How many liters of seawater would have to be processed to recover 1 kg of gold?

Question

A cubic meter of ocean water has 6 x 10^-6 g gold. If the total mass of the water in Earth's oceans is 4 x 10^20kg, how many kilograms of gold are distributed throughout the oceans? Assume that the density of seawater is 1g/cm3. How many liters of seawater would have to be processed to recover 1 kg of gold.

There's two questions to this problem. I would like to know how you would sove this problem and what's the answer?

Answer 1

To get kg of gold, first, you convert your density in g/cc to Kg/m^3 which is 1000 kg/m^3. But since total mass of the water in Earth's oceans is 4 x 10^20kg, you can get the the volume of the water in the oceans.
4 x 10^20kg/1000 kg/m^3 = 4 x 10^17 m^3.

But one cubic meter of ocean water has 6 x 10^-6 g gold, so

4 x 10^17 m^3 x (6 x 10^-6 g gold/m^3) = 24 x 10^11 g of gold
or converting to kilograms = 24 x 10^8 Kg.

To get the number of liters, use 6 x 10^-6 g gold/ m^3 or convert to 6x10^-9 kg/m^3.

and use the following conversion factors,
1 liter = 1000 cc or cm^3
m = 100 cm, m^3 = 10^6 cm^3, you should get

1.667 x 10^11(!!! ) Liters just to recover 1 kg of gold!!!

So you see, nobody is applying to mine the oceans for gold.