Gold is found in seawater at very low levels, about 0.05 ppb by mass. Assuming that gold is worth about $1300 per troy ounce, how many liters of seawater would you have to process to obtain $1,000,000 worth of gold? Assume the density of water is 1.03 g/mL and that your gold recovery process is 50% efficient.

Verified step by step guidance

Step 1: Convert the value of gold from dollars to troy ounces. Since $1,000,000 worth of gold is needed and gold is valued at $1300 per troy ounce, calculate the number of troy ounces required by dividing $1,000,000 by $1300.

Step 2: Convert the number of troy ounces of gold to grams. Use the conversion factor that 1 troy ounce is approximately 31.1035 grams.

Step 3: Calculate the total mass of gold needed in grams, considering the efficiency of the recovery process. Since the process is 50% efficient, you will need twice the amount of gold calculated in Step 2.

Step 4: Determine the mass of gold present in seawater. Given that the concentration of gold in seawater is 0.05 ppb (parts per billion) by mass, express this concentration as grams of gold per gram of seawater.

Step 5: Calculate the volume of seawater needed. Use the density of seawater (1.03 g/mL) to convert the mass of seawater (from Step 4) to volume in liters, ensuring all units are consistent.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Parts per billion (ppb)

Parts per billion (ppb) is a unit of measurement used to describe the concentration of a substance in a solution. It indicates how many parts of a substance are present in one billion parts of the total solution. In this context, 0.05 ppb means that there are 0.05 grams of gold in one billion grams of seawater, which is crucial for calculating the total amount of seawater needed to extract a specific quantity of gold.

Density and volume conversion

Density is defined as mass per unit volume and is essential for converting between mass and volume. In this problem, the density of seawater is given as 1.03 g/mL, which allows us to convert the mass of seawater into volume. Understanding this relationship is vital for determining how many liters of seawater are required to yield the desired amount of gold.

Efficiency of recovery processes

The efficiency of a recovery process indicates the percentage of the target substance that can be successfully extracted from a mixture. In this scenario, a 50% recovery efficiency means that only half of the gold present in the seawater can be obtained. This concept is critical for accurately calculating the total amount of seawater needed to achieve the desired monetary value of gold after accounting for losses during extraction.

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