Ask A Scientist Chemistry Archive

 
name         Nelly
status       student
age          18

Question -   Hi,
I know that diffusion is a passive transport, i.e. does not require energy
expenditure. But certainly there must be energy that drives the movement
of molecules from high concentration to low concentration. So I am
wondering what is the energy that causes diffusion to occur? and how does
concentration gradient provides a driving force for movement?
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Deep thoughts, but not quite the way we understand it today.
Diffusion requires the kinetic energy of heat for "lubrication", but uses none of it up.
It can even be used to give you a little energy as it progresses, and it costs energy to 
reverse it.

Imagine a pot of white potato soup, with you above it, stirring with a stick.
Put in a drop of red food color on the left side, and blue food color on the right.
After a while, it will all be light purple, and you never had to stir any harder.
But if you had to go get every molecule of red dye and put it back on the left side,
that would take work, some  kind of distinct pushing which I haven't yet invented for 
this poor analogy.

Scientists invented a new and different name for the kind of energy you envision.
They call it "Entropy".  It means disorder, randomness, homogenously-mixed-up-ness,
and a lack of special opportunities for making things happen.
Entropy drives diffusion, even sometimes when energy pushes back.

Some compounds make water cold instead of warm when they dissolve.
If it uses up energy, why does it happen?
Because, when molecules temporarily get a little more vibration energy than usual
and use it up to climb out of their solid cluster,
they often fail to fall back into the old grip and return the energy.
Because they simply wander away and get lost.
They diffuse into the water, breaking up the crystal even though that costs energy.
Increasing entropy has justified using up some heat energy.

Such "getting lost" is a matter of probability.
There are more places for a sugar molecule to be, out in the water,
than there are all segregated together in the crystal.
So random wandering will tend to go towards dissolution,
unless overwhelming energy difference captures and holds most of them back.

There is a trade-off between energy and entropy.
When the temperature is high, reversing entropy costs much energy.
When the temperature is absolute zero, it costs nothing.

You can imagine ants in a windstorm trying to keep two kinds of leaves apart.
They are expending energy to keep on pushing back entropy.
If there is no wind, the ants can finish their sorting and altogether stop working .

When scientists measure how much energy it takes to make a molecule,
you usually want the answer at room temperature, which is not absolute zero.
But you normally think of the molecule as standing still (absolute zero),
not hot and vibrating (room temperature).
How do you reconcile the difference?

If you take a bunch of atoms and tie them together in one big, rigid molecule,
the atoms can no longer wiggle as freely as before.
That costs a little of the energy which making the molecular bonds would otherwise have 
given you.
Consider it "Chaos Tax", the price of opposing entropy.

So scientists end up with three answers for the energy of building a molecule:
  - the pure energy of formation done at zero temperature ("enthalpy of formation, H"),
  - the change in disorder ("entropy of formation, S"), in completely different units 
  than energy.
  - and the weighted sum of the two for your favorite temperature T ("free energy of 
  formation, F").    F(T) = H + (S x T)

"Free Energy" means "How much is really left for you to use after you finish fighting 
entropy?"

Try to imagine marbles of two different weights but the same size, in one layer, in a 
large slightly tilted cakepan.
With low vibration, all the heavy marbles will go to the deep end, and lighter marbles 
will be left with the shallow end.
With stronger vibration, they will begin to intermix with the lighter marbles.
This brings us almost back to your diffusion scenario.

sorry this response didn't come sooner...
Jim Swenson                                                                 
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