Gold can be extracted from the surrounding rock by using a...

Gold can be extracted from the surrounding rock by using a solution of sodium cyanide. While effective for isolating gold, toxic cyanide finds its way into watersheds, causing environmental damage and harming human health.$4 \mathrm{Au}(s)+8 \mathrm{NaCN}(a q)+\mathrm{O}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow$.$4 \mathrm{NaAu}(\mathrm{CN})_{2}(a q)+4 \mathrm{NaOH}(a q)$ $2 \mathrm{NaAu}(\mathrm{CN})_{2}(a q)+\mathrm{Zn}(s) \rightarrow 2 \mathrm{Au}(s)+\mathrm{Na}_{2}\left[\mathrm{Zn}(\mathrm{CN})_{4}\right](a q)$.a. If a sample of rock contains $0.009 \%$ gold by mass, how much $\mathrm{NaCN}$ is needed to extract the gold from 1 metric ton ( 1 metric ton $=10^{3} \mathrm{kg}$ ) of rock as $\mathrm{NaAu}(\mathrm{CN})_{2} ?$ b. How much zinc is needed to convert the $\mathrm{NaAu}(\mathrm{CN})_{2}$ from part (a) to metallic gold? c. The gold recovered in part (b) is manufactured into a gold ingot in the shape of a cube. The density of gold is $19.3 \mathrm{g} / \mathrm{cm}^{3} .$ How big is the cube of gold?

Gold can be extracted from the surrounding rock by using a solution of sodium cyanide. While effective for isolating gold, toxic cyanide finds its way into watersheds, causing environmental damage and harming human health.$4 \mathrm{Au}(s)+8 \mathrm{NaCN}(a q)+\mathrm{O}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow$.$4 \mathrm{NaAu}(\mathrm{CN})_{2}(a q)+4 \mathrm{NaOH}(a q)$
$2 \mathrm{NaAu}(\mathrm{CN})_{2}(a q)+\mathrm{Zn}(s) \rightarrow 2 \mathrm{Au}(s)+\mathrm{Na}_{2}\left[\mathrm{Zn}(\mathrm{CN})_{4}\right](a q)$.a. If a sample of rock contains $0.009 \%$ gold by mass, how much $\mathrm{NaCN}$ is needed to extract the gold from 1 metric ton ( 1 metric ton $=10^{3} \mathrm{kg}$ ) of rock as $\mathrm{NaAu}(\mathrm{CN})_{2} ?$
b. How much zinc is needed to convert the $\mathrm{NaAu}(\mathrm{CN})_{2}$ from part (a) to metallic gold?
c. The gold recovered in part (b) is manufactured into a gold ingot in the shape of a cube. The density of gold is $19.3 \mathrm{g} / \mathrm{cm}^{3} .$ How big is the cube of gold?

Key Concepts

Stoichiometry

Stoichiometry involves the quantitative relationships between reactants and products in a balanced chemical reaction. It is used to calculate the amounts of substances required or produced by relating the coefficients in the balanced equations through mole ratios, and it forms the backbone of calculations in chemistry involving conversions between mass, moles, and molecules.

Percent Composition by Mass

Percent composition by mass is a measure that indicates the proportion of a particular component within a mixture or compound, expressed as a percentage of the total mass. This concept is essential when determining how much of a valuable element or substance is present within a larger material sample.

Dimensional Analysis and Unit Conversion

Dimensional analysis and unit conversion are techniques used to switch between different measurement units systematically. These methods ensure that calculations in chemistry, especially those involving mass, volume, or moles, are performed correctly by keeping track of units throughout the process.

Density and Volume Relationship

Density is defined as the mass per unit volume of a substance. Understanding the relationship between density, mass, and volume is critical when determining the physical dimensions, such as calculating the volume of a material from its mass or vice versa, which is useful in applications ranging from material sciences to engineering.

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