[djvan]

I'm reviewing Enthalpy and PV work and how they relate to Internal Energy.  I came across the following:

ΔU = ΔH - PΔV

In an exothermic reaction the system transfers heat to the atmosphere, resulting in negative ΔH.  Looking at this alone, we can see that an exothermic process decreases the internal energy of the system (this makes sense, as the products of an exothermic reaction are more stable - less energy).

My book uses the following equation as an example:

2 Na (s) + 2 H₂O(l)  2 NaOH (aq) + H₂(g)

It mentions that the H₂ gas that is released during the reaction pushes upward on the atmosphere - this requires energy in the form of PV work.  They then state that the calculated  value is "-PΔV = -2.5 kJ".  (I assume this means a positive 2.5 kJ, since both sides are negative?) They also give ΔH = -368.6 kJ.  They then plug and chug: "ΔU = ΔH - PΔV":

ΔU = -368.6 kJ - 2.5 kJ = -371.1 kJ

I thought that an increase in volume was an endothermic process? (If I'm wrong here, please explain why volume increase is exothermic)  Why is an endothermic process additive to an exothermic process? (the equation made ΔU more negative by subtracting a positive "PV".)  Shouldn't an endothermic process make ΔU more positive, in the sense that it should oppose an exothermic process?

Many thanks!

[Corribus]

Internal energy is the sum of all kinetic and potential energy in the system.  In your reaction, the system has lost potential energy in two ways: First, you've lost energy in the form of heat to the surroundings (that's the exothermic, ΔH part you've already identified). Second, you've also lost energy in the form of the capacity to do expansion work (because, essentially, the system has just done expansion work on the surroundings).

Here's a quick guide:

Heat lost to the surroundings, U decreases.
Heat gained from the surroundings, U increases.
Work done on the surroundings by the system, U decreases.
Work done on the system by the surroundings, U increases.

If there's an expansion, the system is doing work on the surroundings.  If there is a contraction, the surroundings are doing work on the system. 

[djvan]

Thank you Corribus, that makes complete sense - I understand why an expansion leads to a decrease in internal energy.  However, isn't an increase in volume usually accompanied by a decrease in temperature (endothermic process)?  I guess I'm trying to apply terms used to describe energy transfers by heat to energy transfer by work.  Maybe that's why I'm running into trouble?