Insects do not have lungs as we do, nor do they breathe through their mouths. In
ID: 1915720 • Letter: I
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 1.48 mm long with a cross-sectional area of 1.16 x 10-9m2. The concentration of oxygen in the air outside the insect is 0.698 kg/m3, and the diffusion constant is 1.24 x 10-5 m2/s. If the mass per second of oxygen is diffusing through a trachea is 1.10 x 10-12 kg/s, then find the oxygen concentration at the interior end of the tube.Explanation / Answer
m = [DA(C2-C1)]t/L This looks like a rate equation if you move 't' to the left side: m/t = DA(C2-C1)/L Note that m/t, not m, equals 1.45E-12 kg/s. Now if C1 is the high concentration I'd think it would be m/t = DA(C1-C2)/L Then m/t*L/(DA) = C1-C2 ==> C2 = C1-m/t*L/(DA) = 0.779-1.45E-12*0.00143/(1.7E-5*1.57E-9) = 0.701312 kg/m^3 (In other words, the same difference from the outside density 0.779 kg/m^3 but downward not upward.)