Gibbs Free Energy Equation: why is the entropy change of the system not q/T ?

Click For Summary
SUMMARY

The Gibbs Free Energy Equation (GFEE) reveals that the entropy change of the system cannot be directly equated to ΔH(syst)/T due to the nature of reversible processes and the conditions stipulated by the equation. The correct relationship is established through the universal entropy change equation ΔS(univ) = ΔS(surr) + ΔS(syst), where ΔS(surr) is defined as ΔH(syst)/T. This indicates that while the system and surroundings exchange heat, their entropy changes are not equal, as ΔG must remain non-zero for the GFEE to hold true. Misinterpretation arises when one assumes that the entropy change of the system mirrors that of the surroundings.

PREREQUISITES
  • Understanding of the Gibbs Free Energy Equation (GFEE)
  • Familiarity with entropy change equations, specifically ΔS=q/T
  • Knowledge of thermodynamic principles, particularly reversible processes
  • Concept of standard states in thermodynamics
NEXT STEPS
  • Study the implications of reversible reactions on entropy changes
  • Explore the concept of standard state conditions in thermodynamics
  • Learn about the relationship between Gibbs Free Energy and chemical equilibrium
  • Investigate phase changes and their effects on entropy calculations
USEFUL FOR

This discussion is beneficial for students and professionals in chemistry and thermodynamics, particularly those studying reaction thermodynamics, entropy, and Gibbs Free Energy applications.

SPG
Messages
1
Reaction score
0
Homework Statement
The way we stipulate the conditions for the Gibbs Free Energy Equation (GFEE) - it seems to me that ΔS(system) must always equal negative ΔS(surroundings) ? Obviously this is incorrect but I can't see why. The GFEE says the magnitude of the entropy change of the surroundings is given by

ΔS(surr) = ΔH(syst)/T

Since the only exchange between the system-surroundings is the heat of ΔH(syst), then the change of heat in the system is -tautologically- also the same ΔH that the surroundings experience. So then surely the magnitude of the entropy change of the system is also the same quantity as the above expression for that of the surroundings. Because both system and surroundings have the same magnitude of heat change at the same temperature with no PV work or matter exchange i.e. it erroneously appears to me that

ΔS(syst) = ΔH(syst)/T = ΔS(surr)

But of course if this were true it would render the GFEE useless since ΔG would always be zero.
So why does the normal entropy equation ΔS=q/T not work for the entropy change of the SYSTEM in the GFEE?
What instead is the expression (or way to consider) the entropy change of the system in the GFEE ?
I have never seen this discussed in my Thermodynamics text books or anywhere online.
Relevant Equations
ΔS(univ) = ΔS(surr) + ΔS(syst)
ΔS = q/T
q=ΔH
ΔS(surr) = ΔH(syst)/T
leading towards Gibbs:
ΔS(univ) = ΔH(syst)/T + ΔS(syst)
multiply by T to give Gibbs Free Energy Equation
T.ΔS(univ) = ΔG(univ) = ΔH(syst) - T.ΔS(syst)
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 the entropy change of the system is given by
ΔS(syst) = q(syst)/T
therefore
ΔS(syst) = ΔH(syst)/T
but I know this isn't correct, i just can't see why this expression for entropy change of the system is incorrect
 
Physics news on Phys.org
SPG said:
Problem Statement: The way we stipulate the conditions for the Gibbs Free Energy Equation (GFEE) - it seems to me that ΔS(system) must always equal negative ΔS(surroundings) ? Obviously this is incorrect but I can't see why. The GFEE says the magnitude of the entropy change of the surroundings is given by

ΔS(surr) = ΔH(syst)/T

Since the only exchange between the system-surroundings is the heat of ΔH(syst), then the change of heat in the system is -tautologically- also the same ΔH that the surroundings experience. So then surely the magnitude of the entropy change of the system is also the same quantity as the above expression for that of the surroundings. Because both system and surroundings have the same magnitude of heat change at the same temperature with no PV work or matter exchange i.e. it erroneously appears to me that

ΔS(syst) = ΔH(syst)/T = ΔS(surr)

But of course if this were true it would render the GFEE useless since ΔG would always be zero.
So why does the normal entropy equation ΔS=q/T not work for the entropy change of the SYSTEM in the GFEE?
What instead is the expression (or way to consider) the entropy change of the system in the GFEE ?
I have never seen this discussed in my Thermodynamics textbooks or anywhere online.
Relevant Equations: ΔS(univ) = ΔS(surr) + ΔS(syst)
ΔS = q/T
q=ΔH
ΔS(surr) = ΔH(syst)/T
leading towards Gibbs:
ΔS(univ) = ΔH(syst)/T + ΔS(syst)
multiply by T to give Gibbs Free Energy Equation
T.ΔS(univ) = ΔG(univ) = ΔH(syst) - T.ΔS(syst)

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 the entropy change of the system is given by
ΔS(syst) = q(syst)/T
therefore
ΔS(syst) = ΔH(syst)/T
but I know this isn't correct, i just can't see why this expression for entropy change of the system is incorrect
If you are talking about a system where a phase change is involved, then it is correct. If you are talking about a system involving a chemical reaction, then G changes as a result of changes in the amounts of the various species present. Which are you referring to?

See the following thread: https://www.physicsforums.com/threads/thermochemistry-challenge-problem-chets-paradox.913567/
 
The equation S=q/T holds true only for reversible reactions, i.e. for a reaction which moves through a sequence of equilibrium states. And in deed in equilibrium ##\Delta G=0##. When you see some ##\Delta G## values, they typically refer to some standard state, where all reactants are at a concentration (more precisely activity) of 1 mole/L, which is but rarely an equilibrium state.
 

Similar threads

Chemistry How to reason about Gibbs energy change due to entropy not enthalpy?
  • · Replies 4 ·
Replies
4
Views
2K
Relation between system enthelpy and surrounding entropy
  • · Replies 3 ·
Replies
3
Views
3K
Chemistry Create a Gibbs Free Energy challenge question
  • · Replies 1 ·
Replies
1
Views
3K
Chemistry Is the differential of heat in a reversible process in an isolated system equal to zero?
  • · Replies 10 ·
Replies
10
Views
3K
Chemistry Show that book levitation by absorption of heat violates 2nd law
  • · Replies 13 ·
Replies
13
Views
3K
Chemistry Entropy in isolated composite system for irreversible process
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Direct Gibbs energy calculation from molecular dynamics
  • · Replies 1 ·
Replies
1
Views
2K
What Are the Standard Enthalpy and Entropy Changes for the Graphed Reaction?
  • · Replies 6 ·
Replies
6
Views
3K
Chemistry Understanding derivation of Clausius-Clapeyron equation
  • · Replies 2 ·
Replies
2
Views
2K
High School Change in entropy of reversible isothermal process
  • · Replies 11 ·
Replies
11
Views
3K