Chemical Forums
Chemistry Forums for Students => Undergraduate General Chemistry Forum => Topic started by: GeLe5000 on December 25, 2014, 10:18:52 AM

Hello.
In a Chemistry book I read that
dSuniv = dSext + dSsyst (relation 1)
(the change in entropy of a system during a chemical reaction + the change in entropy of the environment = the change in entropy of the universe)
And also
dSext =  dH / T (relation 2)
(when a chemical reaction produces heat, it causes an increase in the entropy of the environment)
dSuniv =  dG / T (relation 3)
(it's more difficult to understand why a change in the entropy of the universe is linked to dG which is called change in "free energy" or the "energy available for work")
And we have the wellknown relation
dG = dH – TdS (relation 4) (S is Ssyst)
The relations seem correct since if we change in relation 4, dH for – TdSext, we get
dG =  TdSext – TdSsyst =  T (dSext + dSsyst) = TdSuniv , thus relation 3.
However, in the book "Bioenergetics" by Dr A. L. Lehninger (W. A. Benjamin, 1971), we read p.27
dG = dE – TdS
There are 2 differences with relation 4 :
1) S is Suniv instead of Ssyst
2) dE replaces dH
So I write dG = dE – TdSuniv (relation 5)
dE is said to be the change in "total energy" of the system.
What is the "total energy of the system" ???
Moreover, if we combine the books, we can write
dG = dH – TdSsys = dE  TdSuniv
dE = dH + TdSuniv – T dSsyst
dE = dH + T(dSuniv – dSsyst)
dE = dH + TdSext
since dSext =  dH / T (relation 2)
dE = dH + T( dH / T)
dE = dH – dH = 0
It's a puzzle to me. If you have some energy to spare in order to decrease my "informational entropy"… Thank you.

Never mind, I've the solution by myself.
It was a bit difficult to admit, but Dr Lehninger was wrong in his book.
It's ΔSSyst instead of ΔSUniv.
ΔE is ΔH (change in Enthalpy) and Enthalpy is sometimes called "total energy of the System".
Thus, when we write ΔGSyst = ΔHSyst  TΔSSyst and divide with T, we get ΔGSyst/T = ΔHSyst/T  ΔSSyst
ΔGSyst/T = ΔSext  ΔSSyst =  (ΔSext + ΔSSyst) =  ΔSuniv
Thus, ΔSuniv =  ΔGSyst/T which is given in the first book (relation 3)
ΔSext in a book in French was ΔSSurr (Surr for Surrounding)