Mining for Gold Unlike most metals, gold is found in nature...

Mining for Gold Unlike most metals, gold is found in nature as the pure element. Miners in California in 1849 searched for gold nuggets and gold dust in stream beds, where the denser gold could be easily separated from sand and gravel. However, larger deposits of gold are found in veins of rock and can be separated chemically in a two-step process:$$\begin{aligned}&\text { (1) } 4 \mathrm{Au}(s)+8 \mathrm{NaCN}(a q)+\mathrm{O}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow\\&4 \mathrm{NaAu}(\mathrm{CN})_{2}(a q)+4 \mathrm{NaOH}(a q)\end{aligned}$$.$$\begin{aligned}&\text { (2) } 2 \mathrm{NaAu}(\mathrm{CN})_{2}(a q)+\mathrm{Zn}(s) \rightarrow\\&2 \mathrm{Au}(s)+\mathrm{Na}_{2}\left[\mathrm{Zn}(\mathrm{CN})_{4}\right](a q)\end{aligned}$$.If a $1.0 \times 10^{3} \mathrm{kg}$ sample of rock is $0.019 \%$ gold by mass, how much $\mathrm{Zn}$ is needed to react with the gold extracted from the rock? Assume that reactions (1) and (2) are $100 \%$ efficient.

Key Concepts

Percent Composition

Percent composition refers to the fraction or percentage of a specific component within a mixture or compound by mass. In problems like this, it is used to determine the mass of a particular element (in this case, gold) present in a given mass of ore. This concept is fundamental to calculating the amount of a substance available before performing further stoichiometric analysis.

Stoichiometry

Stoichiometry involves using the quantitative relationships between reactants and products in a balanced chemical equation to predict the amounts of substances consumed and produced in a reaction. It relies on the mole ratios derived from the coefficients in the balanced equations to relate the quantities of different substances involved in the chemical processes.

Mole-to-Mass Conversion

Mole-to-mass conversion is the process of converting a given mass of a substance to moles using its molar mass, and vice versa. This conversion is critical in applying stoichiometric calculations, as chemical equations typically relate substances in terms of moles rather than mass.

Mole Ratio

Mole ratio is the relationship between the coefficients of reactants and products in a balanced chemical equation. It is used to determine how many moles of one substance are needed or produced relative to another. In this context, it allows for the calculation of the amount of zinc required based on the moles of gold present, as dictated by the balanced chemical reactions.

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