Solving the Concentration Gradient: A Calculation Challenge

In summary, the question involves calculating the flux of nitrogen through a 1-mm FCC iron sheet at 1200℃ with concentrations of 0.04 atomic percent and 0.005 atomic percent. The solution uses the formula Ac/Ax to determine the flux and the volume of the cell needs to be included in the calculation. The final answer is 7.57 x 1012 N atoms/cm2-s.
  • #1
tkuehl
2
0
I have a problem with calculating the concentration gradiant. Here is the question and the solution from the solution manual and the numbers don't add up.

A 1-mm sheet of FCC iron is used to contain nitrogen in a heat exchanger at 1200℃. The concentration of N at one surface is 0.04 atomic percent and the concentration at the second surface is 0.005 atomic percent. Determine the flux of nitrogen through the foil in atoms/cm2−s.

solution
(a) Ac/Ax = [.00005 - .0004]*4 atoms/cell(3.589E-8)^3
--------------------------------------------
.1cm
=-3.03 x 1020 N atoms/cm3-cm

(b) J=-D(Ac/Ax) = -0.0034 exp[-34,600/(1.987)(1473)](-3.03 x 1020)
= 7.57 x 1012 N atoms/cm2-s

I would like to know how they get the answer in part a.
 
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  • #2
I figured it out. the volume of the cell needs to be in the denominator. Our professor takes everything out of the solutions manual and never checks it.
 

1. What is a concentration gradient?

A concentration gradient is a gradual change in the concentration of a substance over a distance. It occurs when there is a higher concentration of a substance in one area compared to another, and the substance naturally moves from high to low concentration in order to reach equilibrium.

2. Why is solving the concentration gradient important?

Solving the concentration gradient is important because it allows us to understand how substances move and distribute within a system. This information is crucial in various fields, such as chemistry, biology, and environmental science, as it helps us to predict and control the movement of substances in different environments.

3. What factors affect the concentration gradient?

The concentration gradient is affected by several factors, including the initial concentration of the substance, the size of the system, the permeability of the barrier, and the temperature. Other factors, such as the presence of other substances and the rate of diffusion, can also influence the concentration gradient.

4. How do you calculate the concentration gradient?

The concentration gradient can be calculated by dividing the change in concentration by the distance over which the change occurs. This can be represented by the formula: concentration gradient = (C2 - C1)/d, where C2 is the final concentration, C1 is the initial concentration, and d is the distance.

5. What are some real-life examples of concentration gradients?

Some real-life examples of concentration gradients include the movement of oxygen and carbon dioxide in the lungs during respiration, the diffusion of nutrients and waste products in cells, and the distribution of chemicals in the environment through processes like osmosis and active transport.

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