Problem 42 - Chemistry: An Atoms-Focused Approach

Question

Mining for Gold Unlike most metals, gold occurs in nature as the pure element. Miners in California in 1849 searched for gold nuggets and gold dust in streambeds, 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 the following two-step process: (1) \(4 \mathrm{Au}(s)+8 \mathrm{NaCN}(a q)+\mathrm{O}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow\) $$4 \mathrm{NaAu}(\mathrm{CN})_{2}(a q)+4 \mathrm{NaOH}(a q)$$ (2) \(2 \mathrm{NaAu}(\mathrm{CN})_{2}(a q)+\mathrm{Zn}(s) \rightarrow\) $$2 \mathrm{Au}(s)+\mathrm{Na}_{2}\left[\mathrm{Zn}(\mathrm{CN})_{4}\right](a q)$$ If 23 kilograms of ore is \(0.19 \%\) gold by mass, how much Zn is needed to react with the gold in the ore? Assume that reactions 1 and 2 are \(100 \%\) efficient.

Step-by-Step Solution

Answer

Answer: About 14.5 grams of Zn is needed to react with the gold in the 23 kg ore.

Step 1: Find the mass of gold in the ore

We have 23 kilograms of ore, and it is 0.19% gold by mass. To find the mass of gold in the ore, we multiply the total mass of the ore by the percentage of gold: Mass of gold = (23,000 g) x (0.19 / 100)

Step 2: Convert mass of gold to moles of gold

To calculate the amount of Zn required for the reaction, we need to convert the mass of gold found in step 1 to moles. We can use the molar mass of gold (197.0 g/mol) for this purpose: Moles of gold = Mass of gold / Molar mass of gold

Step 3: Use stoichiometry to find moles of Zn needed

From the second reaction, we can see that 2 moles of NaAu(CN)\(_2\) reacts with 1 mole of Zn. Since there are 2 moles of NaAu(CN)\(_2\) for every 2 moles of gold in the reaction, the number of moles of Zn needed will be equal to the number of moles of gold. Moles of Zn = Moles of gold

Step 4: Convert moles of Zn to mass of Zn

Now, we can use the molar mass of Zn (65.38 g/mol) to convert the number of moles of Zn needed to the mass of Zn needed: Mass of Zn = Moles of Zn x Molar mass of Zn

Step 5: Calculate and write the final answer

Now, we can plug in the values from the previous steps: Mass of gold = (23,000 g) x (0.19 / 100) = 43.7 g Moles of gold = 43.7 g / 197.0 g/mol = 0.222 moles Moles of Zn = 0.222 moles Mass of Zn = 0.222 moles x 65.38 g/mol = 14.5 g So, about 14.5 grams of Zn is needed to react with the gold in the 23 kg ore.

Key Concepts

Understanding Stoichiometry

Stoichiometry is a mathematical concept in chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It is essential in calculating the amounts of substances consumed and produced in chemical reactions. By using stoichiometry, we can predict how much of a material is needed or made in a reaction. To understand stoichiometry, we often look at balanced chemical equations, which show the proportions of reactants and products as fixed ratios.

In our exercise, stoichiometry helps determine the amount of zinc (Zn) required to process gold from ore. Here's how we can break it down:

• First, we calculate the mass of a component, like gold, in the ore.
• Next, we convert this mass into moles using the element's molar mass.
• Then, we use the balanced chemical reaction to find out the mole ratio between gold and zinc.

This series of calculations ensures that we have the right amount of each substance needed to complete the reaction.

Exploring Chemical Reactions

Chemical reactions involve changing substances into new products through the breaking and forming of chemical bonds. In our gold extraction problem, two chemical reactions are used to purify gold from its ore. The first reaction involves the use of sodium cyanide (NaCN) and oxygen to dissolve gold, forming \(\mathrm{NaAu(CN)}_{2}\). This compound can then be separated from the undesired materials.

In the second reaction, zinc is introduced to recover pure gold. Here, zinc replaces the gold in the compound \(\mathrm{NaAu(CN)}_{2}\) and precipitates it out as solid gold, making it accessible for collection. During these reactions, it is crucial to keep them efficient and complete to maximize gold recovery. Utilizing these reactions, miners can extract significant amounts of gold for production.

Role of Molar Mass in Calculations

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It acts as a bridge between the mass of a substance and the number of particles, which include atoms, molecules, or ions.

In the exercise of gold extraction, molar mass plays a crucial part in conversion processes:

• The molar mass of gold (197.0 g/mol) helps us convert grams of gold found in the ore into moles. This allows for stoichiometric calculations of zinc's required amount.
• Similarly, the molar mass of zinc (65.38 g/mol) helps in converting the moles of zinc needed back into grams for practical measurement and use.

By understanding molar masses, one can effectively analyze and work with chemical equations, making sure that they are well-prepared for any amount-based chemical application.