Integrating a concentration profile

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SUMMARY

The discussion focuses on integrating a diffusion profile to determine the increase in mass of a sample based on concentration versus distance. Participants clarify that "moles" alone do not represent concentration, which is typically expressed as moles per unit volume. The integral of the diffusion profile yields units of moles per square centimeter, which can be used to calculate the total number of moles by multiplying by the sample's cross-sectional area. This approach is essential for accurately relating concentration to the overall mass of the sample.

PREREQUISITES
  • Understanding of diffusion profiles and concentration measurements
  • Familiarity with integration techniques in calculus
  • Knowledge of units in chemistry, specifically moles and concentration
  • Basic principles of mass and volume relationships
NEXT STEPS
  • Research how to calculate total moles from concentration profiles
  • Learn about integrating functions in multiple dimensions for diffusion analysis
  • Study the relationship between concentration and mass in chemical systems
  • Explore methods for measuring cross-sectional area in experimental setups
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Researchers in chemistry, physicists studying diffusion processes, and anyone involved in quantitative analysis of concentration profiles in materials science.

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Hello-

I have a diffusion profile, in which I plot the decrease in concentration versus distance of my sample. I am trying to find the increase in mass of the overall sample. How would I do this?

I have integrated the function and am wondering what type of information that would supply my. Units would be concentration*distance. moles*m
 
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How are concentration of something and "mass of the overall sample" related?
If your diffusion (and concentration) is not one-dimensional, you should consider this in the integral.
"Moles" is not a concentration.
 
I did not actually plot the concentration. My diffusion profile consists of an initial amount of substance a in moles n(a) and plots it as a function of distance in the sample. so I am trying to figure out what information I get when I integrate this profile. moles*meters would be the units
 
Again, "moles" is not a concentration. Moles as a function of distance are meaningless, unless it means the total amount of substance between that point and some other point. In that case, I don't see any application of the integral.
 
Concentration is usually expressed as moles per unit volume (e.g., moles/cc). The integral of this is moles/cm2. To get the total number of moles in the sample, you then need to multiply by the cross sectional area of the sample.
 
I do not have a good working knowledge of physics yet. I tried to piece this together but after researching this, I couldn’t figure out the correct laws of physics to combine to develop a formula to answer this question. Ex. 1 - A moving object impacts a static object at a constant velocity. Ex. 2 - A moving object impacts a static object at the same velocity but is accelerating at the moment of impact. Assuming the mass of the objects is the same and the velocity at the moment of impact...

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