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## Main Question or Discussion Point

This is actually a chemistry problem, but I feel it's more appropriate posted here, as I'm not having trouble with the chemistry but rather the mathematics. To avoid mixing subjects, I'll keep chemistry jargon out.

We're given the formula for a component, and the problem request we give another component (which happens to be the derivative of the component given).

Given formula: G

where C, R, and T are constants for our purposes. (For clarity, A and B are different substances. Normal script T is temperature and subscript T is total, or the additive of components A and B for that variable)

In the case of the problem, the component x

and μ

So, solving for μ

Now, onto my question. A certain equation says that

n

And the problem requests I find a differential equation to solve for μ

Any help would be appreciated. Thanks.

We're given the formula for a component, and the problem request we give another component (which happens to be the derivative of the component given).

Given formula: G

_{T}= C + RTln(x_{A})/x_{a}where C, R, and T are constants for our purposes. (For clarity, A and B are different substances. Normal script T is temperature and subscript T is total, or the additive of components A and B for that variable)

In the case of the problem, the component x

_{A}= n_{A}/n_{T}and μ

_{A}= ∂G_{T}/∂n_{A}So, solving for μ

_{A}, we get μ_{A}= RT(1-ln(x_{A}/ x_{A}^{2}n_{T})Now, onto my question. A certain equation says that

n

_{B}dμ_{B}= -n_{A}dμ_{A}And the problem requests I find a differential equation to solve for μ

_{B}, but the required integration doesn't make sense to me. I mean, I assume I'm supposed to integrate both sides using the previously solved for μ_{A}. But I haven't taken a differential equations class, so I'm not sure how to produce a differential equation for this relation using the information given.Any help would be appreciated. Thanks.