What is Gibbs free energy: Definition and 120 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 (



{\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


{\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


{\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







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

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  1. aquastor

    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. T

    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. P

    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. tbn032

    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. wnvl2

    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. samy4408

    Question about the rules of thermodynamics

    Hello , we learned in thermodynamics that to calculate ΔHr °(of the reaction ) using ΔHf °(standard heat of formation ), we have to respect that ΔHf °=ΔHr ° of a reaction forming 1 mol of compound from pure elements in their most stable form at standard state . the problem is when we want to...
  7. samy4408

    Medical Question about reactions in biochemistry

    we assume that we have an exergonic reaction , a substrate going to a product , is the negative ΔG′° the principal reason that the equilibrium favors the product (there is more product than substrate at equilibrium )?, or it is not and that depends on other factors? , thanks .
  8. Yash Agrawal

    Thermodynamics of chemical reactions

    In chemical reactions generally ΔG < 0 , but if we were to consider a reversible path between pure reactants and products at 1 bar pressure , shouldn't the ΔG = 0 for every reaction ? and if it is due to non-pv work , I don't see any non pv work being done in reactions happing in a closed...
  9. patric44

    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...
  10. Z

    DeltaG and DeltaA calculation for heating a gas at constant volume

    Summary:: Gibbs and Helmholtz energies calculations for heating an ideal gas at constant volume I am solving a problem involving an ideal gas that undergoes several chained changes of state. One of the steps asks to calculate the change in Gibbs Energy (DeltaG) and Helmholtz energy (Delta A)...
  11. GranMix

    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...
  12. Rahulx084

    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. TytoAlba95

    Chemistry MCQ- What is the Gibbs free energy value?

    Where have I gone wrong? According to the key, the right option is a.
  14. A

    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. E

    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...
  16. jaumzaum

    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...
  17. sponteous

    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...
  18. S

    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...
  19. K

    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...
  20. K

    Gibbs free energy problem

    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?
  21. MathematicalPhysicist

    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...
  22. W

    I Meaning of 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...
  23. T

    Maxwell Relation, Gibbs Free Energy, Thermal Expansion Coefficient

    Homework Statement By means of a Maxwell relation derived from the Gibbs free energy and making use of the third law of thermodynamics, prove that the thermal expansion coefficient β must be zero at T = 0. I tried but I got something funny. Homework Equations $$G=U-TS+PV$$ $$dG=\mu...
  24. T

    Maxwell Relation, Gibbs Free Energy, Thermal expansion

    By means of a Maxwell relation derived from the Gibbs free energy and making use of the third law of thermodynamics, prove that the thermal expansion coefficient β must be zero at T = 0. I tried but I got something funny. My working:
  25. C

    Gibbs Free Energy -- Connection between V, P, N & T

    Homework Statement For a Particular system the following expression for Gibbs free energy is known: G = -kTN ln (a T^(5/2) / P) where a is a constant (whose dimensions make the argument of the logarithm dimensionless). Obtain expressions for a) The entropy, S b) The connection between V, P...
  26. W

    Helmholtz and Gibbs free energy for an adiabatic process

    Homework Statement Calculate changes in A and G of one mole of an ideal gas that undergoes the following processes respectively. 1. adiabatic expansion from (T1, P1) to (T2, P2) 2. isobaric expansion from (P, V1, T1) to (P, V2, T2) (if it is not isothermal) 3. isochoric expansion from (V, P1...
  27. grandpa2390

    Graphing the Gibbs free energy of mixed gases

    Homework Statement I am needing to graph the Gibbs free energy of mixed gases to determine the range when the gases will form an ideal mixture The two gases have the same Gibbs free energy. Homework Equations ##G = (1-X)G_A + XG_B## for unmixed ##G = (1-X)G_A + (X)G_B + RT(x*ln(x) +...
  28. grandpa2390

    Why is the Gibbs Free energy equal to this:

    Homework Statement the isothermal compressibility of graphite is about ##3*10^{-6} bar^{-1}##, while that of diamond is more than ten times less and hence negligible in comparison. (isothermal compressibility is the fractional reduction in volume per unit increase in pressure, as defined in...
  29. freek_g

    Proving Gibbs energy equals work

    Hi, I'm preparing for my exams in a few weeks, of which one covers Thermodynamics. I was trying to solve a question, where I noticed the Gibb's free energy had to equal the (negative) work. I kind of came to an answer, but was not sure if I did it the right way. All steps are reversible...
  30. Mayan Fung

    Gibbs Free Energy and Enthelpy

    When I studied chemistry in high school, I learned that if the change of enthalpy of a reaction ΔH > 0 , the reaction is endothermic, and if ΔH<0, it is exothermic. However in thermodynamic class, I learnt: $$ ΔG = ΔH - TΔS $$ For a reaction of a battery, the data reads ΔG = -394kJ/mol. (which...
  31. A

    Why is Qir < than Qr? Carnot cycle and change in G

    I am learning physics on khan academy and they do a proof to show that delta G for a reversible reaction is negative and how for a irreversible reaction it is positive. However in the proof, they assume that the heat put in by the isotherm is less for an irreversible reaction compared with a...
  32. doulyftbruh

    Change in Gibbs free energy at equillibrium

    I understand that the change in Gibbs Free Energy at equillibrium is 0 and this leads to the equation -deltaH=TdeltaS. My questions here is that if a reaction is at equillibrium, how can there be any change in enthalpy or entropy at all? Why wouldn't these terms be 0?
  33. E

    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...
  34. E

    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...
  35. E

    Is Gibbs free energy just potential energy reduction?

    So I know that things in the Universe tend to move toward a state of least potential energy. This is why forces point in the direction of decreasing potential energy, as everything is trying to minimize its potential energy. So my main question is: does Gibb's free energy basically just...
  36. I

    Is the minimum Gibbs free energy the same for every material?

    We were learning about the change in free energy in class, but I was wondering since the Gibbs free energy decreases as a system becomes more stable, is the minimum absolute free energy for a material the same for every material, or can other materials be more stable than others?
  37. A

    Estimating Vapor Pressure of Mercury at 25°C Using Appendix D Data

    Homework Statement Estimate the vapor pressure of mercury at 25 ∘C (use data from Appendix D from the textbook). Homework Equations Using the appendix I can find ΔG, ΔH, and ΔS. The Attempt at a Solution I have no idea where to start. I think that maybe vapor pressure would be found when...
  38. R

    Gibbs free energy -- mathematical expression

    I am not able to understand the mathematical expression of "change in Gibbs free energy", For a chemical reaction occurring at constant temperature and constant pressure, (ΔS)total = (ΔS)system + (ΔS)surrounding Considering that reaction is exothermic, ΔH be the heat supplied by system to...
  39. C

    What is Enthelpy Conceptually?

    So I understand that enthalpy is energy. But what energy specifically? Is enthalpy heat energy? Is it the energy that bonds atoms together and that's why it can either be released or absorbed? Or is that what Gibbs free energy is? I'm trying to make sense of the equation: ΔG=ΔH-TΔS...
  40. B

    Contradiction of Gibbs adsoprtion?

    1. Surfactant molecule is made from water-loving head and grease-loving tail (Figure 1). http://tinypic.com/r/2j2gdah/9 (Figure 1) My question: How do we measure the cross-sectional area of the alkyl chain of surfactant? Do we measure it vertically (refer to GREEN DOUBLE ARROWS of Figure 1) or...
  41. A

    Gibbs Free Energy, Maxwell Relations

    Homework Statement We have a Gibbs Free Energy function G=G(P, T, N1, N2) I am not writing the whole function because I just want a push in the right direction. Find expressions for the entropy, volume, internal energy, enthalpy and chemical potential. Homework Equations Maxwell Relations...
  42. T

    Freezing/Melting of water and gibbs free energy

    Hello, I get that ΔG measures the spontaneity/capacity of a system to do non-mechanical work, and that if: ΔG>0, the reaction is not spontaneous ΔG<0, the reaction is spontaneous ΔG=0, the reaction is at equilibrium So why is Gibbs free energy zero for phase changes at constant temperature and...
  43. MexChemE

    Exploring Thermo in Batman: Arkham Origins

    Hello, PF! Days ago, while playing Batman: Arkham Origins, I was wandering through the Batcave when I noticed something that caught my eye immediately. There's a nice, cozy lab in there which includes a blackboard where Bruce Wayne apparently did some kind of thermodynamic calculations, which...
  44. Eureka99

    Trouble with Gibbs free energy equation

    Hi everybody! Lately I tried to overcome some problems with understanding thermodynamics laws, and unfortunately I couldn't find anything about my question:nb) and I really hope someone can help me here... My question is: This version of Gibbs formula dG= VdP-SdT, can be applied to any close...
  45. T

    Does Gibbs Free Energy play a role in the storage of energy in ATP?

    Hello, Gibbs free energy describes the maximum of useful work that can be done by a chemical reaction. My question is(Sorry I am not into chemistry and biochemistry) : during a chemical reaction that creates ATP, we say that ATP stores energy between its chemical bonds . For exemple this is the...
  46. T

    Gibbs Free Energy and maximum work

    Hello, The Gibbs free energy is the maximum amount of non-expansion work that can be extracted from a closed system; this maximum can be attained only in a completely reversible process. This maximum work is equal to H-TS. My question is this TS energy is what kind of energy? and from where it...
  47. R

    Gibbs free energy various forms

    What is the difference between 1) ΔG°' and ΔG° and 2) ΔG°' and ΔG ? ΔG° I think it is the gibbs free energy at standard state means at room temperature 1 atm pressure.
  48. Paulo Bernardo

    Meaning of Free Energy (Gibbs free energy)

    Hello everyone, I'm reading some basics of chemistry thermodynamics, and it's hard for me to figure out what is the actual meaning of free energy. could someone please help clarifying this giving specify, real life examples, like applications in mechanical engineering. Thanks
  49. S

    Gibbs Free Energy Calculation

    ΔG=ΔH-TΔSsystem and ΔSsystem=qp/T and isn't qp=ΔH? Which means ΔG=0 always which is obviously wrong. But the derivation for Gibbs Free Energy is based on qsurrounding=-qsystem so shouldn't the term be equals to 0?
  50. S

    Gibbs Free Energy for non-standard conditions

    ΔG=ΔG°+RTlnQ are for reactions that are not under standard conditions. What does it mean under non-standard conditions for the ΔG? And what is the Q in this case? Is it Qp where it is based on the partial pressure of the gas or Qc which is based on the concentration? Thanks