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 }}
.

View More On Wikipedia.org
  1. Useful nucleus

    Gibbs Free Energy and the Grand Potential

    Gibbs Free Energy is the appropriate potential when there is both heat exchange and mechanical work (G=E-TS+PV). On the other hand the grand potential is appropriate when there is heat exchange and chemical work (g=E-TS-μN). Is there any issue in defining a potential of the form (E-TS-μN+PV)...
  2. S

    Gibbs free energy going to zero (equilibrium)

    Hi I have a 4 part question about phase changes and I hope you guys can help me out here thanks :) The chemical equation for vaporization for water is H2O(l)-->H2O(g) 1) When ΔG is 0 during a phase change we would use the formula ΔH=TΔS and put in values to get the boiling/melting point by...
  3. electricspit

    Gibbs Free Energy and Equation of State

    I'm wondering why the Gibbs function is related to the equation of state as follows (supposedly): V=(\frac{∂G}{∂P})_T I found a thread on here that mentions this relationship, but doesn't explain it at all. Any help understanding this would be appreciated, this is my first introduction to...
  4. S

    Gibbs free energy and the first law of thermodynamics

    Hi thanks for reading. I have 2 questions regarding the topics mentioned that I'm having trouble with. Hope you guys can help me out here :) 1) The first law is ΔU=Q+W so we can rearrange this to get ΔH=ΔU+PΔV so would this indicate that ΔH only measures the heat given out at constant...
  5. Z

    Quick question about Gibbs free energy

    In the expression defining Gibbs free energy, G = U - TS +pV, are T and p the temperature and pressure of the environment, or of the system itself? Or is it a requirement that the system has the same temperature and pressure as the environment for the Gibbs free energy to be defined?
  6. A

    Difference between enthelpy, Helmholtz free energy,& Gibbs free energy

    I am study chapter 5 of An Introduction to Thermal Physics by Schroeder and I am having trouble understanding his explanation of the differences between enthaply, Helmholtz free energy, and Gibbs free energy. Schroeder defines enthalpy of a system as its energy plus the work needed to make...
  7. N

    Gibbs Energy Change and Maximum Work

    Homework Statement I am trying to understand the implications of the principle that the maximum non-expansion work, dwadd is equal to the Gibbs energy change for a reversible process. Homework Equations For a reversible process, dwadd = dG. This is provided that the process takes...
  8. H

    Relation between gibbs free energy and equilibrium constant

    I am familiar with the equation ΔG=ΔG°+RT ln(Q).But I can't derive it.We have to use the equation to derive nernst equation. So please help.
  9. L

    How can i derive this Gibbs energy equation?

    Homework Statement For an electrochemical cell Gibbs free energy is is given by G=-nFE Gibbs free energy for a reaction at any moment in time and standard state free energy is given by G=Go + RT lnQ Derive an expression relating standard state cell potential and equilibrium constant for...
  10. B

    What Is the Correct Symbol for Gibbs' Energy Under Standard Conditions?

    My thermodynamics textbook says that chemical potential can take any of the following symbols: μ (condition-dependent), μ∇ (standard), μΘ (standard) (superscript plimsoll line) and μO (standard), with which one of the latter 3 being used depending on the temperature chosen to define standard...
  11. D

    Understanding Free Gibbs Energy: The Role of TΔS in Thermodynamics

    I´m having serious problems with free gibbs energy equation. My main problem is that i don't know the meaning of TΔS that appears in free gibbs formula. I know that S is entropy and T temperature; but some books say that TΔS is energy lost or dispersal energy; energy unavailable to do work; but...
  12. C

    Understanding Gibbs' Phase Rule Basics

    I am having some trouble fully understanding the basics and I just wanted to see if somebody would please clarify this for me. First, say you have a one component system in two phases: vapor and liquid. Gibbs' phase rule restricts the system to one independent, intensive variable that may be...
  13. T

    Purpose of natural log in gibbs free energy equation

    Hi,Im just beginner and I m trying to learn integrals.I m just in starting phase,but still in few tences,not details...How or why we get logarithm in gibbs free energy equation?Because of integration of this equation or due to probability and statistics laws? Thanks
  14. A

    How Does Gibbs Free Energy Relate to Phase Changes?

    Hi, As I understand, during the process of phase change from a liquid to solid (or any phase change for that matter,) the temperature of the substance remains constant as the energy being applied to the substance is used in changing phase. How does this relate to Gibbs free energy? I read that...
  15. J

    Quick question about Gibbs Free Energy

    If this isn't the correct place to ask this, please point me to where I should. I feel there are quite a few guidelines to what can be posted and what cannot, so I hope I don't break any rules! I'm working on a problem, that deals with a superheated steam, that goes from an initial state to...
  16. Telemachus

    Estimate molarity from enthelpy, gibbs energy and entropy of formation

    Hi there, I have to solve this problem: Use the following data to estimate the molarity of a saturated aqueous solution of ##Sr(IO_3)_2## So, I think I should use the Van't Hoff equation in some way, but I don't know how. I also have: ##\Delta_r G=\Delta G^o+RT\ln K## ##K## is the...
  17. D

    Gibbs Free Energy of Formation: 1°C or 25°C? (And other exciting questions.)

    Hi there: When using ΔG=ΔG°+RT ln Q to calculate the energy yield of a reaction, does it matter if I use ΔG° calculated at 1°C or 25°C? Also, why are there two choices and when are they each applicable? Finally, I have also seen ΔG°' written (note the prime). What does this mean and how does...
  18. V

    Gibbs Free Energy/Enthelpy/Entropy Question

    Homework Statement Assume that ΔH° and ΔS° are independent of temperature. Calculate ΔG° for the following reaction at 533 K. 2Cu(+)(aq) ----> Cu(s) + Cu(2+)(aq) Cu(2+)(aq) enthalpy (H) of formation = 64.77 kJ mol^-1; molar entropy (S) = -99.6 J K^-1 mol^-1 Cu(s) enthalpy (H) of formation =...
  19. P

    Gibbs Random Field: Positive Probability Distribution Explained

    Hello everyone, I am trying to understand markov random fields and how it is related to the Gibbs measure and basically trying to understand the Gibbs-MRF equivalancy. Anyway, while browsing Wikipedia documents, I was looking at the page on MRFs and when I came across the following line...
  20. S

    Dirac delta function / Gibbs entropy

    Homework Statement This is an issue I'm having with understanding a section of maths rather than a coursework question. I have a stage of the density function on the full phase space ρ(p,x); ρ(p,x) = \frac {1}{\Omega(E)} \delta (\epsilon(p,x) - E) where \epsilon(p,x) is the...
  21. A

    Constraints on the Gibbs Equation, Tds = dh - vdP

    Homework Statement What constraints are imposed on the use of the Gibbs equation Tds = dh - vdP Homework Equations Tds = dh - vdP The Attempt at a Solution I seem to be stuck on this question. So far I have come up with the following constraints, but I'm not even sure if they are...
  22. R

    How Does Gibbs' Phase Rule Limit the Number of Coexisting Phases in a System?

    Homework Statement "By applying Gibbs' phase rule to show that for an n component system, no more than n+2 phases may coexist at equilibrium Homework Equations P+F=C+2 The Attempt at a Solution Because the question says that P = n +2 I subbed this in => n+F=C. I'd like to sub...
  23. S

    Is the Helmholez or Gibbs free energy every used outside of reactions?

    I'm trying to figure out if the Helmholtz & Gibbs free energy are ever used outside of chemical reactions (I suppose they could be used in nuclear reactions in a plasma as well.) It seems to me that they are not, as I can only recall using them for chemical reactions in my thermodynamics course...
  24. S

    Gibbs Free Energy Change/Entropy

    Hi, seen as it's Physical Chemistry I am asking about and Physical Chemistry is essentially applied Physics I figured that it would be okay to ask here. I have an exam this tuesday, and my lecturer went over some seminar questions. He provided answers to the calculations but did not provide...
  25. P

    How to calculate Gibbs energy of formation at a temp T using standard state data?

    I hope this isn't deemed school related. It is something I learned in school, but I'm now trying to figure out a reaction model for my work. In the process of calculating the reaction constant, usually you first determine the Gibbs energy of formation of each species, find the difference...
  26. S

    Gibbs free energy doesn't increase (constant T and P) - proof doesn't seem right

    First my notes discover that for an isothermal transformation; ΔW ≥ ΔF Where W is the work done and F is the Helmholtz Free Energy, F = E - TS. Then it defines the Gibbs free Energy; G = F + PV "For a system at constant temperature and pressure, G never increases"; So ΔG = ΔF...
  27. I

    Gibbs Free Energy of Atomic Hydrogen Ionization

    Homework Statement Despite extensive searches of the web and my old honors freshman chem text, I have yet to find a kj /mol value for either the standard Gibbs' Free Energy (Delta-G-naught (298° K)) or standard ENTROPY (Delta-S-naught) for the ionization of gaseous ATOMIC Hydrogen (or for...
  28. S

    Gibbs sampler as a Markov process

    I'm trying to learn more about Markov chains and came across the Gibbs sampler x_1{t+1} ~ p(x_1|x_2 = x_2{t},...x_n{t}) x_2{t+1} ~ p(x_2|x_1 = x_1{t+1},x_3 = x_3{t},...,x_n{t}) . . . x_i{t+1} ~ p(x_i|x_1 = x_1{t+1},...,x_(i-1) = x_(i-1){t+1},x_(i+1) = x_(i+1){t},...,x_n{t}) Supposedly...
  29. K

    Gibbs free energy from partial pressures

    Homework Statement Consider the following reaction: CH3OH(g) <-> CO(g)+2H2(g) Calculate ΔG for this reaction at 298 K under the following conditions: PCH3OH=0.895atm PCO=0.115atm PH2=0.200atm Homework Equations ΔG=-R*T*ln(K) where R is the gas constant 8.314 J/molK, T is 298 in...
  30. L

    Calculating Molar Gibbs Function

    Homework Statement For this question I'm to calculate the molar Gibbs function, G-G0, at 2000K for BSi given that the bond distance is 1.905A^{\circ}, ω^{~} = 772cm-1, the ground electronic state has a degeneracy of 4, and the lowest energy excited electronic state, 8000cm-1 above the ground...
  31. S

    Maximizing Gibbs Entropy in Canonical Ensemble

    Hey, Here is the problem: The method by which we solve is by Langrange Multipliers, and so I believe I found the derivative of f with respects to P(i) but I have two quantities I'm sure what they equal: Summations over i=1 to N : Ʃln(P(i)) and ƩE(i) Thanks for any help, S
  32. B

    Definition of the Gibbs free energy

    In the equation \Delta G^{\ominus} = \Delta H^{\ominus} - T\Delta S^{\ominus} does the temperature refer to the temperature of the system, or the temperature of the surroundings? BiP
  33. J

    Confused about gibbs free energy

    Wikipedia says : In thermodynamics, the Gibbs free energy (IUPAC recommended name: Gibbs energy or Gibbs function; also known as free enthalpy[1] to distinguish it from Helmholtz free energy) is a thermodynamic potential that measures the "useful" or process-initiating work obtainable from a...
  34. J

    Gibbs free energy change at constant pressure is zero?

    gibbs free energy change at constant pressure is zero?? IS gibbs free energy change at constant pressure zero? ΔS = q / T. At constant pressure q = ΔH so ΔS = ΔH / T So ΔG = ΔH - ΔH/T . T = 0 I think i am wrong but where? My friend tells me that q involved in enetropy is...
  35. N

    Does the N Gibbs factor SAVE or DESTROY extensivity?

    So we all know the argument that shows that a factor \frac{1}{N!} makes entropy extensive: it makes the entropy the same for system A and system B where system A is a box of indistinguishable/indistinguished particles and where B is system A is split into two isolated parts. But regard this...
  36. A

    Gibbs Free Energy Change of a Reaction

    So, in my thermo book, it says that the gibbs free energy change of a reaction is the free energy received by the system at constant T,p and constant chemical potential when the extent of the reaction varies by one mol. The part that is confusing me is the "constant chemical...
  37. C

    Gibbs Free Energy: Explained & Explored

    I don't think I completely understand what Gibbs energy is, Is it the work you can get out of a system at fixed Temperature and pressure. Does anyone have another angle on it cause It seems weird to me.
  38. T

    Gibbs and Helmholtz equations for thermodynamic processes

    For a thermodynamic process, what equations would be used to find the change in Gibbs and Helmholtz free energy when: a.)The process is adiabatic b.)The process is isothermic c.)The process is at constant volume d.)The process is at constant pressure I know ΔG=ΔH-TΔS and ΔA=ΔU-TΔS but do...
  39. P

    Standard Gibbs of a reaction

    Homework Statement For the reaction N2(g) + 3H2(g) <---> 2NH3(g) I am supposed to determine the equilibrium constant at 298K and 1 bar. We have been given a table that states that for NH3(g): \Delta_{r}G^{\Theta}= -16.45 kJ/mol I know that \Delta_{r}G^{\Theta}= \Sigma v...
  40. J

    Finding Standard Gibbs Free energy for half cell reaction.

    The standard potential of the Cl−(aq.)|AgCl(s)|Ag(s) electrode in the vicinity of T = 298 K has been found to fit the expression E\theta/V = -0.00558 + 2.6967x10^-3(T/K) - 8.2299x10^-6(T/K)^2 + 5.869x10^-9(T/K)^3 Find the standard Gibbs free energy, the standard enthalpy, and the standard...
  41. S

    Possible error in temperature dependence of Gibbs energy in textbook?

    Homework Statement In the attached picture, I am wondering if there is an error in equation (6.34). In equation (6.33), the partial differential of G/T is taken with respect to T. In (6.34), however, the partial differential of G/T is taken with respect to 1/T and the same outcome is...
  42. J

    Using entropy to solve for Free Gibbs energy

    1.00 mol of perfect gas at 25 C is expanded isothermally from an initial pressure of 5.00 atm to a final pressure of 1.00 atm in two ways:(a) reversibly (b) against a constant external pressure of 1.00 atm. Calculate the values for q, w, dU, dH, dG, dSsys, dSsur, dStot for each path. (I pretty...
  43. M

    Derive Gibbs function for dry air .

    Homework Statement 1. Derive the Gibbs function g(T,P) for dry air. T = temp, P = pressure 2. Derive the speed of sound (c) from the Gibbs function. Plot c as a function of temp and pressure. Homework Equations c = gp*squareroot(gTT/(g^2TP - gTT*gpp) I wasn't sure how to type it in...
  44. N

    Why specific heat at near critical point equals differentiate twice Gibbs energy?

    Please teach me this: Why specific heat near critical point equals differentiate twice Gibbs free energy with respect to temperature, but not differentiate once with respect to temperature as usually doing. Thank you very much in advance.
  45. S

    Gibbs free energy partial derivative

    g = u + Pv - Ts To find the partial derivative of g with respect to T at constant P, we do the following. dg = du + vdP + Pdv - Tds - sdT and du = Tds - Pdv. Therefore, dg = vdP - sdT. At constant pressure, dg = - sdT. Therefore, the partial derivative is - s. I think we could...
  46. R

    Gibbs Free Energy, How to find G with only Hstand and Gstand

    Homework Statement For the decomposition of Ag2O(s), what is the Gibbs free energy change at 500K (assuming delta H and delta S do not vary with temparature? delta standard Gformation: -61.0 kJ/mol delta standard Hformation: -29.7 kJ/mol Homework Equations deltaG = deltaH -...
  47. A

    Gibbs-Maxwell Relation: A Derivation Explained

    So, this is not a homework problem. Merely for my own understanding. This is (or should be) relatively simple I believe. Anyway, start of with Gibbs free energy and take the derivate, we arrive at: dG = -SdT + VdP + \mu dN take the partials we can see that with respect to dP we get V...
  48. Simfish

    Is Gibbs free energy ever relevant for particle physics?

    And are reactions in particle physics reversible at all? If so, why don't we ever see Gibbs free energy used in particle physics equations?
  49. Topher925

    Electrochemical cells: Is gibbs free energy dependent upon concentration?

    Is the gibbs free energy of some reaction in an electrochemical cell dependent upon reactant concentration? The Nernst equation clearly states that open circuit potential is dependent upon concentration, and basic thermodynamics states that open circuit potential is directly proportional to...
  50. L

    Exploring Fourier Series and Gibbs Phenomenon

    Homework Statement http://img684.imageshack.us/img684/4496/fourier.png Homework Equations http://en.wikipedia.org/wiki/Small-angle_approximation The Attempt at a Solution This is part of a larger question, I have underlined in Red the areas I am struggling with and have cut out...
Back
Top