Download Chapter 20b - U of L Class Index

The pH meter is a familiar example of
electrochemistry under nonstandard
conditions. It is actually a voltmeter
attached to a glass electrode. The
bulb at the bottom of the glass
Silver wire
electrode is made of a very thin layer
of glass – so thin that a surface
AgCl (s)
potential difference is created when
the internal [H+] and external [H+]
KCl (saturated)
differ. Because the protons cannot
Porous membrane
actually cross the glass membrane,
this potential can be measured (by the
0.1 M HCl
voltmeter) and used to calculate the
external [H+] – which is readily
Glass membrane
converted to the pH of the solution.
Essentially, we are dealing with an
The Glass Electrode
electrochemical cell in which both
half-reactions involve H+/H2 and all of the cell potential is
coming from the concentration gradient. The glass electrode
also contains two Ag+/Ag reference electrodes which are not
included in our calculations. Thus, our half-cells are:
2 H+(aq) + 2 e- → H2(g)
H2(g) → 2 H+(aq) + 2 e-
and
To calculate the external (solution) [H+], we use the Nernst
equation:
RT
E = E° -
nF
lnQ
The standard state cell potential of an H+/H2 anode and H+/H2
cathode would be 0 V therefore all of the potential is coming
from the concentration gradient:
Eglass
=0electrode
RT
lnQ
nF
The reaction quotient is [H+]2inside / [H+]2outside and, as we can see
in the half-cell equations, 2 electrons are transferred, so n = 2:
Eglass
=0electrode
2
[H+ ]inside
RT
ln + 2
2F [H ]
outside
This reduces to:
Eglass
+
RT [H ]inside
ln
=electrode
F [H+ ]
outside
We know that ln(x) = 2.303 log10(x), R = 8.3145 J·mol-1·K-1,
F = 96485 C·mol-1 and under standard conditions T = 298.15 K.
This gives:
+
Eglass
electrode
= - 0.0592log
[H ]inside
[H+ ]outside
Switching to the natural logarithm allows us to calculate pH
values directly (since pH = -log[H+]):
Eglass
electrode
0.0592
Or:
Eglass
= - (log[H+ ]inside − log[H+ ]outside)
electrode
0.0592
= pHinside - pHoutside
Finally, we get:
pHoutside = pHinside
−
Eglass
electrode
0.0592
The reason we have to calibrate pH meters is that the two
reference electrodes aren’t 100% identical, and the electrons
don’t move 100% efficiently. Calibration lets us factor this in.
As you will be aware from lab, pH meters (glass electrodes)
suffer a few limitations – particularly at extreme pH values:
• In strongly acidic solutions (very low pH), pH meters tend
to read high, for reasons that are not yet understood.
• In solutions where [H+] is low and [Na+] is high, the pH
meter will begin to respond to Na+ as well as H+.
• The pH meter measures [H+] in the solution immediately
next to the electrode. In well-buffered solutions, it
responds to changes in [H+] very quickly. In poorly
buffered solutions, it responds to changes in [H+] slowly.
• A dry glass electrode needs to be soaked in water for hours
before it can be used to [H+] with any accuracy.
Cell Potentials and Equilibrium Constants
As we have seen, the Nernst equation allows us to relate cell
potential to the reaction quotient under nonstandard conditions:
E = E° -
RT
lnQ
nF
This equation is very similar to an equation we used to relate
Gibbs free energy to reaction quotient:
∆G = ∆G° + RT lnQ
This should come as no surprise given that cell potential is really
Gibbs free energy “in disguise”. (∆G = nFE).
If we consider the system at equilibrium (E = 0, Q = K), we can
therefore relate cell potential to the equilibrium constant under
standard conditions:
0 = E° -
RT
lnK
nF
or
E° =
RT
lnK
nF
This is a common way to measure equilibrium constants –
measure the cell potential under standard (non-equilibrium)
conditions then use the above formula to calculate K.
e.g. The cell potential for the reaction below under standard
conditions is +0.11 V. Calculate the equilibrium constant
at 25 ˚C.
Ni(s) + Sn 2+(aq)
Ni 2+(aq) + Sn(s)
Commercial Voltaic Cells and Storage Batteries
Thus far, we have looked at voltaic cells schematically. We can
construct cells of the types shown – and they work – but they
wouldn’t be particularly portable or practical. More familiar
voltaic cells come in batteries. Technically, the term battery
refers to a series of voltaic cells connected in series so that their
voltages add up.
e.g. A 12 V car battery is really a series of six 2 V cells.
A 9 V radio battery is really a series of six 1.5 V cells.
A standard 1.5 V “battery” is just one 1.5 V cell.
We can divide commercial voltaic cells into two categories:
• primary batteries, which can only be used once
• secondary batteries, which can be recharged
The category of the cell depends on whether or not the redox
reactions are reversible.
Note that, in most commercial voltaic cells, pastes of inorganic
salts are used. This allows compact storage of the salts. The
water in the paste dissolves some salt to make a saturated
solution in which the ion concentrations do not significantly
decrease until near the end of the cell’s usefulness. The solution
also allows for ion migration (necessary for flow of charge).
Dry Batteries (Zinc-Carbon Cell, or Leclenché Cell)
“Flashlight batteries” are primary
batteries that are single voltaic cells.
The anode is zinc with an insulating
wrapper, and the cathode is a carbon
rod at which manganese is reduced.
Anode (oxidation; E˚ = + 0.76 V)
Zn → Zn2+ + 2eCathode (reduction; E˚ = + 0.74 V)
2 MnO2 + 2 NH4+ + 2 e- →
Mn2O3 + 2 NH3 + 2 H2O
This gives a total voltage of 1.5 V for a fresh dry cell. The
ammonia forms co-ordination complexes with zinc cations,
[Zn(NH3)4]2+. If this gas is generated too quickly, though, it
forms an insulating layer around the cathode and the battery
needs to “rest” before it can be used again.
Alkaline Batteries
“Flashlight batteries” have a limited shelf-life because the acidic
NH4Cl corrodes the zinc can. They also “die” quickly relative to
other types of batteries (as the voltage drops quickly with use).
A common alternative is the alkaline battery. It uses similar
redox chemistry, but in an alkaline (basic) environment. This
minimizes corrosion of the zinc can and prevents the build-upof-ammonia problem. Alkaline batteries also tend use purer
starting materials and have better construction. As such, they
are worth their slightly higher cost and, today, most common
batteries are alkaline. They are also 1.5 V cells, operating under
nonstandard conditions. ([OH-] > 1 M.)
(+)
Cathode(+): paste containing
MnO2, graphite, and water
Outer steel jacket
Plastic sleeve
Anode(-): Paste containing
powdered zinc, KOH, and water
Inner steel jacket
Brass collector
(-)
Cell base
Anode (oxidation; E˚ = + 1.25 V)
Zn + 2 OH- → ZnO + H2O + 2eCathode (reduction; E˚ = + 0.15 V)
2 MnO2 + H2O + 2 e- → Mn2O3 + 2 OH-
Lithium Batteries
Like alkaline batteries, many lithium
batteries reduce manganese at the
cathode and have a basic environment.
The difference is that lithium is
oxidized at the anode (instead of zinc).
Otherwise, the design is similar.
Anode (oxidation; E˚ = + 3.04 V)
Li → Li+ + eCathode (reduction; E˚ = + 0.15 V)
2 MnO2 + H2O + 2 e- → Mn2O3 + 2 OHThere are also a variety of other lithium batteries using different
reductions at the cathode.
Mercury Batteries
Mercury batteries are relatively expensive and deliver 1.34 V
(less than the Mn-based cells). They are, however, very small
and maintain a fairly constant voltage throughout their lifetime.
As such, they are often used for hearing aids and other devices
requiring excellent reliability. They have a zinc-mercury
amalgam as the anode, and a graphite-HgO paste as the cathode.
Anode (oxidation; E˚ = + 1.25 V)
Zn + 2 OH- → ZnO + H2O + 2eCathode (reduction; E˚ = + 0.09 V)
HgO + H2O + 2 e- → Hg + 2 OH-
Zinc-Air Batteries
Similar to the mercury batteries in both construction and
application, zinc-air batteries have the interesting property that
the species reduced at the cathode is oxygen from the air. As
such, they have air holes (which must be uncovered before use).
Anode (oxidation; E˚ = + 1.25 V)
Zn + 2 OH- → ZnO + H2O + 2eCathode (reduction; E˚ = + 0.40 V)
½O2 + H2O + 2 e- → 2 OH-
Lead Acid Batteries
Unlike the examples we have looked
at thus far, lead acid batteries are
rechargeable (i.e. secondary batteries).
Generally, several lead acid cells (2 V
each) are connected in series to give a
higher-voltage battery.
Both the
cathode and anode involve reactions
between a lead source and hydrogen
sulfate (from the sulfuric acid used to
make the cell).
Anode (oxidation; E˚ = + 0.35 V)
Pb + HSO4- → PbSO4 + H+ + 2eCathode (reduction; E˚ = + 1.69 V)
PbO2 + HSO4- + 3 H+ + 2 e- → PbSO4 + 2 H2O
When the battery is recharged, a voltage is applied which makes
the two reactions run in reverse. As such, the PbSO4 deposited
on both electrodes is converted back into Pb, PbO2 and HSO4-.
Nickel-Cadmium Batteries (aka. Ni-cad batteries)
Ni-cad batteries are also rechargeable. They are more expensive
than lead acid batteries, but they have the advantages of being
smaller, longer lived and more easily recharged.
Anode (oxidation; E˚ = + 0.49 V)
Cd + 2 OH- → Cd(OH)2 + 2eCathode (reduction; E˚ = + 0.82 V)
NiO(OH) + H2O + e- → Ni(OH)2 + OHBecause they are not operating under standard conditions, the
nominal voltage of a Ni-cad battery is 1.2 V (not 1.3 V).
Electrolytic Cells
Recharging a battery is just one application
of electrolysis (the process by which a
reversible reactant-favoured redox reaction
is forced to go forward by applying a
voltage.) Electrolysis can also be used to
produce metals from solutions of their
cations – either as pure samples or in a
process called electroplating (adding a thin
layer of metal to the outside of an existing
object, see picture at right1).
Many steel parts are electroplated for strength:
• Car bumpers can be coated with first nickel then chromium.
• Bolts are often coated with either zinc or cadmium.
• Light fixtures can be coated with nickel then either chrome
or brass. (This is more for appearance than strength.)
A third example of electrolysis is the commercial production of
chlorine gas and sodium hydroxide from salt-water:
2 NaCl + 2 H2O → 2 NaOH + Cl2 + H2
What species is being oxidized?
What species is being reduced?
We generally measure the efficiency of an electrolytic cell by
comparing the number of moles of electrons consumed with the
number of moles of products made (factoring in stoichiometry
as necessary). Measuring the current gives us information from
which we can calculate the number of moles of electrons made:
1
http://en.wikipedia.org/wiki/Electroplating, last visited on April 5, 2006.
I=q
t
where I is current (in Amperes), q is charge (in Coulombs) and t
is the time for which the current was applied (in seconds). We
also know that the charge of one mole of electrons is 96 485
Coulombs per mole (Faraday’s constant, F).
Therefore:
I=
ne F
t
or
ne = It
F
(a) If you electrolyze a solution of Ni2+(aq) to form Ni(s) using a
current of 0.15 amp for 10 minutes, what mass of solid
nickel should be produced?
(b) If the electrolysis described in part (a) produced 25 mg of
nickel, what was the percent efficiency of this process?
Important Concepts from Chapter 20
• Assigning oxidation states, redox reactions, etc.
• Using half-reactions to balance redox reactions (in acid and in
base)
• Voltaic cells vs. electrolytic cells
• Cell potential (and how it relates to Gibbs free energy)
• Components of a voltaic cell
o electrodes (cathode and anode)
o salt bridge
• Cell notation
• Cells under nonstandard conditions (the Nernst equation)
• Relationship between E˚ and equilibrium constant
• Practical considerations for batteries, pH meters, etc.
• Applications of electrolytic cells
• Determining efficiency of electrolytic cells