# What is Gibbs: Definition and 199 Discussions

In thermodynamics, the Gibbs free energy (or Gibbs energy) is a thermodynamic potential that can be used to calculate the maximum reversible work that may be performed by a thermodynamic system at a constant temperature and pressure. The Gibbs free energy (

Δ
G
=
Δ
H

T
Δ
S

{\displaystyle \Delta G=\Delta H-T\Delta S}
, measured in joules in SI) is the maximum amount of non-expansion work that can be extracted from a thermodynamically closed system (one that can exchange heat and work with its surroundings, but not matter). This maximum can be attained only in a completely reversible process. When a system transforms reversibly from an initial state to a final state, the decrease in Gibbs free energy equals the work done by the system to its surroundings, minus the work of the pressure forces.The Gibbs energy (symbol

G

{\displaystyle G}
) is also the thermodynamic potential that is minimized when a system reaches chemical equilibrium at constant pressure and temperature. Its derivative with respect to the reaction coordinate of the system vanishes at the equilibrium point. As such, a reduction in

G

{\displaystyle G}
is necessary for a reaction to be spontaneous at constant pressure and temperature.
The Gibbs free energy, originally called available energy, was developed in the 1870s by the American scientist Josiah Willard Gibbs. In 1873, Gibbs described this "available energy" as
the greatest amount of mechanical work which can be obtained from a given quantity of a certain substance in a given initial state, without increasing its total volume or allowing heat to pass to or from external bodies, except such as at the close of the processes are left in their initial condition.
The initial state of the body, according to Gibbs, is supposed to be such that "the body can be made to pass from it to states of dissipated energy by reversible processes". In his 1876 magnum opus On the Equilibrium of Heterogeneous Substances, a graphical analysis of multi-phase chemical systems, he engaged his thoughts on chemical-free energy in full.
If the reactants and products are all in their thermodynamic standard states, then the defining equation is written as

Δ

G

=
Δ

H

T
Δ

S

{\displaystyle \Delta G^{\circ }=\Delta H^{\circ }-T\Delta S^{\circ }}
.

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1. ### Thermodynamics Question Regarding Gibbs Free Energy, Enthalpy, Entropy

Hello, is someone able to explain why these two are wrong. I am not sure how to figure out the enthalpy direction as the reaction is not changing state of matter, nor is it changing temperature. (Please solve without calculating anything) Thank you
2. ### I Rewriting of Gibbs Free Energy in Peksin (Equations 13.35/13.36)

Hey all, On page 446 in Peskin, he provides 2 different ways of writing the Gibbs Free Energy: $$\textbf{G}(M,t) = M^{1+\delta}h(tM^{-1/\beta})$$, and $$\textbf{G}(M,t) = t^{\beta(1+\delta)}f(Mt^{-\beta})$$ where ##h## and ##f## are some initial condition functions that have a smooth limit as...
3. ### Understand Gibbs Free Energy & Activation Energy

Hi everybody, I don't understand what changes between these two graphs. In particular, why does free energy reach a minimum in one graph and a maximum in the other? Shouldn't a chemical reaction always have an energy maximum, represented by the activation energy?
4. ### Chemistry Confusion in relation of Gibbs free energy and equilibrium constant

SO2(g)+1/2O2(g)⇌SO3(g);ΔHo=-98.32KJ/mole,ΔSo=-95J/(mole-K). find Kp at 298 Kelvin? In given question at first Δ G will be calculated using formula ΔG = Δ H – T x ΔS, by putting the given values in formula we get ΔG = -70.01 kJ/mol. Then Keq will be calculated using equation = Δ G = -RT ln Keq...
5. ### I Effect of attractive interactions on Gibbs free energy

Will the presence of attractive interactions between gas molecules raise or lower the molar Gibbs energy of a gas relative to its ‘perfect’ value? I would think that these attracting forces result in a lower energy state. A decrease in the energy state implies a decrease in the enthalpy. A...
6. ### Gibbs free energy for superconductor in intermediate state

hi guys I am trying to derive the Gibbs free energy for a superconductor in the intermediate state , the book(Introduction to Superconductivity by A.C. Rose-Innes) just stated the equation as its : $$G(Ha) = Vgs(0)+\frac{V\mu_{o}H_{c}}{2n}[H_{a}(2-\frac{H_{a}}{H_{c}})-H_{c}(1-n))]$$ I am not...
7. ### Engineering Deriving the Wassiljewa mixture model equation

Hello, I'm in the process of deriving the Wassiljewa mixture model equation for a binary solution. I have to find an expression gE which represents the excess g term which is added to gIS, the ideal solution, to predict the g for a real solution. I have gotten up to a point but now I'm stuck...
8. ### A Why Do We Need Alchemical Methods to Compute Gibbs Energy Changes?

Hi, To compute, for example, the Gibbs energy change for a ligand binding to a protein, various so called alchemical methods are used in molecular dynamics simulations. My question is why can't we just obtain averaged Gibbs energies for 1) the free ligand and protein in the same water box, and...
9. ### I Gibbs paradox: an urban legend in statistical physics

Hi, I recently discovered that there is no real paradox in the question of the mixing of classical distinguishble particles. I was shocked. Most books and all my professors suggest that an extensible entropy could not be defined for distinguishble particles. I believe that many of you will be...
10. ### Thermodynamic meaning of molar Gibbs free energy

I know that when it is ΔG>0 , it means there is no spontaneity, when ΔG=0 there is equilibrium, and when ΔG<0, there is spontaneity. But what happens when this is in the context of partial molar properties, when G is molar? I suppose molar ΔG is referred to a solution. Right? In that case, is...
11. ### Gibbs "Paradox" and the Entropy of mixing

(not a paradox nowadays, but it was an issue for years) https://en.m.wikipedia.org/wiki/Gibbs_paradox It's not a question about a formula. I don't understand the motivation in physics to claim Gibbs mixing "paradox", the discontinuity point. What bothers the physicist to ask for a continuous...
12. ### Thermodynamics: Single/Homogeneous Phase Differences

#Can somebody please explain what is the difference between single phase and homogeneous phase in context with thermodynamics? #Also in the fundamental relations in thermodynamics like dg=vdp-sdT , it says this is applicable to homogeneous phase of constant composition. Isn't this equation...
13. ### Chemistry MCQ- What is the Gibbs free energy value?

Where have I gone wrong? According to the key, the right option is a.
14. ### I Why must the Gibbs Free Energy be proportional to N?

In the textbook Thermal Physics by Daniel Schroeder he says the following: However, I don't follow this argument. Let's say that G was the following: $$G(T, P, N) = (TPN)^{1/3}$$ Then $$G(\lambda T, \lambda P, \lambda N) = \lambda G$$ So $$G$$ is extensive, but $$G \not \propto N.$$
15. ### I How does the N signify the indistinguishability in the Gibbs Paradox?

Gibbs introduced the N! to then make S extensive. He then attributed the N! to the particles being indistinguishable. How does the N! signify the indistinguishability?
16. ### Gibbs' theorem and partial molar volume

In the chemical engineering text of Smith, VanNess, and Abbott, there is a section on partial molar volume. It states that Gibbs theorem applies to any partial molar property with the exception of volume. Why is volume different? In other words, when evaluating the partial molar volume of a...
17. ### Gibbs free energy problem

Summary: Please help me with this problem ,I can't do it The normal boiling point of liquid bromine is 58.2°C. At 9.3°C the equilibrium vapor pressure of liquid bromine is 100 torr. From this data, calculate the standard state Gibbs energy of formation of bromine vapor at room temperature...
18. ### Chemistry Create a Gibbs Free Energy challenge question

I was thinking about giving the bond energy to calculate the enthalpy change of some exothermic and spontaneous reaction. Than using that exothermic enthalpy to heat the own products and reagents. That would change the Gibbs free energy of the equation (as the elements will be in a different...
19. ### Confusion about the use of partial molar Gibbs free energy

If this belongs in classical physics, please move it there. But it seems like the kind of question chemistry people would know so I'm putting it here. I was reading a textbook on chemical thermodynamics, and it says to raise the partial molar Gibbs free energy of n moles a substance from...
20. ### Gibbs Free Energy Equation: why is the entropy change of the system not q/T ?

What is the entropy change of the system in the Gibbs Free Energy Equation? The general expression for entropy change is ΔS=q/T The only exchange between the system and the surroundings is ΔH done reversibly, with no PV work and no matter transfer, therefore q(syst) = ΔH(syst) therefore surely...
21. ### Standard Gibbs free energy equal to zero?

At equilibrium, we know that deltaG = 0. But what about deltaG_zero, i.e. the standard Gibbs free energy? When is deltaG_zero = 0? In the solution manual it says that it means that K = 1, but by calculating an equilibrium constant you are already stating that we are at equilibrium? I.e. that...
22. ### Gibbs phenomenon caused by digital signal processing?

Hi, I'm an electrical engineer for a few years now, but it's been a while since I had to deal with this kind of stuff, I turned out to become mostly a programmer in the end, but i was thinking: is Gibbs phenomenon, which was demonstrated to me during my studies while working on Fourier series...
23. ### Why is DeltaG Negative for H2O(l) to H2O(g) at Equilibrium?

Calculate deltaG for the reaction: H2O(l) = H2O(g). 100 degrees celsius, water is clean. P(H2O) = 0.1 bar. Given that it is an equilibrium, I'd think that deltaG would be zero. But the answer is in fact negative. How is that possible?
24. ### I What Are the Differences Between Boltzmann and Gibbs Entropies?

Hi everyone, I have a few questions I'd like to ask regarding what I have read/heard about these two definitions of entropy. I also believe that I have some misconceptions about entropy and as such I'll write out what I know while asking the questions in the hope someone can correct me. Thanks...
25. ### Surface tension in terms of temperature and concentration of an added substance

Hi! Here's a tricky thermodynamics problem, I hope you can help with it. 1. Homework Statement The boundary between two different materials can be divided into two different kind of phases: bulk phases and surface phases. For example, let's consider a boundary between water and air. We can...
26. ### I Gibbs Energy Confusion: Proving dG≤0 Constant T,P

By Clausius' inequality δq - TdS ≤ 0. For a constant T,P process in a closed system and no non-expansion work my text states that dG = dH - TdS = δq - TdS ≤ 0 but this seems incorrect to me. If pressure is constant such that dH = δq, doesn't this mean that δq = δqrev since dH is a state function...
27. ### Question about Gibbs free energy from Kubos' Thermodynamics

Advanced Problems textbook. (It's on pages 212-213). I'll post the question and following it the solution in the book: The question: The Solution: What I don't understand is how did they arrive at the identities with ##\frac{\bar{G}_1''-\bar{G}_1'}{0}## and...
28. ### I Why is the 'TS term' included in the expression for Gibbs free energy?

Hello. I'd like to ask a question about meaning of Gibbs free energy. In undergraduate school, I learned that Gibbs free energy is "available" energy we can extract from system at constant pressure and temperature. G=H-TS=U+PV-TS In above expression, however, I can't understand why "TS term" is...
29. T

48. ### Resolution to Gibbs' entropy paradox?

It seems to me that Gibbs' Paradox (that the entropy of a classical ideal gas, calculated by phase-space volume, is not extensive) can be resolved without assuming that particles are indistinguishable. Suppose instead the opposite: that particles are distinguishable, meaning that each one can...
49. ### Trouble with Gibbs Free Energy & Equilibrium Constant Calc.

Hello. A known equation that is useful for calculating equilbrium constants is: ΔG° = -RT * ln(K) This is all well and good. Given a standard gibbs free energy of reaction for some given reaction, the equilibrium constant for the reaction can be found. My trouble is in which ΔG° to use. For...
50. ### La Chatlier & Gibbs Free Energy Contradiction?

Say I have an exothermic reaction, whose change in Entropy is positive. (not the most common of reactions, but it can still happen) If I increase the temperature, by La Chatlier's principle, the reaction should move to the left. However, by Gibbs free energy, if I increase the temperature, the...