298
5 – Applications
where F denotes the Faraday constant, we obtain
E
8F
1
2
2
CO
a
H O
a
CH
a
O
c
2
2
4
2
μ
μ
μ
μ
Δ =
+
−
−
`
j
By expanding the chemical potentials, the preceding equation becomes
E
8F
1
2
2
8F
RT
ln P
P
P
P
CO
H O
CH
O
CO
H O
2
CH
O
(c) 2
2
2
4
2
2
2
4
2
μ
μ
μ
μ
Δ =
+
−
−
+
#
#
#
°
°
°
°
`
`
j
j
By using
G
2
c CH
C O
H O
CH
4
2
2
4
μ
μ
μ
Δ
=
+
−
°
°
°
°
and
8F
G
E
c CH
CH /CO
4
4
2
Δ
Δ
= −
°
°
we obtain
E
E
4 F
RT
ln P
P
P
P
CH /CO
CO
H O
2
CH
O
2(c)
4
2
2
2
4
2
Δ
Δ
=
+
#
#
#
°
where Δ c G CH 4
° and ΔE
/
CH CO
4
2
°
are respectively the standard free enthalpy
of combustion for methane and the standard emf associated to the pair
CH 4 / CO 2 .
2. The standard enthalpies of formation Δ f H i ° allow us to calculate the standard
reaction enthalpy Δ r H K
298 °
at 298 K
H
H
r 298 K
i f i
i
υ
Δ
Δ
=
°
°
/
The Kirchhoff equation allows us to calculate it at 1 073 K
H
H
Cp dT
r 1073 K
r 298 K
i
298
1073
Δ
Δ
Δ
=
+
°
°
^
h
#
Numerical evaluation gives
H
802.2 kJ mol
r 298 K
1
Δ
= −
−
°
H
775.2 kJ mol
r 1073 K
1
Δ
=−
−
°
In the same way, based on the absolute standard entropies, we obtain the
change in the standard reaction entropy at 298 K
S
S
r 298 K
i i,298 K
i
υ
Δ
=
°
°
/
We next calculate the absolute standard entropies at 1 073 K
S
S
Cp T
dT
r 1073 K
r 298 K
i
298
1073
Δ
Δ
Δ
=
+
°
°
^
h
#
Numerical evaluation gives
S
213.6 (2 188.7) (2 205) 186.2
r 298 K
Δ
=
+
−
−
#
#
°
5 – Applications
where F denotes the Faraday constant, we obtain
E
8F
1
2
2
CO
a
H O
a
CH
a
O
c
2
2
4
2
μ
μ
μ
μ
Δ =
+
−
−
`
j
By expanding the chemical potentials, the preceding equation becomes
E
8F
1
2
2
8F
RT
ln P
P
P
P
CO
H O
CH
O
CO
H O
2
CH
O
(c) 2
2
2
4
2
2
2
4
2
μ
μ
μ
μ
Δ =
+
−
−
+
#
#
#
°
°
°
°
`
`
j
j
By using
G
2
c CH
C O
H O
CH
4
2
2
4
μ
μ
μ
Δ
=
+
−
°
°
°
°
and
8F
G
E
c CH
CH /CO
4
4
2
Δ
Δ
= −
°
°
we obtain
E
E
4 F
RT
ln P
P
P
P
CH /CO
CO
H O
2
CH
O
2(c)
4
2
2
2
4
2
Δ
Δ
=
+
#
#
#
°
where Δ c G CH 4
° and ΔE
/
CH CO
4
2
°
are respectively the standard free enthalpy
of combustion for methane and the standard emf associated to the pair
CH 4 / CO 2 .
2. The standard enthalpies of formation Δ f H i ° allow us to calculate the standard
reaction enthalpy Δ r H K
298 °
at 298 K
H
H
r 298 K
i f i
i
υ
Δ
Δ
=
°
°
/
The Kirchhoff equation allows us to calculate it at 1 073 K
H
H
Cp dT
r 1073 K
r 298 K
i
298
1073
Δ
Δ
Δ
=
+
°
°
^
h
#
Numerical evaluation gives
H
802.2 kJ mol
r 298 K
1
Δ
= −
−
°
H
775.2 kJ mol
r 1073 K
1
Δ
=−
−
°
In the same way, based on the absolute standard entropies, we obtain the
change in the standard reaction entropy at 298 K
S
S
r 298 K
i i,298 K
i
υ
Δ
=
°
°
/
We next calculate the absolute standard entropies at 1 073 K
S
S
Cp T
dT
r 1073 K
r 298 K
i
298
1073
Δ
Δ
Δ
=
+
°
°
^
h
#
Numerical evaluation gives
S
213.6 (2 188.7) (2 205) 186.2
r 298 K
Δ
=
+
−
−
#
#
°