Electrolysis of water, explained

I had never found a satisfactory explanation anywhere
for how electrolysis of water works, so finally, with the
help of a friend, I figured it out, and explain it here.

Electrolysis of water is when you stick two electrodes
into a container of water, apply electricity, and get
hydrogen gas and oxygen gas bubbling out.

The standard explanations on the Internet and in chemistry
textbooks, which I find unsatisfactorily incomplete,
go something like this:

When attempting electrolysis with plain water, it doesn’t
work very well.  The concentrations of H+ and of OH- in
pure water are very low, so there is very little migration
of ions when an electric field is applied.  OH- accumulates
near the cathode, and H+ near the anode, making those
parts of the solution electrically charged, so that it
starts to take very high voltages to push electric
current through.  After the first few bubbles, the
reaction slows down to a snail’s pace.  However, adding
salt to the water makes the water easily conduct
electricity by movement of salt ions, and the electrolysis
reaction easily continues.

I can see how adding salt makes the water conductive,
but what I didn’t get about this was: how does that help
divide H2O into H2 and O2?  I mean, you could short-circuit
the electrodes by joining them with a piece of wire.
That would allow electricity to flow between them, but
it wouldn’t split water molecules.  What exactly is it
about the movement of salt ions that facilitates electrolysis?

There are two mechanisms.  Mechanism I, which begins in
full force as soon as the electricity is applied, involves
progressively changing concentrations of ions.  Gradually,
Mechanism II takes over, which can continue in a steady
state — steady except for the continual bubbling away
of oxygen and hydrogen and resultant reduction in volume
of water, which I ignore here.

Mechanism I works like this: positive salt ions approach
the cathode and remain there, producing an ever-increasing
concentration of these ions very close to the cathode.
Similarly, negative salt ions accumulate close to the anode.
These are accompanied by an ever-increasing concentration
of OH- near the cathode and of H+ near the anode, making
the solution approximately electrically neutral, although
alkaline near the cathode and acidic near the anode.

The OH- is formed at the cathode when electrons are added
to the water and H2 bubbles away:

2H2O + 2e- –> 2OH- + H2

The H+ is formed at the anode when electrons are removed
from the water and O2 bubbles away:

2H2O –> O2 + 4H+ + 4e-

But Mechanism I can’t go on forever.  It requires
continually increasing concentrations.  Eventually
something’s going to go bust.  Besides, people have
run electrolysis experiments for days, bubbling away
as hydrogen and oxygen half or more of the volume
of water.  There aren’t enough salt ions in the
solution to electrolise that much water via Mechanism I.
It has been argued that the salt ions diffuse back
and are recycled to participate in Mechanism I again;
however, although diffusion does occur, this can’t
explain the continuing reaction: moving in the opposite
direction would be undoing their work, cancelling the
effect and reducing the rate of electrolysis.

No, another mechanism is needed.  Luckily, once those
ion concentrations reach significant levels, something
wonderful happens:  it is no longer true that the
concentrations of H+ and of OH- are too low to support
much ion movement.  No, their concentrations become
considerable, and their migration becomes a significant
factor in the continuing electrolysis reaction.

After Mechanism I has been going for a while and some
diffusion has occurred, we have alkaline solution near
the cathode, gradually gradating to reduced alkalinity
further from the cathode, neutral in a 2-dimensional zone
(surface) perhaps halfway between the electrodes, and
gradually increasing acidity towards the anode.  When
Mechanism II is the only thing happening, these
concentrations are not changing with time.

In the alkaline zone, because there is a gradient in
the concentration of positive salt ions, there ions
have a tendency to diffuse away from the cathode.
Once steady state is reached, this tendency is exactly
balanced by the tendency to migrate towards the cathode
due to the applied electricity.

The numerous OH- ions in the alkaline zone have the same
tendency to diffuse away from the cathode that the
positive salt ions have, because they have approximately
the same concentrations and gradients of concentration.
However, their electric charge is the opposite, which
means that their push to migrate due to the electricity
is also away from the cathode, not the opposite direction
as is the case with the salt ions.  It’s like when your
salary and your sense of moral duty are both pushing
you to perform the same actions.

So, throughout the alkaline part of the solution, we have
significant migration of OH- away from the cathode.
Similarly, H+ is migrating away from the anode throughout
the acidic part of the solution.  The role of the salt
ions is to cancel electric charge: in Mechanism I
so that the concentrations of H+ and OH- can increase,
and in Mechanism II so that their concentrations can
remain high, allowing migration to occur.

Since there is ion migration without changes in
concentrations, there must be a source and a sink for
each of these ions.  The OH- are generated at the cathode
and the H+ at the anode in the reactions described above;
and these two types of ions disappear when they meet
in the middle and join to form H2O.  They must join,
in almost all cases, because you can’t have high
concentrations of both these ions in the same part
of an aqueous solution.

In effect, in order to split one water molecule, there
are three reactions:  one water molecule splits at the
cathode, and part of it contributes to the production
of H2.  Another water molecule splits at the anode,
and part of it contributes to the production of O2.
The two remaining parts migrate to the middle of the
solution and join.  These three reactions add up to a
net splitting of one water molecule.  Heat is
given off at the neutral part of the solution, where
the rejoining occurs.

Since concentrations are not changing with time and
there is therefore no accumulation of these ions
anywhere, the total flux of ions has to be the
same at different distances from the cathode, to
carry the same amount of current.  To achieve this,
the velocity of the ions is higher where their
concentration is lower.  The higher velocity must
be caused by a greater electric field.  Therefore,
the voltage drop is larger at and near the surface
where the solution is chemically neutral, (perhaps
midway between the electrodes).  The ions approaching
the neutral surface act like water approaching
a waterfall:  slowly at first, then gradually
speeding up and thinning out until suddenly they’re
rushing off the edge — or into the arms of a
waiting ion of the opposite charge.

Somewhat related links:

Cathy Woodgold’s home page http://www.ncf.ca/~an588/index.html

U.S. Department of Defense report on Cold Fusion http://www.lenr-canr.org/acrobat/BarnhartBtechnology.pdf

Status of Cold Fusion (2010), Storms, Naturwissenschaften http://www.springerlink.com/content/9522x473v80352w9/

Thanks to Abd ul-Rahman Lomax for enlightening
discussion, without which &c.

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About woodgold

Interested in math and science; social justice and the environment; natural health care, barter systems, voting systems and other systems for empowering large numbers of people
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