Over the years, the thermite reaction has been used for welding railroad rails, in incendiary bombs, and to ignite solid-fuel rocket motors. The reaction is $$\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+2 \mathrm{Al}(s) \longrightarrow 2 \mathrm{Fe}(l)+\mathrm{Al}_{2} \mathrm{O}_{3}(s)$$ What masses of iron(III) oxide and aluminum must be used to produce \(15.0 \mathrm{g}\) iron? What is the maximum mass of aluminum oxide that could be produced?

Stoichiometry is the part of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. Specifically, it involves calculations to determine the amounts of substances that are consumed and produced in a reaction. For instance, the thermite reaction uses iron(III) oxide and aluminum to produce iron and aluminum oxide.

When solving stoichiometric problems, the first step is to ensure you have a balanced chemical equation. This equation tells you the ratio in which reactants combine and products form, often referred to as the stoichiometric coefficients. In our thermite example, the balanced equation is: \[Fe_2 O_3 (s) + 2 Al (s) \rightarrow 2 Fe (l) + Al_2 O_3 (s)\].

These coefficients are used to convert between moles of one substance to moles of another. By understanding the stoichiometry of the reaction, we can answer questions like how much aluminum is needed to react with a certain mass of iron(III) oxide, or how much aluminum oxide is produced when a set amount of iron is formed.

Balancing chemical equations is essential for performing stoichiometric calculations. An equation must reflect the conservation of mass, which means the number of atoms for each element in the reactants must equal the number in the products. To achieve this balance, we adjust coefficients in front of the chemical formulas without changing the formulas themselves.

Looking at our thermite equation again, the balanced form is: \[Fe_2 O_3 (s) + 2 Al (s) \rightarrow 2 Fe (l) + Al_2 O_3 (s)\].

This shows that one molecule of iron(III) oxide reacts with two atoms of aluminum to produce two atoms of iron and one molecule of aluminum oxide. Balancing is the foundation for stoichiometry, as it ensures the mole ratios needed for calculations represent the actual consumption of reactants and formation of products.

The molar mass of a substance is the weight of one mole of that substance, typically expressed in grams per mole (\(g/mol\)). It is a crucial value for converting between the weight of a substance and the amount in moles, which is the basis for all stoichiometric calculations.

For example, iron (Fe) has a molar mass of 55.85\(g/mol\). This means that one mole, or 6.022 x 10²³ atoms, of iron weighs 55.85 grams. When given a mass of iron, like the 15.0 grams in our thermite problem, we can use its molar mass to find the number of moles. These molar mass values of reactants and products are essential for step-by-step stoichiometric calculations.

When working with stoichiometric problems, converting between moles and mass is a common task that relies on the molar mass of the substances involved. After determining the number of moles from a balanced equation, we can calculate the corresponding mass using molar mass.

In the thermite reaction scenario, we first converted the desired mass of iron into moles. Then, using the stoichiometric coefficients and molar masses of iron(III) oxide (159.69\(g/mol\)) and aluminum (26.98\(g/mol\)), we converted moles back into mass to find out how much of each reactant is needed. This process is fundamental for predicting the amounts of materials required or produced in a given reaction.