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Enthalpy

Page history last edited by Joe Redish 8 years, 8 months ago

Working content

 

Prerequisites:

 

When you've studied the energy changes associated with chemical reactions in your chemistry class, the quantity you've looked at was the change in enthalpy.  But what is enthalpy really?  Is it just the same thing as the change in energy?  If not, what's the difference?  And when is it useful to use enthalpy vs. energy?

 

This page will try to answer these questions.  The key is in which variables are held constant, and which variables are allowed to change.  (This is often the key when we make decisions about how to model a system!)

 

When a chemical reaction takes place, there is a net output or input of energy, which is associated with the making or breaking of chemical bonds (and therefore represents changes in potential and kinetic energy at the atomic and molecular level).  If this reaction took place inside a sealed container with rigid walls (i.e. constant volume), that would be the end of the story, at least as far as the energy in the system was concerned:  the energy "cost" of the reaction would just be this change in internal energy.  Energy would change from one form to another (say, chemical to thermal, for an exothermic reaction) and the total energy of the system would not change. But frequently, in chemistry and biology, the systems we're interested in don't have constant volume, but do have constant pressure (often atmospheric pressure).

 

Consider first a constant volume example:  you're boiling water on a stove in a closed pot.  (There are no holes in the lid for the steam to escape.)  The reaction H2O (l) -> H2O (g) is endothermic:  it takes energy to break the hydrogen bonds that hold the water molecules together in the liquid phase, so that they can move freely in the gas phase.  As the water boils and becomes vapor, there are more molecules hitting the lid of the pot, and they are therefore exerting more force (per area) on the lid.  Thus the pressure inside the pot is increasing.  (Eventually, the lid would blow off!) All the energy that can into the pot from the burner was put into the water.

 

Now let's say, instead of a pot, you're boiling water inside a container that can freely expand and contract (like a balloon, but one that won't melt or pop and whose surface tension can be ignored!).  Then the pressure inside this container will always end up equal to atmospheric pressure (i.e. the pressure outside):  if the pressure is greater inside than outside, there will be a net force pushing the walls of the container outward, so it will expand (which decreases the pressure inside) until the pressure inside is equal to the pressure outside (so the net force is zero).  If the pressure outside is greater than the pressure inside, the reverse will happen: the container will shrink (increasing the pressure) until the pressure is equal inside and outside.

 

So what happens when the water boils?  Instead of the pressure building up inside the container, the container expands, keeping the pressure inside equal to atmospheric pressure.  But when the water (vapor) inside the container expands, it does work on its surroundings (since it's exerting a force over a displacement).

 

How much work? 

 

     Work = (Force) * (displacement)

              = (Force / area) * (area * displacement) = (Pressure) * (change in volume)

 

So if we want to find the total energy that it takes to make this change happen at constant pressure, we have to consider not only the change in energy involved in breaking/making bonds for converting liquid to gas, we also have to add the energy to "make room" for the products of the reaction (i.e. the work involved in changing the volume).

 

This total energy is called the enthalpy.  The symbol is H, and it is defined as U + pV (internal energy + pressure * volume), for the reasons discussed above.

 

But what we typically care about is the change in enthalpy:  ΔH = ΔU + pΔV.  This is what you looked up (for various reactions) in the back of your chemistry textbook. Since the change in enthalpy depends on pressure, the tables had to assume a pressure -- typically 1 atmosphere.

 

Enthalpy is the relevant quantity for systems at constant pressure.  Biologically relevant systems at constant pressure include:

 

  • Cells, since the membrane can expand or contract to stay at atmospheric pressure (like the balloon in our example)
  • Anything open to the environment (imagine the pot of boiling water had the lid off)

 

A positive change in enthalpy means that energy is being input to the system (and remember, this is the net energy after you consider the work involved in keeping the system at constant pressure); in other words, the process is endothermic.  A negative change in enthalpy means that energy is being released from the system to its surroundings (again, including the work to keep the system at constant pressure).

 

Follow-ons:

  • Making sense of entropy -- sharing
  • Gibbs free energy

 

 

Ben Dreyfus 12/26/2011

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