A solid containing species $a$ has been analyzed and the mole fraction profile has been found to obey the following function of $y$ alone:

\[x_{a}=a_{o}\left(y-K y_{o}\right)^{\frac{1}{3}} \quad a_{o}, y_{o}, K \text { - constants. }\]

a. Assuming a constant value for the diffusivity, $D_{a b}=D_{a b o}$, and a dilute solution of $a$ in $b$, has the system reached a steady state, i.e., does it obey the continuity equation in one dimension?

b. Assuming $a$ diffused through stagnant $b\left(N_{b} \approx 0\right)$ and has reached steady state, what can you say about how the diffusivity varies as a function of composition?