An aluminum plant produces 5.8 ×10^7 kg of aluminum per year. How much aluminum oxide is requir

step 1 So in this problem, we're given that the aluminum plant produces 5 .8 times 10 to the 7 kilogram

An aluminum plant produces 5.8 ×10^7 kg of aluminum per...

An aluminum plant produces $5.8 \times 10^{7} \mathrm{~kg}$ of aluminum per year. How much aluminum oxide is required? How much bauxite is required? (It takes $2.1 \mathrm{~kg}$ of crude bauxite to produce $1.0 \mathrm{~kg}$ of aluminum oxide.)

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Key Concepts

Mass Conversion and Molar Mass

Mass conversion in chemistry often requires the use of molar mass, which is the mass of one mole of a substance. This concept is central when converting between the mass of an element and the mass of a compound it is a part of. By understanding the molar mass of a compound and the percentage of the target element present, one can compute the necessary mass of the compound required to yield a desired mass of the element.

Ratio and Proportion

The principle of ratio and proportion is fundamental in applying specific conversion factors provided in a problem, such as the amount of raw material needed to produce a unit mass of a processed compound. In this context, the given ratio (e.g., 2.1 kg of bauxite to produce 1.0 kg of aluminum oxide) is applied to scale up the calculations to determine the total raw material needed for large-scale production.

Stoichiometry

Stoichiometry is the branch of chemistry that involves calculating the relative quantities of reactants and products in chemical reactions. It generally uses balanced chemical equations to convert between masses of substances, ensuring that the proportions correspond to the elements and compounds involved. In problems like this, stoichiometry allows us to determine how much compound is needed to yield a given amount of a constituent element.

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