## Physical Chemistry Lesson of the Day – The Difference Between Changes in Enthalpy and Changes in Internal Energy

Let’s examine the difference between a change enthalpy and a change in internal energy.  It helps to think of the following 2 scenarios.

• If the chemical reaction releases a gas but occurs at constant volume, then there is no pressure-volume work.  The only way for energy to be transferred between the system and the surroundings is through heat.  An example of a system under constant volume is a bomb calorimeter.  In this case,

$\Delta H = \Delta U + P \Delta V = \Delta U + 0 = q - w + 0 = q - 0 + 0 = q$

This heat is denoted as $q_v$ to indicate that this is heat transferred under constant volume.  In this case, the change in enthalpy is the same as the change in internal energy.

• If the chemical reaction releases a gas and occurs at constant pressure, then energy can be transferred between the system and the surroundings through heat and/or work.  Thus,

$\Delta H = \Delta U + P \Delta V = q - w + P \Delta V = q$

This heat is denoted as $q_p$ to indicate that this is heat transferred under constant pressure.  Thus, as the gas forms inside the cylinder, the piston pushes against the constant pressure that the atmosphere exerts on it.  The total energy released by the chemical reaction allows some energy to be used for the pressure-volume work, with the remaining energy being released via heat.  (Recall that these are the 2 ways for internal energy to be changed according to the First Law of Thermodynamics.)  Thus, the difference between enthalpy and internal energy arises under constant pressure – the difference is the pressure-volume work.

Reactions under constant pressure are often illustrated by a reaction that releases a gas in cylinder with a movable piston, but they are actually quite common.  In fact, in chemistry, reactions under constant pressure are much more common than reactions under constant volume.  Chemical reactions often happen in beakers, flasks or any container open to the constant pressure of the atmosphere.

$H = U + PV$.
$\Delta H = \Delta U + P\Delta V$.