Diffusion across a thin film


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> [![enter image description here](https://i.stack.imgur.com/Y68zw.png)](https://i.stack.imgur.com/Y68zw.png)
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> Given this concentration profile, I am to (1) determine at which side substance A will diffuse out of the membrane and (2) chose one of the following profiles below which represents the concentration of a substance A at steady-state.
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> [![enter image description here](https://i.stack.imgur.com/G1xYW.png)](https://i.stack.imgur.com/G1xYW.png)
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(1) *Diffusion occurs from an area of high concentration to an area of low concentration*. Therefore, substance A would diffuse from the left to the right. However, in the question when they ask "at which side will the substance diffuse out of the membrane", should I answer at the right side or that the substance stays within the membrane? 


(2) I know that the concentration profile at steady-state should be linear, however I'm wondering what the difference between (A) and (B) is. I assume that (A) is the correct answer to this question since substance A has a higher concentration than the concentrations at the membrane wall and hence the slope should start a little above the concentration at the wall. Is this correct or does steady-state affect the concentration profile of the substance?





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> (1) determine at which side substance A will diffuse out of the membrane
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> > should I answer at the right side or that the substance stays within the membrane?
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Neither, because the concentration is higher in the membrane than either side, the substance will flow out of both sides **initially** at least. After a while the material will flow from left to right (high concentration to low concentration) and converge towards steady state.



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> (2) chose one of the following profiles below which represents the concentration of a substance A at steady-state.
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First thing - When doing diffusion problems immediately refer to [Fick's laws of diffusion](https://en.wikipedia.org/wiki/Fick%27s_laws_of_diffusion).


Fick's first law assumes a steady state system and is given as:


$$J = -c D\frac{dx}{dz}\quad \text{or more simply} \quad J = -D\frac{\Delta C(x)}{\Delta z} \quad \text{or more generally}\quad J = -cD\ \nabla x$$


Where $J$ is flux (mols through an cross-sectional area per time), $c$ is total concentration, $C(x)$ is the concentration at point $x$, $D$ is the diffusion constant, $x$ is the mole fraction and $z$ is position. 


For steady state to occur, $J$ must by definition be constant through the entire membrane and thus $-D\frac{\Delta C(x)}{\Delta z}$ must be constant through the entire interface. Since $D$ is already a fixed constant, we can assume $\frac{\Delta C(x)}{\Delta z}$ must also be constant. Thus the plot with a constant slope is the steady state profile which is **B**.


Q.E.D.


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