Solutions to exercises
285
3. The electrochemical chain describing the Na / S battery is
Na ℓ / Na 1.67 Mg 0.67 Al 10.33 O 17 / S
4. At the anode, sodium is oxidized
Na ℓ m Na
+ + e
At the cathode, the two following reactions occur:
5S + 2e m S 5
2−
then
x
S
x
e
1 5
5
2
5
2
−
+
−
`
j
m S x
5
2 −
−
The overall operating reaction
2 for the first step is
5S + 2Na ℓ m Na 2 S 5
2 and for the second step is
x
Na
x
Na S
5
2
1 5
2 5
+ −
,
`
j
m Na 2 S 5 − x
5. The theoretical energy density is expressed by
W
m
Q E
th
Δ
=
#
Q is the expected electric charge and ΔE is the potential difference at the
terminals of the battery. Taking as reference the global reaction involving
the first cathodic reaction, we obtain
W
2M
5 M
2F E
th
Na
S
Δ
=
+
#
Numerical evaluation gives
(
) (
)
.
W
k J kg
2 23
5 32 10
2 96 480 2 08
1948
th
3
1
=
+
=
−
−
#
#
#
#
#
6
@
W
Wh kg
541
th
1
=
−
6. In evaluating W p , we must account for the mass of the electrolyte, the sodium
and sulfur containers, the heating system, the thermal isolation apparatus, …
Because more mass must be considered, the specific energy density is thus
lower.