Question

The basic equation describing the diffusion of one medium through another stationary medium is (a) \(j_{A}=-C D_{A B} \frac{d\left(C_{A} / C\right)}{d x}\) (b) \(j_{A}=-D_{A B} \frac{d\left(C_{A} / C\right)}{d x}\) (c) \(j_{A}=-k \frac{d\left(C_{A} / C\right)}{d x}\) (d) \(j_{A}=-k \frac{d T}{d x}\) (e) none of them

Short answer

a) \(j_{A}=-C D_{A B} \frac{d\left(C_{A} / C\right)}{d x}\) b) \(j_{A}=-D_{A B} \frac{d\left(C_{A} / C\right)}{d x}\) c) \(j_{A}=-k \frac{d\left(C_{A} / C\right)}{d x}\) d) \(j_{A}=-k \frac{d T}{d x}\) e) none of them Answer: e) none of them

Step-by-step solution

Review Fick's law of diffusion

First, let us recall Fick's law of diffusion, which describes the diffusion of one medium through another stationary medium. It states the following: \(j_A = -D_{AB} \frac{dC_A}{dx}\) Where: - \(j_A\): Diffusion flux of medium A through medium B (i.e., the amount of A that would flow through a unit area per unit time). - \(D_{AB}\): Diffusion coefficient, which represents the ability of medium A to diffuse through medium B. - \(\frac{dC_A}{dx}\): The concentration gradient of medium A in the mixture, with respect to the distance x.

Compare Fick's law to the given options

Next, we will compare Fick's law of diffusion to each of the given options (a) through (e): (a) \(j_{A}=-C D_{A B} \frac{d\left(C_{A} / C\right)}{d x}\): This is not the correct formula, as it involves an additional factor of C, the overall concentration of the mixture, which isn't present in Fick's law. (b) \(j_{A}=-D_{A B} \frac{d\left(C_{A} / C\right)}{d x}\): This option looks similar to Fick's law, but the term in the derivative is the ratio of \(C_A\) to C, which is not the same as in Fick's law. (c) \(j_{A}=-k \frac{d\left(C_{A} / C\right)}{d x}\): This option also involves the ratio \(C_A / C\), and the diffusion coefficient has been replaced by a constant k. This is not Fick's law. (d) \(j_{A}=-k \frac{d T}{d x}\): This option is not correct either, as it does not include the variables related to the concentration of medium A. Instead, it involves the temperature T, which is not a part of Fick's law. (e) none of them: As none of the given options match Fick's law of diffusion, we conclude that the answer must be (e) none of them.