Question

In class, we determined that the larger insect was not able to achieve a sufficient rate of diffusion from point X to point Y in its tracheal satisfy the oxygen demand of its cells without increasing the cross-sectional area of its tracheal tubes.

The variables of Fick's Law that we determined for our larger insect with thin trachea is shown in the table below:
Assuming that the cells of the insect require an oxygen supply of 2.0 * 10-6 mL÷min (= 0.000002), use Fick's Law to determine what the cross-sectional area (A) of this larger insect has to minimally be in µm2 to maintain the minimal rate of diffusion of oxygen of 2.0 * 10-6 mL÷min.
Round your answer to the nearest full µm2.

Answer 1

To calculate the minimum cross-sectional area of the insect's tracheal tubes, use Fick's Law and the given rate of diffusion. The necessary values for diffusivity, partial pressure differences, and path length must be known and substituted into the rearranged version of Fick's Law to solve for the cross-sectional area, which is then rounded to the nearest full µm².

Step-by-step explanation:

In order to determine the minimum cross-sectional area (A) required for the larger insect's tracheal tubes to maintain a diffusion rate of oxygen at 2.0 * 10-6 mL/min using Fick's Law, we would use the formula:

J = (D * A * (P2 - P1)) / L

Where:

• J is the flux (rate of diffusion - which is given as 2.0 * 10-6 mL/min in this scenario)
• D is the diffusivity of oxygen in the medium
• A is the cross-sectional area of the tracheal tubes we need to find
• P2 and P1 represent the partial pressures of oxygen at two points X and Y respectively
• L is the path length between points X and Y

To solve for A, we rearrange the equation to:

A = J * L / (D * (P2 - P1))

Substitute the known values into the equation, and determine the value of A. Assuming that diffusivity (D), the difference in partial pressures (P2 - P1), and the path length (L) have been given in the problem, which have not been provided in the question. The final answer would be rounded to the nearest full µm2 as required by the student's question.