Question

I have been picturing functions like enthalpy and Gibbs free energy as mathematical tools, which were defined in such a way as to be useful for some specific cases. I understood enthalpy as a useful tool for calculating heat when the only work being done was P-V and the system was closed and at constant pressure. Enthalpy being a state function can be represented as a function of intensive properties, this makes it useful to calculate heat, heat being a path function it is difficult to tabulate experimental values to calculate heat in other cases (different temperature ranges, different substances, etc), but for enthalpy it is not, it is easy to tabulate experimental values that do not depend on mass or path.

For Gibbs energy I did the same, i thought it was a useful function to determine if a process would be spontaneous or not, or in an equilibrium with quantities easier to measure and to control in experimental settings, those being temperature and pressure.

But now that I've been studying solutions all the meaning I had given to Gibbs energy has been thrown out the window. My text book just grabs Gibbs energy to study solutions without a particular justification to do so

If nG=f(T,P,n1,..,nj)
the total differential is

d(nG)=nVdp−nSdT+∑iμidni

Where a new a new property is introduced, the chemical potential. I can follow the math and everything, but what does Gibbs free energy mean here? Why it gets picked up to study solutions? Why not enthalpy or enthropy? Physically now what does G
mean? It's not work or heat, nor a criteria to determine spontaneity, I don't know what it is and neither why does it work. Not resolving these doubts makes it difficult to follow what happens in the rest of the chapter. Everything is build upon this function, but what is this function? A result of G=2Jmol
in this context what would it mean? How does G
manage to keep everything together?

Another thing, this is an easier question to answer, why do thermodynamics books always use ≡
to define such functions? Why not just =
?

Answer 1

Gibbs free energy is used in solution chemistry to predict process spontaneity and chemical equilibria at constant temperature and pressure. It accounts for usable energy after entropy—a crucial factor in chemical reactions. The chemical potential μ is introduced to understand the contributions of different species in a solution.

Step-by-step explanation:

Gibbs Free Energy in the Context of Solutions

The Gibbs free energy (G), defined by Josiah Willard Gibbs, is a thermodynamic property that combines the system's enthalpy (H) and entropy (S) as G = H - TS. In the realm of solutions, Gibbs energy becomes extremely useful because it allows us to predict the spontaneity of processes at constant temperature and pressure, conditions under which most chemical reactions occur. When dealing with solutions, it is often more practical to consider changes in Gibbs energy since it reflects the usable energy after accounting for entropy, which is crucial for understanding and predicting chemical equilibria.

Introducing the chemical potential μ in the total differential of Gibbs energy is essential for solutions as it accounts for the contribution of each species (ni) in the system. The value of G is not a direct measure of work or heat but represents the maximum non-expansion work that can be obtained from a system at constant temperature and pressure. A result such as G=2 J/mol indicates the amount of useful energy available from the system to perform work under the specified conditions.

The use of ≡ to define thermodynamic functions emphasizes that these are precise, fundamental definitions rather than empirical equations or approximations. This distinction is important because thermodynamic functions like Gibbs free energy are foundational concepts with specific mathematical definitions in the field of thermodynamics.