1. Lead-Acid Battery 1
The basic electrochemical reaction equation2 in a lead-acid battery can be written as follows:
Pb + 2H2SO4 + PbO2
<---- Charging
+ PbSO4 + 2H2O + PbSO4
Discharging---->
1.1 Discharging the Lead-Acid Battery
During the discharge portion of the reaction, lead dioxide (positive plate) and lead
(negative plate) react with sulfuric acid to create lead sulfate, water and energy.
1.2 Charging the Lead-Acid Battery
During the recharge phase of the reaction, the cycle is reversed: the lead sulfate and
water are electro-chemically converted to lead, lead oxide and sulfuric acid by an
external electrical charging source.
1.3 Problems of Lead-Acid Battery
The biggest problem in lead-acid cells is sulfation due to chronic undercharging.
Here the sulfate ions have entered into deep bonds with the lead on the cell's
plates. The sulfate ions can bond with the lead at three successively deeper energy
levels. Level One is the bond we use when we normally charge and discharge the
cell. After a month or so at Level One, some of the bonds form Level Two bonds
which require more electric power to break. After several months of being at
Level Two bond, the sulfate ions really cozy up to the lead and form Level Three
bonds. Level Three bonds are not accessible electrically. No amount of
recharging will break Level Three bonds. The longer the lead sulfate bond stays
at a level the more likely it is to form a closer acquaintance and enter the next
deeper level. This is why it is so important to fully, regularly, and completely,
recharge lead-acid cells.
1.4 Lead-Acid Battery Equalization Charges
If the loss in capacity is due to Level Two bonding, then a repeated series of
equalizing charges will break the Level Two bonds. Under equalization the Level
Two bonds will first be transformed into Level One bonds, and then the sulfate ion
can be kicked loose of the lead entirely and reenter the electrolyte solution. If
your lead-acid cells have lost capacity, then a regime of equalizing charges is the
first procedure to try. An equalization charge is a controlled overcharge of an
already fully recharged cell. First recharge the cell and then continue to charge
the cell at a C/20 rate for five to seven hours. During equalization charges, the
cell voltage will become very high, about 2.7 VDC per cell. This overcharge
contains the necessary power to break the Level Two bonds and force them to
Level One. Once they reach Level One, the bond is easily broken and the sulfate
ions reenter into solution in the electrolyte.
1.5 Lead-Acid Battery Care3
The Lead acid battery is made up of plates, lead, and lead oxide (various other elements
are used to change density, hardness, porosity, etc.) with a 35% sulfuric acid and 65% water
solution. This solution is called electrolyte which causes a chemical reaction that produce
electrons. When you test a battery with a hydrometer you are measuring the amount of sulfuric
acid in the electrolyte. If your reading is low, that means the chemistry that makes electrons is
lacking. So where did the sulfur go? It is stuck to the battery plates and when you recharge the
battery the sulfur returns to the electrolyte.
State of Charge Specific Gravity
1.265
1.225
1.190
1.155
1.120
100%
*75%
50%
25%
Discharged
Voltage
6V
12V
6.3
12.7
6.2
12.4
6.1
12.2
6.0
12.0
6.0
11.9
*Sulfation of Batteries starts when specific gravity falls below 1.225 or voltage measures less than
12.4 (12v Battery) or 6.2 (6 volt battery). Sulfation hardens the battery plates reducing and
eventually destroying the ability of the battery to generate Volts and Amps.
The alternator is a battery charger. It works well if the battery is not deeply discharged. The
alternator tends to overcharge batteries that are very low and the overcharge can damage
batteries.
2. THERMODYNAMICS
First Law of Thermodynamics : You can’t create or destroy energy
Second Law of Thermodynamics: Energy spontaneously disperses from being localized
to becoming spread out if it is hindered.
Third Law of Thermodynamics: The entropy of a perfect crystal is zero when the
temperature of the crystal is equal to absolute zero (0K).
Thermodynamic Properties of Selected Substances 4
For one mole at 298K and 1 atmosphere pressure
Enthalpy Gibbs Entropy Specific heat Volume
Substance (form)
CP(J/K)
V(cm3)
∆fH (kJ) ∆fG (kJ) (J/ K
Al (s)
28.33
24.35
9.99
-2594.29 -2443.88 83.81
121.71
44.09
Al2SiO5 (andalusite) -2590.27 -2442.66 93.22
122.72
51.53
Al2SiO5 (sillimanite) -2587.76 -2440.99 96.11
124.52
49.90
Ar (g)
0
0
154.84
20.79
...
C (graphite)
0
0
5.74
8.53
5.30
C (diamond)
1.895
2.900
2.38
6.11
3.42
CH4 (g)
-74.81
-50.72
186.26
35.31
...
C2H6 (g)
-84.68
-32.82
229.60
52.63
...
C3H8 (g)
-103.85
-23.49
269.91
73.5
...
C2H5OH (l)
-277.69 -174.78
160.7
111.46
58.4
Al2SiO5 (kyanite)
0
0
C6H12O6 (glucose)
-1268
-910
212
115
...
CO (g)
-110.53 -137.17 197.67
29.14
...
CO2 (g)
-393.51 -394.36 213.74
37.11
...
H2CO3 (aq)
-699.65 -623.08
187.4
...
...
HCO3- (aq)
-691.99 -586.77
91.2
...
...
Ca (aq)
-542.83 -553.58
-53.1
...
...
CaCO3 (calcite)
-1206.9 -1128.8
92.9
81.88
36.93
CaCO3 (aragonite)
-1207.1 -1127.8
88.7
81.25
34.15
CaCl2 (s)
-795.8
-748.1
104.6
72.59
51.6
0
0
223.07
33.91
...
56.5
-136.4
17.3
2+
Cl2 (g)
-
Cl (aq)
-167.16 -131.23
Cu (s)
0
0
33.150
24.44
7.12
Fe (s)
0
0
27.28
25.10
7.11
H2 (g)
0
0
130.68
28.82
...
H (g)
217.97
203.25
114.71
20.78
...
0
0
0
0
...
H+ (aq)
H2O (l)
-285.83 -237.13
69.91
75.29
18.068
H2O (g)
-241.82 -228.57 188.83
33.58
...
He (g)
0
0
126.15
20.79
...
Hg (l)
0
0
76.02
27.98
14.81
N2 (g)
0
0
191.61
29.12
...
NH3 (g)
-46.11
-16.45
192.45
35.06
...
Na+(aq)
-240.12 -261.91
59.0
46.4
-1.2
NaCl (s)
-411.15 -384.14
72.13
50.50
27.01
NaAlSi3O8 (albite)
-3935.1 -3711.5 207.40
205.10
100.07
NaAlSi2O6 (jadeite)
-3030.9 -2852.1
133.5
160.0
60.40
Ne (g)
0
0
146.33
20.79
...
O2 (g)
0
0
205.14
29.38
...
O2 (aq)
-11.7
16.4
110.9
...
...
-148.5
...
OH- (aq)
Pb (s)
-229.99 -157.24 -10.75
0
0
64.81
26.44
18.3
PbO2(s)
-277.4
-217.33
68.6
64.64
...
PbSO4(s)
-920.0
-813.0
148.5
103.2
...
SO42- (aq)
-909.27 -744.53
20.1
-293
...
HSO4- (aq)
-887.34 -755.91
131.8
-84
...
SiO2 (α quartz)
-910.94 -856.64
41.84
44.43
22.69
H4SiO4(aq)
-1449.36 -1307.67 215.13
468.98
...
Data from Schroeder, Daniel V., An Introduction to Thermal Physics, Addison-Wesley,
2000.
Enthalpy Change5
Definitions
•
•
•
•
•
The heat content of a chemical system is called the enthalpy (symbol: H)
The enthalpy change ( H) is the amount of heat released or absorbed when a chemical reaction
occurs at constant pressure.
H = H(products) - H(reactants)
H is specified per mole of substance as in the balanced chemical equation for the reaction
The units are usually given as kJ mol-1 (kJ/mol) or sometimes as kcal mol-1 (kcal/mol)
1 calorie (1 cal) = 4.184 joules (4.184 J)
Energy changes are measured under standard laboratory conditions
25oC (298K) & 101.3kPa (1 atmosphere)
Type of
Exothermic
Reaction
Energy Energy is released.
absorbed Energy is a product of the reaction.
or
Reaction vessel becomes warmer.
released Temperature inside reaction vessel increases.
Relative
Energy
of
Energy of the reactants is greater than the
reactants energy of the products
&
products
Sign of
H = H(products) - H(reactants) = negative (-ve)
H
Writing N2(g) + 3H2(g) -----> 2NH3(g) + 92.4 kJ
the
N2(g) + 3H2(g) ---> 2NH3(g)
H=-92.4 kJ
equation mol-1
Energy of reactants (N2 &
H2) is greater than the
energy of the products
(NH3).
Energy is released.
Energy
H is negative.
Profile
H is measured from the
energy of reactants to the
energy of products on the
Energy Profile diagram.
Enthalpy comes from the Greek “heat inside”
Endothermic
Energy is absorbed.
Energy is a reactant of the reaction.
Reaction vessel becomes cooler.
Temperature inside reaction vessel decreases.
Energy of the reactants is less than the energy
of the products
H = H(products) - H(reactants) = positive (+ve)
2NH3(g) + 92.4 kJ -----> N2(g) + 3H2(g)
2NH3g ---> N2(g) + 3H2(g)
H=+92.4 kJ
mol-1
Energy of reactants (NH3) is
less than the energy of the
products (N2 & H2).
Energy is absorbed.
H is positive.
H is measured from the
energy of reactants to the
energy of products on the
Energy Profile diagram.
Entropy6 is defined as the degree of freedom that particles of matter have. The letter “S”
is used to symbolize entropy. Gases have greater entropy than pure liquids, which have
greater entropy than pure solids. Solutions have greater entropy than pure liquids as the
particles in a solution are more separated and solvent molecules separate the solute
particles:
S gas > Ssoln > Sliq > Ssolid
Entropy is merely the way to measure the energy that spreads out in a process
(as a function of temperature). Entropy change, S, measures how much
energy is spread out in a system, or how spread out is the energy of a system
(both always involving T). As an example of reversible process, melting ice to
water at 273 K where S = q/T. So, in that equation, it's easy to see that q (the
enthalpy of fusion) is how much "heat" energy was spread out in the ice to
change it to water. The absolute entropy is obtained by integrating entropy
change from absolute zero to T.
The enthalpy data in the table are relative data (∆H), which compare each compound
with its elements. The data are relative because there is no absolute zero on the enthalpy
scale. All we can measure is the heat given off or absorbed by reaction. Thus, all we can
determine is the difference between the enthalpies of the reactants and the products of a
reaction. We therefore define the enthalpy of formation of the elements in their most
thermodynamically stable states as zero and report all compounds as either more or less
stable than their elements.
The entropy data are different. The third law defines absolute zero on the entropy scale.
As a result, the absolute of any element or compound can be measured by comparing it
with a perfect crystal at absolute zero. The entropy data are therefore given as absolute
numbers, S0.
The Gibbs free energy7 of a system, represented by the letter “G”, is defined as the
energy of a system that is free to do work at constant temperature and pressure.
Mathematically, it is defined as:
G=H-TS
Where:
G is the free energy
H is the enthalpy
T is the temperature
S is the entropy of the system
The change in free energy is calculated as:
∆G = ∆H - T∆S
3. Electrolysis of Water8
By providing energy from a battery, water (H2O) can be dissociated into the
diatomic molecules of hydrogen (H2) and oxygen (O2). This process is a good
example of the application of the four thermodynamic potentials.
The electrolysis of one mole of water produces a mole of hydrogen gas and a
half-mole of oxygen gas in their normal diatomic forms. A detailed analysis of the
process makes use of the thermodyamic potentials and the first law of
thermodynamics. This process is presumed to be at 298K and one atmosphere
pressure, and the relevant values are taken from a table of thermodynamic
properties.
Quantity
H2O
Enthalpy -285.83 kJ
H2
0.5 O2
Change
0
0
∆H = 285.83 kJ
Entropy 69.91 J/K 130.68 J/K 0.5 x 205.14 J/K T∆S = 48.7 kJ
ΔH=H(products)-H(reactants)=H(H2) +H(0.5O2) -H(H2O)=0+0-(-285.83)=285.83kJ
TΔS
The process must provide the energy for the dissociation plus the energy to
expand the produced gases. Both of those are included in the change in enthalpy
included in the table above. At temperature 298K and one atmosphere pressure,
the system work is
W = P∆V = (101.3 x 103 Pa)(1.5 moles)(22.4 x 10-3 m3/mol)(298K/273K) = 3715 J
Where: P=101.3x103 Pa(Pascal)= 1 atm; V=22.4x10-3 m3/mol @ T=273K and P=1 atm
Since the enthalpy H= U+PV, the change in internal energy U is then
∆U = ∆H - P∆V = 285.83 kJ - 3.72 kJ = 282.1 kJ
This change in internal energy must be accompanied by the expansion of the
gases produced, so the change in enthalpy represents the necessary energy to
accomplish the electrolysis. However, it is not necessary to put in this whole
amount in the form of electrical energy. Since the entropy increases in the
process of dissociation, the amount T∆S can be provided from the environment
at temperature T. The amount which must be supplied by the battery is actually
the change in the Gibbs free energy:
∆G = ∆H - T∆S = 285.83 kJ - 48.7 kJ = 237.1 kJ
Since the electrolysis process results in an increase in entropy, the environment
"helps" the process by contributing the amount T∆S. The utility of the Gibbs free
energy is that it tells you what amount of energy in other forms must be supplied
to get the process to proceed.
4. Hydrogen Fuel Cell
Hydrogen and oxygen can be combined in a fuel cell to produce electrical
energy. A fuel cell uses a chemical reaction to provide an external voltage, as
does a battery, but differs from a battery in that the fuel is continually supplied in
the form of hydrogen and oxygen gas. It can produce electrical energy at a
higher efficiency than just burning the hydrogen to produce heat to drive a
generator because it is not subject to the thermal bottleneck from the second law
of thermodynamics. It's only product is water, so it is pollution-free. All these
features have led to periodic great excitement about its potential, but we are still
in the process of developing that potential as a pollution-free, efficient energy
source (see Kartha and Grimes).
Combining a mole of hydrogen gas and a half-mole of oxygen gas from their
normal diatomic forms produces a mole of water. A detailed analysis of the
process makes use of the thermodynamic potentials. This process is presumed
to be at 298K and one atmosphere pressure, and the relevant values are taken
from a table of thermodynamic properties.
Quantity
H2
0.5 O2
Enthalpy
0
0
H2O
Change
-285.83 kJ ∆H = -285.83 kJ
Entropy 130.68 J/K 0.5 x 205.14 J/K 69.91 J/K T∆S = -48.7 kJ
Energy is provided by the combining of the atoms and from the decrease of the
volume of the gases. Both of those are included in the change in enthalpy
included in the table above. At temperature 298K and one atmosphere pressure,
the system work is
W = P∆V = (101.3 x 103 Pa)(1.5 moles)(-22.4 x 10-3 m3/mol)(298K/273K) = -3715 J
Since the enthalpy H= U+PV, the change in internal energy U is then
∆U = ∆H - P∆V = -285.83 kJ - 3.72 kJ = -282.1 kJ
The entropy of the gases decreases by 48.7 kJ in the process of combination
since the number of water molecules is less than the number of hydrogen and
oxygen molecules combining. Since the total entropy will not decrease in the
reaction, the excess entropy in the amount T∆S must be expelled to the
environment as heat at temperature T. The amount of energy per mole of
hydrogen which can be provided as electrical energy is the change in the Gibbs
free energy:
∆G = ∆H - T∆S = -285.83 kJ + 48.7 kJ = -237.1 kJ
For this ideal case, the fuel energy is converted to electrical energy at an
efficiency of 237.1/285.8 x100% = 83%! This is far greater than the ideal
efficiency of a generating facility which burned the hydrogen and used the heat to
power a generator! Although real fuel cells do not approach that ideal efficiency,
they are still much more efficient than any electric power plant which burns a fuel.
Comparison of electrolysis and the fuel cell process
In comparing the fuel cell process to its reverse reaction, electrolysis of water, it is useful
treat the enthalpy change as the overall energy change. The Gibbs free energy is that
which you actually have to supply if you want to drive a reaction, or the amount that you
can actually get out if the reaction is working for you. So in the electrolysis/fuel cell pair
where the enthalpy change is 285.8 kJ, you have to put in 237 kJ of energy to drive
electrolysis and the heat from the environment will contribute T∆S=48.7 kJ to help you.
Going the other way in the fuel cell, you can get out the 237 kJ as electric energy, but
have to dump T∆S = 48.7 kJ to the environment.
Reference 9
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
9.
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/leadacid.html
http://www.flex.com/~kalepa/technotes.htm
http://www.batterystuff.com/battery/battery_tutorial.htm
http://hyperphysics.phy-astr.gsu.edu/hbase/tables/therprop.html
http://www.ausetute.com.au/enthchan.html
http://members.aol.com/profchm/entropy.html
http://www.shodor.org/UNChem/advanced/thermo/
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/electrol.html
Fuel Cells FactFile Published by IEE, Jan 2003.