## Internal Energy and Enthalpy

#### Learning Objective

• Review enthalpy of reaction

#### Key Points

• At constant volume, the heat of reaction is equal to the change in the internal energy of the system.
• At constant pressure, the heat of reaction is equal to the enthalpy change of the system.
• Most chemical reactions occur at constant pressure, so enthalpy is more often used to measure heats of reaction than internal energy.

#### Terms

• enthalpyIn thermodynamics, a measure of the heat content of a chemical or physical system.
• internal energyA property characteristic of the state of a thermodynamic system, the change in which is equal to the heat absorbed minus the work done by the system.
• first law of thermodynamicsHeat and work are forms of energy transfer; the internal energy of a closed system changes as heat and work are transferred into or out of it.

In thermodynamics, work (W) is defined as the process of an energy transfer from one system to another. The first law of thermodynamics states that the energy of a closed system is equal to the amount of heat supplied to the system minus the amount of work done by the system on its surroundings. The amount of energy for a closed system is written as follows:

[latex]\Delta U = Q - W[/latex]

In this equation, U is the total energy of the system, Q is heat, and W is work. In chemical systems, the most common type of work is pressure-volume (PV) work, in which the volume of a gas changes. Substituting this in for work in the above equation, we can define the change in internal energy for a chemical system:

[latex]\Delta U=Q-P\Delta V[/latex]

## Internal Energy Change at Constant Volume

Let’s examine the internal energy change, [latex]\Delta U[/latex], at constant volume. At constant volume, [latex]\Delta V=0[/latex], the equation for the change in internal energy reduces to the following:

[latex]\Delta U = Q_V[/latex]

The subscript V is added to Q to indicate that this is the heat transfer associated with a chemical process at constant volume. This internal energy is often very difficult to calculate in real life settings, though, because chemists tend to run their reactions in open flasks and beakers that allow gases to escape to the atmosphere. Therefore, volume is not held constant, and calculating [latex]\Delta U[/latex] becomes problematic. To correct for this, we introduce the concept of enthalpy, which is much more commonly used by chemists.

## Standard Enthalpy of Reaction

The enthalpy of reaction is defined as the internal energy of the reaction system, plus the product of pressure and volume. It is given by:

[latex]H=U+PV[/latex]

By adding the PV term, it becomes possible to measure a change in energy within a chemical system, even when that system does work on its surroundings. Most often, we are interested in the change in enthalpy of a given reaction, which can be expressed as follows:

[latex]\Delta H = \Delta U +P\Delta V[/latex]

When you run a chemical reaction in a laboratory, the reaction occurs at constant pressure, because the atmospheric pressure around us is relatively constant. We will examine the change in enthalpy for a reaction at constant pressure, in order to see why enthalpy is such a useful concept for chemists.

## Enthalpy of Reaction at Constant Pressure

Let’s look once again at the change in enthalpy for a given chemical process. It is given as follows:

[latex]\Delta H=\Delta U + P\Delta V[/latex]

However, we also know that:

[latex]\Delta U=Q-W=Q-P\Delta V[/latex]

Substituting to combine these two equations, we have:

[latex]\Delta H=Q-P\Delta V+P \Delta V=Q_P[/latex]

Thus, at constant pressure, the change in enthalpy is simply equal to the heat released/absorbed by the reaction. Due to this relation, the change in enthalpy is often referred to simply as the “heat of reaction.”