1. I found it always helpful to find an answer to a question in many different ways. This allows us to check the self-consistency of different methods. With that in mind, I'm constructing this question, the answer to which is not clear to me. I would hope that I would learn something from your efforts. Consider the case of Langmuir adsorption with a surface exposed to a solution of a species of concentration C. We are interested to find the adsorbed amount. B. We can obtain the desired result by Method 1 in the hint that I provided. Here you write down the total Helmholtz free energy, from which you determine the chemical potential of the species in the bulk.