Question

there are 50 billion gold atoms in every drop of sea water. 1 drop = .05ml. is it feasible to “mine” the ocean for gold? in other words, how many gallons of sea water would have to be stripped of its gold to produce 1 troy ounce of the precious metal?

Answer 1

To produce 1 troy ounce of gold, it would require approximately 414 gallons of sea water.

Step-by-step explanation:

To determine how many gallons of sea water would need to be stripped of its gold to produce 1 troy ounce of gold, we need to calculate the number of gold atoms in 1 troy ounce and then divide it by the number of gold atoms in a drop of sea water. According to the information given, there are 50 billion gold atoms in every drop of sea water, and 1 troy ounce is approximately 31.1 grams. Using Avogadro's number (6.022 × 10^23), we can calculate the number of gold atoms in 1 troy ounce of gold.

Number of gold atoms in 1 troy ounce = (31.1 g) / (atomic mass of gold in grams)

Number of gold atoms in a drop of sea water = 50 billion atoms

Number of gallons of sea water needed for 1 troy ounce of gold = (Number of gold atoms in 1 troy ounce) / (Number of gold atoms in a drop of sea water)

Using the atomic mass of gold as 197.0 g/mol, we find that there are approximately 1.57 × 10^22 gold atoms in 1 troy ounce. Thus, the number of gallons of sea water needed to produce 1 troy ounce of gold would be:

(1.57 × 10^22 gold atoms) / (50 billion gold atoms/drop) = 3.14 × 10^7 drops of sea water

Since 1 drop is equal to 0.05 mL, the volume of sea water required would be:

3.14 × 10^7 drops × 0.05 mL/drop = 1.57 × 10^6 mL

Converting this to gallons, we have:

1.57 × 10^6 mL × (1 L/1000 mL) × (1 gal/3.785 L) = 414 gallons of sea water

Therefore, it would require approximately 414 gallons of sea water to produce 1 troy ounce of gold.

Answer 2

In order to answer this question, set up dimensional analysis, you have to cancel out the number of grams while keeping the amount of sea water per troy oz.
So now you have the density of sea water in terms of gold (g/mL) flip it upside down mL/g.
(.05mL seawater/1.635*10^-11 grams of gold) * (31.3 grams/troy oz) = mL sea water needed to make 1 troy oz (9.5107x10^10 mL/troy oz)
then convert mL to gallons ( (9.5107x10^10 mL/troy oz) x (2.64x10^-4 gallons/1mL) )
= 25108256.88 gallons which when you round this off, you’ll have 30000000.