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For partial molar entropy there is a bar that is positioned above the $G$ with a subscript I that is sometimes added to the $G~(\bar{G}).$ The bar I read sometimes denote the "partial nature of the $G$".

However, is it not rhetorical. I am looking for the explanation as to what is so partial about this quantity with regard to it's occurrence in the equation.

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  • $\begingroup$ The bar denotes we took the derivative with respect to composition. Molar free energy would just be the free energy divided by "n" the composition. For a pure component these are the same, but not for a mixture. Not everyone uses a bar also...Like all notation, you have to pay attention with each new article you read, what they mean. $\endgroup$ – Charlie Crown Jul 15 at 4:11
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Thermodynamic properties are functions of composition, which can be represented as $(\chi _1,...,\chi _N)$ where $\chi _i$ is the mole fraction of component $i$ present in the system. Now imagine a change in the composition such that the amount of component $i$ is increased by a very small quantity $dn _i$ (alternately, imagine the system to be infinitely large), and a thermodynamic property $X$ is changed by $dX$. Then (using the notation you describe) we define the partial molar property as $$\bar{X}=\left(\frac{\partial X}{\partial n_i}\right)_{p,T,n_j}$$ This notation means that we make a limiting, infinitely small change in $n_i$, such that the change in $X$ is for all practical purposes nil, ie $\Delta X=0$. The partial molar quantity describes the slope of the property $X$ (which can be represented as a surface in a multidimensional manifold) along the composition coordinate $n_i$, at a specific composition $(\chi _1,...,\chi _N)$.

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