- #1

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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.