Chemical potential and it's implications in an open system
Too long for a comment, so here goes.

It's quite subtle and I'm really not sure how to explain in words, but the gist is that the chemical potential does not reflect a real, physical process of adding a substance that can be carried out. If that were the case, then the chemical potential would be the difference in the Gibbs free energies of the two systems:


System 1: $n$ moles of substance and $\mathrm{d}n$ moles of substance, separated by some imaginary barrier
System 2: $n + \mathrm{d}n$ moles of substance


and measuring the chemical potential would simply mean removing the imaginary barrier, allowing intermolecular attractions to form, etc. But that's not the case.

The chemical potential is the difference between these two systems:


System 1: $n$ moles of substance
System 2: $n + \mathrm{d}n$ moles of substance


That's all there is to it. Where do the extra $\mathrm{d}n$ moles come from? It doesn't come from anywhere. There's no real physical process going from System 1 to 2 here, so don't think of it as one.

Since Gibbs free energy is an extensive property, the $\mathrm{d}n$ moles of substance carry their own Gibbs free energy, just like they carry their own internal energy. That is why the chemical potential is positive - yes, the formation of intermolecular forces, etc. will affect the exact value of the chemical potential, and in a sense that is why the chemical potential is a partial derivative - but remember just simply having more of the substance means that there is more Gibbs free energy.