Chromium metal can be produced from high-temperature...

Chromium metal can be produced from high-temperature reactions of chromium(III) oxide with silicon or aluminum: $$\begin{aligned}\mathrm{Cr}_{2} \mathrm{O}_{3}(s)+2 \mathrm{Al}(\ell) & \rightarrow 2 \mathrm{Cr(\ell)+\mathrm{Al}_{2} \mathrm{O}_{3}(s) \\2 \mathrm{Cr}_{2} \mathrm{O}_{3}(s)+3 \mathrm{Si}(\ell) & \rightarrow 4 \mathrm{Cr}(\ell)+3\mathrm{SiO}_{2}(s)\end{aligned}$$ a. Calculate the mass of aluminum required to prepare 400.0 grams of chromium metal by the first reaction. b. Calculate the mass of silicon required to prepare 400.0 grams of chromium metal by the second reaction.

Chromium metal can be produced from high-temperature reactions of chromium(III) oxide with silicon or aluminum:
$$\begin{aligned}\mathrm{Cr}_{2} \mathrm{O}_{3}(s)+2 \mathrm{Al}(\ell) & \rightarrow 2 \mathrm{Cr(\ell)+\mathrm{Al}_{2} \mathrm{O}_{3}(s) \\2 \mathrm{Cr}_{2} \mathrm{O}_{3}(s)+3 \mathrm{Si}(\ell) & \rightarrow 4 \mathrm{Cr}(\ell)+3\mathrm{SiO}_{2}(s)\end{aligned}$$
a. Calculate the mass of aluminum required to prepare 400.0 grams of chromium metal by the first reaction.
b. Calculate the mass of silicon required to prepare 400.0 grams of chromium metal by the second reaction.

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Key Concepts

Mass-to-Mole Conversions

Converting mass to moles (and vice versa) is a critical step in stoichiometry. It involves using the molar mass of a substance to relate the measured mass to the number of moles, enabling further calculations based on the mole ratios from the balanced chemical equation.

Molar Mass

Molar mass is the mass in grams of one mole of a substance, serving as a conversion factor between the mass of a substance and the number of moles. It is essential for translating between the macroscopic scale (grams) and the microscopic scale (moles) in stoichiometric calculations.

Balanced Chemical Equations

A balanced chemical equation shows the exact proportions in which reactants combine and products form, maintaining the conservation of mass. The coefficients in the equation are used to convert quantities of one substance into quantities of another during stoichiometric calculations.

Stoichiometry

Stoichiometry involves using balanced chemical equations to determine the proportionate amounts of reactants and products in a chemical reaction. It allows one to calculate the mass or moles of a substance involved in the reaction based on the molar ratios provided by the balanced equation.

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