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Homework Help: Concentration and diffusion of oxygen in the Earth's atmosphere

  1. Feb 4, 2013 #1
    1. The problem statement, all variables and given/known data

    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?

    2. Relevant 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) [itex]c(r) = c_{0} (1-\frac{R}{r})[/itex]
    where [itex] c(∞) = c_{0}[/itex] and [itex] c(R) = 0 [/itex]

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

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

    3. 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

    [itex] J = -D \frac{∂ c(r)}{∂r} = -\frac{c_{0}D}{R}[/itex]

    Would this be the final answer, or is the question asking for the total flux, [itex] \Phi [/itex].

    I feel like I'm over thinking the first question, any ideas would be really appreciated. Thanks.
  2. jcsd
  3. Feb 4, 2013 #2
    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.
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