Concentration and diffusion of oxygen in the Earth's atmosphere

[Yuriick]

Homework Statement

1. Estimate the concentration of oxygen in the Earth's atmosphere (in molecules / m^3), at room temperature and at sea-level, assuming the fact that oxygen comprises 21 percent of the Earth's atmosphere by volume.

2. If you were to place a perfect oxygen sensor of molecular size (e.g. radius of 1 Angstrom) on the surface of the Earth, at what rate would it collect oxygen molecules?

Homework Equations

The perfect absorber, at steady state, sees a concentration profi le of the reagent that it is absorbing (e.g. oxygen) given by:

(1) $c(r) = c_{0} (1-\frac{R}{r})$
where $c(∞) = c_{0}$ and $c(R) = 0$


(2) $J = -D \frac{∂ c(r)}{∂r}$
where J is the diffusion flux and D is the diffusion coefficient

The total flux of oxygen:
(3) $\Phi = Area*J = 4\pi R^{2}J$

The Attempt at a Solution

I'm really stuck at question 1, I'm not quite sure how to star it.

I'm pretty sure I know what to do for # 2. I'm given the diffusion coefficient D. Using the formula for c(r) I can use equation (2), to get

$J = -D \frac{∂ c(r)}{∂r} = -\frac{c_{0}D}{R}$

Would this be the final answer, or is the question asking for the total flux, $\Phi$.

I feel like I'm over thinking the first question, any ideas would be really appreciated. Thanks.

 

[Chestermiller]

Here is a hint for part 1: You need to use the ideal gas law. Use it to find the number of moles of nitrogen plus oxygen per unit volume.