A cublic meter of ocean water contains 6x10^-5 g of gold. If the total mass of the water in Earth's oceans is 4x10^20 kg, how many kilograms of gold are distributed throughout the ocean? (Assume that the density of seawater is 1 g/cm3.) How many literes of seawater would have to be processed to recover 1kg of gold.(which as the value of about $8850 )
To calculate the mass of gold distributed throughout the ocean, we can multiply the mass of water in Earth's oceans by the concentration of gold in seawater.
Step 1: Calculate the mass of gold in one cubic meter of ocean water.
Given: Concentration of gold = 6x10^-5 g/m^3
Step 2: Calculate the total mass of water in Earth's oceans.
Given: Mass of water = 4x10^20 kg
To convert cubic meters to liters, we know that 1 cubic meter is equivalent to 1000 liters.
Step 3: Calculate the volume of seawater required to recover 1kg of gold.
Let's calculate each step one-by-one:
Step 1: Calculate the mass of gold in one cubic meter of ocean water.
Mass of gold in one cubic meter = Concentration of gold x Volume of water
Given: Concentration of gold = 6x10^-5 g/m^3
Volume of water = 1 m^3
Mass of gold in one cubic meter = (6x10^-5) g/m^3 x 1 m^3
Mass of gold in one cubic meter = 6x10^-5 g
Step 2: Calculate the total mass of water in Earth's oceans.
Given: Mass of water = 4x10^20 kg
Step 3: Calculate the volume of seawater required to recover 1kg of gold.
Given: Mass of gold = 1 kg
Density of seawater = 1 g/cm^3
1 kg = 1000 g
Volume of seawater required = Mass of gold / Density of seawater
Volume of seawater required = 1000 g / 1 g/cm^3
Volume of seawater required = 1000 cm^3
Since 1 liter is equal to 1000 cm^3, we have:
Volume of seawater required = 1000 cm^3 / 1000 cm^3
Volume of seawater required = 1 liter
Therefore, to recover 1kg of gold, you would need to process 1 liter of seawater.
Note: The given value of $8850 for 1kg of gold is not directly relevant to the calculation. It is the value of gold and does not affect the process of calculating the mass of gold distributed throughout the ocean or the volume of seawater required to recover 1kg of gold.