Question

We're told oxygen is the most common element in the Earth's solid crust. But how much oxygen is there? Let's compare to the amount of oxygen in the Earth's atmosphere, like this:

The most common minerals in the Earth's crust are feldspars, and albite
NaAlSi3O8
is a typical feldspar. Let's assume the entire crust is made of albite, with a density of /2.6gcm3.
The radius of the Earth is 6371.km and let's say the crust is the upper 75.0 km of it.
Let's model the Earth's atmosphere as a layer on top of the Earth about
100.km thick with an average density of
/0.99gm3, and which is 23.1% oxygen by mass.
Use this information to calculate the ratio of the mass of oxygen in the Earth's atmosphere to the mass of oxygen in the Earth's crust. Round your answer to the correct number of significant digits.

Answer 1

To find the ratio of the mass of oxygen in the Earth's atmosphere to that in the crust, we calculate the masses of the crust and atmospheric layers considering their volumes and densities, then account for the proportion of oxygen in albite and atmospheric gases.

Step-by-step explanation:

Ratio of the Mass of Oxygen in Earth's Crust vs. Atmosphere

To calculate the ratio of the mass of oxygen in the Earth's atmosphere compared to that in the Earth's crust, we need to apply a mathematical approach to the given data. The mass of a cylindrical shell of the Earth's crust can be found using the formula for the volume of a sphere (V = ⅔3π
`r^(3)`) and subtracting the inner spherical volume from the outer to get a shell volume, and then multiplying by the density of albite. Similarly, the mass of the atmospheric shell can be calculated using the same shell volume formula and multiplying by the density of the atmosphere.

Once we have these masses, we then find the percentage of oxygen in each material - albite in the crust and atmospheric compounds - and multiply this by the total masses to get the mass of oxygen in both. Finally, the ratio is the mass of atmospheric oxygen divided by the mass of crustal oxygen. Based on the provided data, the mass of crustal oxygen is quite higher than that in the atmosphere due to the large volume and high percentage of oxygen in silicates like albite.