Solid fuel in the booster rockets for spacecraft consists of...

Solid fuel in the booster rockets for spacecraft consists of aluminum powder as the fuel and ammonium perchlorate as the oxidizing agent. $3 \mathrm{NH}_{4} \mathrm{ClO}_{4}(s)+3 \mathrm{Al}(s) \longrightarrow$ $$ \mathrm{Al}_{2} \mathrm{O}_{3}(s)+\mathrm{AlCl}_{3}(s)+6 \mathrm{H}_{2} \mathrm{O}(g)+3 \mathrm{NO}(g) $$ If a rocket launch burns $2.200 \times 10^{3} \mathrm{~kg}$ of aluminum, calculate the energy produced in joules. Calculate the volume of the gas produced, assuming it was cooled back to $298 \mathrm{~K}$ at 1 atm. The standard enthalpy of formation of solid ammonium perchlorate is $-295.3 \mathrm{~kJ} / \mathrm{mol}$

Solid fuel in the booster rockets for spacecraft consists of aluminum powder as the fuel and ammonium perchlorate as the oxidizing agent. $3 \mathrm{NH}_{4} \mathrm{ClO}_{4}(s)+3 \mathrm{Al}(s) \longrightarrow$
$$
\mathrm{Al}_{2} \mathrm{O}_{3}(s)+\mathrm{AlCl}_{3}(s)+6 \mathrm{H}_{2} \mathrm{O}(g)+3 \mathrm{NO}(g)
$$
If a rocket launch burns $2.200 \times 10^{3} \mathrm{~kg}$ of aluminum, calculate the energy produced in joules. Calculate the volume of the gas produced, assuming it was cooled back to $298 \mathrm{~K}$ at 1 atm. The standard enthalpy of formation of solid ammonium perchlorate is $-295.3 \mathrm{~kJ} / \mathrm{mol}$

Key Concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. By using the balanced chemical equation, one can determine the ratios of moles in which substances react and are produced, which is essential for calculating the amounts of reactants used or products formed in a reaction.

Thermochemistry

Thermochemistry focuses on the changes in energy, particularly heat, during chemical reactions. It involves calculating the heat released or absorbed in reactions, often using concepts such as the enthalpy change of a reaction, which is central to understanding the energy output of chemical processes like combustion.

Enthalpy of Formation

The enthalpy of formation is defined as the heat change that occurs when one mole of a compound is formed from its elements under standard conditions. It serves as a fundamental building block in thermochemistry for determining reaction enthalpies using Hess’s Law, which allows the calculation of the total energy released or absorbed during a chemical reaction.

Ideal Gas Law

The ideal gas law relates the pressure, volume, temperature, and quantity (in moles) of a gas using the equation PV = nRT. This law is a fundamental tool for calculating the volume that a given amount of gas will occupy under specified conditions, making it essential for estimating the volume of gaseous products in chemical reactions.

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