Is There the Fourth Law of the Thermodynamics?
Authors: Chernomorskii Alexandr I. 
Published: February 2024

The Gibbs energy change ∆
G
in half-reactions Me →Me
n+
+ ne and halogens 1/2Hal2 + e → Hal- were analyzed using cycles
∆
G
Me
= ∆
G
subl.
+ ∑
I
- ∆
G
hydr.
-
W
e
(1)
∆
G
Hal
= ∆G
dissoc.

-
E
affinity
- ∆
G
hydr.

+
W
e
(2)
including energies of metal sublimation +∆G
subl.
, ionization of metal vapor +∑I
, chemical hydration of Me
n+
ions -∆G
hydr.
, condensation of free electrons from vacuum onto electrode - W
e
; dissociation of halogen molecules + ∆G
dissoc.
, acceptance of electrons from vacuum by halogens - E
affinity, chemical hydration of Hal- anions -∆G
hydr.
, abstraction of electrons from electrode into vacuum + W
e.
[1,2].
The Gibbs energy ∆G*

Me
and ∆G*

Hal
were calculated using known constants Eqns. (3, 4) [1]
∆
G*
Me
= ∆
G
subl.
+ ∑
I
- ∆
G
hydr.
(3)
∆
G*
Hal
= 1/2 ∆
G
dissoc.
-
E
affinity
- ∆
G
hydr.
(4)
The relations between ∆G*/

n
by Eqns. (3), (4),
n
- number of electrons, for metals and halogens (electron bonds decrease in them) and corresponding standard potentials
Eo

are linear and extrapolated to
Eo

= - 4.72 V SHE at ∆G*/

n

= 0 (Fig.1;lines 1, 2).
Calculated ∆G*/

n
= 4.95 eV (Cu)and ∆G*
= -5.27 eV (I2
) are close in value (Fig.1). According to Eqns. (1, 2), ∆G/

n
in half-reactions of weak reductant Cu and oxidant I
2 should tend to zero (metals - non-metals transition).For this, calculated ∆G* = 4.95 eV (Cu)and ∆G*
= -5.27 eV (I2
) should be decreased and increased on
W
e
~ 5.1 - 5.2 eV respectively [1,2].
The intermediate
W
e,interm.
= 5.19 eV is determined to some substance (metals - non-metals transition) which electrons should be bound by non-specific (non-chemical) definite Coulomb bond [2, 3].
The linear relations for metals (line 1) and halogen (line 2) are displaced in the parallel direction by -5.19 and 5.19 eV respectively (Fig.1) when account is taken
W
e,interm.
= 5.19 eV, i.e., we obtained linear relations 1’ and 2’ between ∆G/

n
of chemical half-reactions by Eqns. (1, 2) and their
Eo
.
Relations 1’ and 2’ intersect with
E o

– axis at ∆G/

n
= 0 at potential
Eo

= ~ + 0.47 V SHE close to Billiter potential + 0.475 V SHE corresponded by [1-3] to hypothetical electrode between metals and non-metals without own chemical activity or to chemical equilibrium half-reactions.
According to Eqns. (3, 4), limiting separated electrons (vacuum) and ions without any bonding are formed from metals, non-metals with spending decreased ∆G*/

n
(lines 1, 2, Fig.1). When ∆G*/

n =
0 (
Eo

= - 4.72 V SHE), all components of Eqns. (3) and (4) are degenerated. For such a system ∆G*

= - A
max = 0, the entropy change is equal ∆
S
= 0. Hence, the entropy
S
tends to constant and infinity
S
max
→ ∞.
The Gibbs energy ∆G*/

n
= 5.19 eV (Fig.1)of limiting separation of definite Coulomb bound electrons – ions (transfer + 0.475 V SHE → - 4.72 V SHE) per electron
5.19 eV x 1.6021 x 10-19 J/eV = 8.314899 x 10-19 J (5)
and the gas constant
R
= 8.31441 J/mol.K have equal bases.
Then,
R
= 8.3144 J/mol. K is sufficient for limiting separation per 1 K of 1019 such non-chemically bound electrons - ions (
W
e,interm.
= 5.19 eV;
Eo

= + 0.475 V SHE, Fig.1). These electrons - ions should be analogous to non - chemically interacting particles of ideal gas at STP conditions.
The energy
R
Δ
T
is equal to the energy 5.19 eV = 500703.548 J/mol of limiting separation of definite Coulomb bound electrons – ions at the change of temperature Δ
T

Δ
T =
5.19 eV / 8.3144 J/mol K = 500703.548 J/mol / 8.3144 J/mol K = = 60221.25 K (6)
which the base corresponds to Avogadro number and mole of limiting separated electrons – ions is equal to
6.022 . 104 K x 1019 mol-1 K-1 = 6.022.1023 mol-1 (7)
Hence, the origin of Avogadro number is number of electrons - ions condensing from limiting separated state (without bonding) to their state with non-chemical definite Coulomb bonds (analogous ideal gas).
The 4th thermodynamics law: limiting separated state of electrons - ions with entropy
S
max
→∞ occurs with increasing temperature on Δ
T =
6.022 . 104 K from STP, at 6.022. 104 oC. The released heat leads only to increase in kinetic energy and temperature of limiting separated electrons - ions.
Reference
1.A.I.Chernomorskii, Zh. Fiz. Khim.,
52, 757 (1978).
2.A.I.Chernomorkii, The Intermediate Electron Bond and Half-reactions (Scientific Resources, New Yopk, NY) (1999).
3.A.I.Chernomorkii, Journal of The Electrochemical Society, 2021,168, 116514.

Figure 1