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Total mass of each of these elements in Earth's crust?

I've been on this problem for days and really need help. Work would be amazing, but even the theory on how to do this would be helpful. Thanks!

Earth's surface area is 5.10x10^8 km^2; it's crust has a mean thickness of 35 km and a mean density of 2.8 g/cm^3. The two most abundant elements in the crust are oxygen (4.55x10^5 g/t, where t stands for metric ton; 1 t= 1000 kg) and silicon (2.72x10^5 g/t), and the two rarest nonradioactive elements are ruthenium and rhodium, each with an abundance of 1x10^-4 g/t. What is the total mass of each of these elements in Earth's crust?

Answers (2)

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  1. calculate the volume of the crust in km^3:

5.1 X 10^8 km^2 X 35 km = 1.785X10^10 km^3

  1. convert volume into cm^3:

1.785 X 10^10 km^3 X (1000 m/km)^3 X (100 cm/m)^3 = 1.785 X 10^25 cm^3

  1. Use the density to calculate the mass of the crust, first in g and then convert that to metric tons:

11.785 X 10^25 cm^3 X 2.8 g/cm^3 = 5.0 X 10^25 g

5.0 X 10^25 g X 1 kg/1000 g X 1 t / 1000 kg = 5.0 X 10^19 t

  1. Now, use the mass and abundance to calculate the mass of an element:

5.0 X 10^19 t X (2.72 X 10^5 g/t) = 1.4 X 10^25 g (which you could convert back to metric tons, if you like)

5.0 X 10^19 t X (1X10^-4 g/t) = 5X10^15 g