Insects do not have lungs as we do, nor do they breathe through their mouths. In

Question

Insects do not have lungs as we do, nor do they breathe through their mouths. Instead, they have a system of tiny tubes, called tracheae, through which oxygen diffuses into their bodies. The tracheae begin at the surface of the insect's body and penetrate into the interior. Suppose that a tracheae is 1.20 mm long with a cross-sectional area of 2.98 x 10-9m2. The concentration of oxygen in the air outside the insect is 0.670 kg/m3, and the diffusion constant is 1.97 x 10-5 m2/s. If the mass per second of oxygen is diffusing through a trachea is 1.20 x 10-12 kg/s, then find the oxygen concentration at the interior end of the tube.

I have entered the calculations and the answer is showing up as 1.36e15. I know that is not right but every time I rework it that is still what I get. Can I get a verification of math. I know only one way to work it.

Explanation / Answer

m = [DA(C2-C1)]t/L

m/t = DA(C2-C1)/L

Note that m/t, not m, equals 1.20 x 10-12 kg/s.

m/t = DA(C1-C2)/L

Then

m/t*L/(DA) = C1-C2

C2 = C1-m/t*L/(DA) = 0.670-1.20 x 10-12*0.00120/(1.97 x 10-5*2.98 x 10-9) = 0.645 kg/m^3

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