[orgo814]

This attached question in my study book asks for the relationship between chemical potentials of two components in one phase at equilibrium.

We know that u1n1 + u2n2 = 0 so solving for u1 like the question asks I get option C. My book however says the answer is B. I can't figure out what I am missing here.

[mjc123]

Ever considered posting your pictures the right way up?

The answer is A. Species in equilibrium have the same chemical potential.

We know that u1n1 + u2n2 = 0

This is not true. At equilibrium, for a small change in composition μ₁dn₁ + μ₂dn₂ = 0

[orgo814]

The answer is B according to the ACS. And they are face up from my device so I'm not sure why you're seeing the picture from another point of view

[mjc123]

Does the book just say "B" or does it give some explanation? It might be just a typo - these mistakes do happen in textbooks. But it's definitely a mistake.

[orgo814]

No explanation just says B. Although I looked in Atkins textbook and response C seems to be the correct one not A. I'm open to hearing what you say though.

Apparently in deriving this expression the fact that G is a state function is used. I'm not sure how that applies here.

[mjc123]

I'm sure Atkins doesn't say that; are you reading him correctly?
G = n₁μ₁ + n₂μ₂
At equilibrium G is a minimum (not zero), (dG/dn₁)_n1+n2 = 0.
μ₁dn₁ + μ₂dn₂ + n₁dμ₁ + n₂dμ₂ = 0
From the Gibbs-Duhem equation (answer B to the previous question on your picture, whatever it was) Σn_idμ_i = 0 at constant T,P; and dn₂ = -dn₁.
Hence μ₁ - μ₂ = 0
Chemical potential is an intensive property which is equal in substances in chemical equilibrium - there is no tendency for reaction to go in either direction because ΔG for a small deviation is zero. In this it is analogous to other "potential" quantities, e.g. temperature (which can be regarded as thermal potential) is the same in two bodies at thermal equilibrium, and heat won't flow between them; charge won't flow if there is no electric potential gradient, etc.