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.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# How can you find this differential equation?

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