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
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
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...
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?
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...
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...
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...
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...
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...
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...
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...
(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...
#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...
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 $$G \not \propto N.$$
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?
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...
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...
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...
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...
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...
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...
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...
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?
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...
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...
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...
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...
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...
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...
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:
Homework Statement
Calculate the change in the molar Gibbs energy of a perfect gas when it expands isothermally and reversibly at a temperature of 25{\circ} Cfrom a molar volume of 4 \, \text{dm}^3 to a molar volume of 9 \, \text{dm}^3
Homework Equations
I derived the following equation
\Delta...
1. Robert Dehoff 4.12
A system is designed that permits continuous programmed control of the pressure and volume of the gas that it contains. The system is filled with 1 g atom of helium and brought to an initial condition of one atmosphere and 18 liters. It is then reversibly compressed to 12...
Hi, i'll apologize for my english in advance, so here's the question.
I was wondering about the equilibrium condition for a chemical reaction. We know that a closed system is in equilibrium if the Gibbs free energy's function has a minimun in that point. So, taking Temperature and Pressure as...
Why do the time-evolution operator in quantum mechanics ##\exp{iHt}## and the Gibbs-weight operator in statistical physics ##\exp{-H/T}## have the same functional form? – i.e. both exponentials of the Hamiltonian operator.
The Matsubara trick/method just takes this as a fact in thermal QFT; but...
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...
How would one approach part I and II? In terms of thermodynamics I'm not sure how I can show that this hypothesis is true. Could I work out the equilibrium constant and make a decision based on its magnitude? For example if it is >>> 1 then the hypothesis is true, would that be correct?
For the...
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...
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) +...
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...
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...
Let's consider an isotherm isobaric adsorption of gas (A) on the adsorbent (B). There are two phases in the system:
- volume phase (1) that consists of gas and adsorbent.
- surface phase (2) that contains a layer of adsorbed gas on the surface of adsorbent.
When deriving Gibbs adsorption...
Hi.
Trying to solve the Gibbs paradox for two identical volumes of ideal gas with ##N## particles each, I found the mixing entropy to be
$$\Delta S=2N \log(2)-\log((2N)!)+2\log(N!)\enspace .$$
The usual approach now uses Stirling's approximation to the order ##\log (n!)\approx n\log (n)-n##...
Homework Statement
Calculate the vapor pressure of water at 25°C, based on the Gibbs free energy when vaporising from liquid water to vapor (so at 1 atm and 25°C ).
Homework EquationsThe Attempt at a Solution
After integrating d g/d p= RT/p. I get my formula p = p0*exp (-delta gm(p0, T)/RT). I...
When I studied chemistry in high school, I learned that if the change of enthalpy of a reaction ΔH > 0 , the reaction is endothermic, and if ΔH<0, it is exothermic.
However in thermodynamic class, I learnt:
$$ ΔG = ΔH - TΔS $$
For a reaction of a battery, the data reads
ΔG = -394kJ/mol. (which...
I have a doubt regarding gibbs phase rule in thermodynamics.. It says the number of independent intensive properties required to specify the state of a system is F=C-P+2 where C is number of components and P is the number of phase.. So for a water and water vapour system, C=1, P=2 . So F=1. If...
I understand that the change in Gibbs Free Energy at equillibrium is 0 and this leads to the equation -deltaH=TdeltaS. My questions here is that if a reaction is at equillibrium, how can there be any change in enthalpy or entropy at all? Why wouldn't these terms be 0?
Homework Statement
Are the Gibbs and Boltzmann entropies always equivalent?
Homework Equations
$$ S=k_{B}ln\Omega $$ [Boltzmann entropy, where ##\Omega## is the number of available microstates
$$ S=-k_{B}\sum_{i}p_{i} ln(p_{i}) $$ [Gibbs entropy, where ##p_{i}## is the probability of a...
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...
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...
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...