Integrating a concentration profile

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To determine the increase in mass of a sample from a diffusion profile, one must integrate the concentration function, which is typically expressed in moles per unit volume. The discussion clarifies that simply plotting moles against distance is insufficient, as moles alone do not represent concentration. The integral yields units of moles per square centimeter, which can then be multiplied by the sample's cross-sectional area to find the total moles present. It is emphasized that a proper understanding of concentration is crucial for accurate calculations. Ultimately, integrating the diffusion profile provides valuable insights into the mass distribution within the sample.
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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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