Originally Posted by **knickers** I’m now trying to figure out the mass flow of water into the container each time the lid is opened |

I'm not sure using Fick's law will give you the best result in a situation where mixing occurs (i.e. fluid inside the container mixes with fluid outside of the container). You'll probably get better results using some kind of advective mass transfer equation.

For example, if you consider the total mass of water vapour inside the container to change, then you have an equation:

$\displaystyle \frac{dM}{dt} = -\dot{m}A$

where $\displaystyle \dot{m}$ is the mass flux (in kg/(s.m2)) and A is the surface area of the opening.

You might also gain some insight by looking into psychrometrics, which deals with humidity of air based on different transitions along a chart. It gives a set of formulae to deal with changes in humidity based on different kinds of processes.