Oxygen Concentration: Insects & Tracheae

In summary: Therefore, the concentration of oxygen at the interior end of the tube is 0.09 kg/m3.In summary, the concentration of oxygen inside an insect's body is determined by the diffusion of oxygen through its tracheae, which are tiny tubes that penetrate into the interior. Using the equation m/t = (DA(deltaC)) / L, we can calculate the concentration of oxygen at the interior end of a trachea based on the mass flow rate of oxygen, diffusion constant, and length and cross-sectional area of the trachea. In this case, the concentration of oxygen inside the insect is found to be 0.09 kg/m3.
  • #1
ElikuAberts
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Homework Statement



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 trachea is 1.9 mm long with a cross-sectional area of 2.1 10-9 m2. The concentration of oxygen in the air outside the insect is 0.23 kg/m3, and the diffusion constant is 1.1 10-5 m2/s. If the mass per second of oxygen diffusing through a trachea is 1.7 10-12 kg/s, find the oxygen concentration at the interior end of the tube.

Homework Equations



m/t = (DA(deltaC)) / L

The Attempt at a Solution



m/t = (DA(deltaC)) / L
1.7 E-12 = ((1.1 E-5 m^2/s)(2.1 E-9 m^2)(change in C)) / .0019 m
change in c = .3698268
(inside concentration - outside concentration) = .3698268
(inside concentration - .23 kg/m^3) = .3698268
inside concentration = .5998 kg/m^3

Thats not the right answer... but that is what I keep getting. Someone at school told me that the equation m/t = (DA(deltaC)) / L was correct, so that means I must be messing up after that, but I don't know where and I can't figure it out! If anyone would help me, I would reeeally appreciate it! :-)
 
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  • #2
For this system, the mass flux of oxygen is given by
[tex]j = D \frac{(c_o - c_i)}{L}[/tex]
Where [itex]j = \frac{f}{A}[/itex], and f is the mass flow rate of oxygen. I can derive the above equation if needed to. What we need is to find the concentration of oxygen inside the insect, so
[tex]c_i = c_o - \frac{fL}{DA}[/tex]
[tex]c_i = 0.23 \frac{kg}{m^3} - \frac{\left(1.7 \cdot 10^{-12} \frac{kg}{s} \right) (1.9 \cdot 10^{-3} m)}{ \left( 1.1 \cdot 10^{-5} \frac{m^2}{s} \right) (2.1 \cdot 10^{-9} m^2)} = 0.09 \frac{kg}{m^3}[/tex]
This result is logical, if oxygen diffuses from the exterior into the body of the insect, then the concentration of oxygen in the outside must always be greater than the concentration in the inside.
 

Related to Oxygen Concentration: Insects & Tracheae

1. What is the role of oxygen concentration in insects?

Oxygen concentration is crucial for the survival of insects as it is needed for cellular respiration, which provides energy for all physiological processes. Insects have a high demand for oxygen due to their small body size and fast metabolism.

2. How do insects obtain oxygen?

Insects have a specialized respiratory system called tracheae, which are tiny tubes that extend throughout their bodies. These tracheae allow oxygen to directly diffuse into their tissues, eliminating the need for a circulatory system.

3. What factors affect oxygen concentration in insects?

Oxygen concentration in insects can be influenced by various factors such as temperature, humidity, and altitude. Insects in warmer temperatures require more oxygen for metabolic processes, while those in high altitudes may have to adjust to lower oxygen levels.

4. Can insects survive in low oxygen environments?

Some insects, such as diving beetles and mosquito larvae, have adaptations that allow them to survive in low oxygen environments. They have the ability to store oxygen in their bodies or have specialized respiratory structures that can extract oxygen from water or air with low oxygen levels.

5. How does oxygen concentration affect the size and behavior of insects?

Research has shown that oxygen concentration can affect the size and behavior of insects. In low oxygen environments, insects may grow smaller and have slower development rates. Additionally, high oxygen levels have been linked to increased aggression and mating behavior in some insect species.

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