Predicting Product Quantities

The fuel used to power the booster rockets on space shuttles is a mixture of aluminum metal and ammonium perchlorate. The following balanced equation represents the reaction:

[tex] 3 \, \text{Al} + 3 \, \text{NH}_4\text{ClO}_4 \rightarrow \text{Al}_2\text{O}_3 + \text{AlCl}_3 + 3 \, \text{NO} + 6 \, \text{H}_2\text{O} [/tex]

What is the mole ratio of [tex] \text{Al} [/tex] to [tex] \text{Al}_2\text{O}_3 [/tex]?



Answer :

To determine the mole ratio of aluminum (Al) to aluminum oxide (Al₂O₃) in the given chemical reaction, we first need to examine the balanced equation:

[tex]\[3 \text{Al} + 3 \text{NH}_4\text{ClO}_4 \rightarrow \text{Al}_2\text{O}_3 + \text{AlCl}_3 + 3 \text{NO} + 6 \text{H}_2\text{O}\][/tex]

This balanced equation tells us the stoichiometric relationship between the reactants and products. Let's focus on the species of interest:

- Aluminum (Al)
- Aluminum oxide (Al₂O₃)

From the balanced equation, we see that:

- 3 moles of Al react.
- 1 mole of Al₂O₃ is produced.

To find the mole ratio of Al to Al₂O₃, we consider the coefficients in front of each species in the equation.

The coefficient for Al is 3, and the coefficient for Al₂O₃ is 1.

Therefore, the mole ratio of Al to Al₂O₃ is:
[tex]\[ \frac{3 \, \text{moles of Al}}{1 \, \text{mole of Al}_2\text{O}_3} \][/tex]

This simplifies to:
[tex]\[ 3:1 \][/tex]

In decimal form, this ratio is 3.0.

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