Al_{2}O_{3}(s) + 10AlCl_{3}(s) + 20H_{2}O(l) + 10N_{2}(g)\]

Considering the Molar Masses

We need to take the molar masses of Aluminum (Al) and ammonium perchlorate (\(NH_{4}ClO_{4}\)) into consideration in order to convert from molecular scale to macroscopic scale. The molar mass of Aluminum (Al) is approximately 26.98 g/mol and that of ammonium perchlorate (\(NH_{4}ClO_{4}\)) is approximately 117.49 g/mol.

Calculating the Mass

In the now balanced equation, we see that the ratio between Aluminum (Al) and ammonium perchlorate (\(NH_{4}ClO_{4}\)) is 6:10 or 3:5. Therefore, for every 3 moles of Al, we need 5 moles of \(NH_{4}ClO_{4}\). To calculate the mass of \(NH_{4}ClO_{4}\) per mass of Al -- Use the molar masses to convert from moles to grams. Thus, \[(117.49 \, g/mol * 5 \, moles) / (26.98 \, g/mol * 3 \, moles)\] Calculate the above expression to get the mass of \(NH_{4}ClO_{4}\) per gram of Al.

Converting to Kilograms

The previous step provides the mass per gram of Al but the asked quantity in the task is per kilogram. Since there are 1000 grams in a kilogram, multiply the result calculated in step 3 by 1000 to get the result.

Key concepts

Balancing Chemical Equations

Balancing chemical equations is a fundamental step in understanding any chemical reaction. It ensures that the same number of atoms of each element are present on both sides of the equation, aligning with the Law of Conservation of Mass. This law states that matter cannot be created or destroyed in a closed system. For the reaction involving ammonium perchlorate and aluminum in the space shuttle fuel, balancing begins by listing all the elements present in the reactants and products. Our goal is to adjust the coefficients (numbers in front of compounds) to ensure that the number of atoms for each element is equal on both sides.

In the original unbalanced equation:\[Al(s) + NH_{4}ClO_{4}(s) \rightarrow Al_{2}O_{3}(s) + AlCl_{3}(s) + H_{2}O(l) + N_{2}(g)\]Balancing started with Chlorine (Cl), then moved to Hydrogen (H), Oxygen (O), Aluminum (Al), and finally Nitrogen (N). The balanced equation becomes:\[6Al(s) + 10NH_{4}ClO_{4}(s) \rightarrow 5Al_{2}O_{3}(s) + 10AlCl_{3}(s) + 20H_{2}O(l) + 10N_{2}(g) \]This shows that 6 moles of aluminum react with 10 moles of ammonium perchlorate. By balancing, we ensure the reaction accurately reflects what happens physically.

Molar Mass Calculations

Molar mass calculations serve as the bridge between the microscopic world of individual molecules and the macroscopic world of grams we measure in the lab. Each element has a specific atomic mass, which contributes to the molar mass of a compound. To perform these calculations, you add up the atomic masses of all atoms in a formula.

For aluminum, Al, the atomic mass is approximately 26.98 g/mol. For ammonium perchlorate, \(NH_{4}ClO_{4}\), the calculation is:

• N: 1 atom x 14.01 g/mol
• H: 4 atoms x 1.008 g/mol
• Cl: 1 atom x 35.45 g/mol
• O: 4 atoms x 16.00 g/mol

Adding these gives a molar mass for \(NH_{4}ClO_{4}\) of about 117.49 g/mol. Using these molar masses, you can convert moles of a substance to grams, making it easier to measure and work with chemical quantities in the lab.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products through the breaking and forming of chemical bonds. The combination of ammonium perchlorate and aluminum showcases a redox reaction, where there is a transfer of electrons between atoms.

In this specific reaction, ammonium perchlorate acts as the oxidizer, providing oxygen for the combustion of aluminum. As these compounds react, they produce products like aluminum oxide \(Al_2O_3\), aluminum chloride \(AlCl_3\), water \(H_2O\), and nitrogen gas \(N_2\).

Understanding the type of chemical reaction is crucial, as it helps predict the products and conditions needed for the reaction to occur. This knowledge is essential for applications in industries ranging from aerospace, as demonstrated with the space shuttle, to everyday chemical manufacturing. Studying chemical reactions also underscores the importance of reaction conditions like temperature and pressure, which can significantly affect outcomes.