This chapter is concerned with energy changes in chemical and physical processes. Read the first section very carefully, noting in particular the definitions of the terms. Subtle differences between related terms (temperature vs. heat, for example) are very important. Confusing terms like this will result in problems with your understanding of the material.

The two main types of energy are potential (energy based on an object's position) and kinetic (energy based on an object's motion.) Types of potential energy include gravitational, electrostatic, mechanical, and chemical. Although energy can be transformed from one type to another, energy cannot be created or destroyed (if we ignore mass-energy transformations) - this is a statement of the Law of Conservation of Energy. The Law of Conservation of Energy is also the First Law of Thermodynamics.

The kinetic energy of an object is given by

where m is the object's mass and v is its velocity.

Chemical reactions usually involve the absorption or release of heat. The energy available from a chemical reaction is chemical potential energy. If a reaction releases energy, it is called an exothermic reaction; one that takes in heat is called endothermic. You learned about the Law of Conservation of Mass in chapter 1. Remember the wording of this law: there is no detectable change in mass in the course of an ordinary chemical reaction. The word "detectable" is very important, since there is always a change in mass if a reaction gives off energy or takes in energy. Consider the combustion of a mole of methane, CH₄. The balanced equation is

If we have stoichiometrically equivalent masses of reactants and products, we have a mass of 80 grams on each side of the equation, apparently indicating that there is no mass change. Consider now that this reaction is exothermic, releasing 890 kJ of heat. The only way in which energy can be released is if the products of the reaction have a smaller mass than the reactants - after all, the energy released is a result of the conversion of some mass into energy. This mass equivalent of the 890 kJ can be calculated by Einstein's equation of mass/energy equivalence:

,

which is obviously an insignificant percentage.

System and Surroundings
When energy is transferred, it is important to define what is losing the energy and what is gaining it. By definition, the system is that part of the universe, enclosed within defined boundaries, on which we focus our attention. Usually, this includes reactants and products in a chemical reaction, or a single substance in the case of a physical change like melting or boiling. The surroundings is everything else in the universe which is not included in the definition of the system. The surroundings usually includes the container which holds the reactants and products, any solvent which is not considered a reactant or product, and the rest of the universe. For example, if aqueous solutions of hydrochloric acid and sodium hydroxide are mixed, heat is released by the system - in this case, the reactants. The surroundings - the water, the container holding the solutions, the air in the room, the rest of the country, etc. - absorb the heat. Any heat lost by the system must be gained by the surroundings, and vice-versa.

Internal Energy
The internal energy of a system is the sum of all possible forms of energy in the system. In a system consisting of pure water, for example, all of the following types of energy are present: kinetic energy of each of the individual water molecules in the system; gravitational potential energy; electrostatic potential energy arising from attractions between opposite dipoles on water molecules; electrostatic potential energy arising from repulsions between like dipoles; rotational energy of the water molecules; vibrational energy in the bonds of the molecule; electrostatic potential energy of electron-proton attractions in the atoms; electrostatic potential energy of electron-electron repulsion; etc. You probably realize that there are a lot more. In fact, it is impossible to determine all of the possible forms of energy in a system. This means that it is impossible to determine the potential energy of a system. So what use is this concept?

As it turns out, it isn't the absolute internal energy of a system which is important. What is important is the change in internal energy when a system changes from one state to another. And this can be determined. What is meant by a system changing from one state to another is not necessarily that it is changing state (gas to liquid, etc.), although this is a possible interpretation. More broadly, what it means when a system goes from state 1 to state 2 is that enough information is specified about the states that they can be unambiguously identified. There are usually two types of transformations which dictate a change from state 1 to state 2:

1. A change in physical state (liquid to gas, solid to liquid, etc.). Energy is absorbed or released by these processes.
2. A chemical reaction, in which the reactants represent the initial state and the products represent the final state. Chemical reactions are accompanied by a gain or loss of energy.

It is important to recognize that internal energy is a state function: its value depends only on the state of the system, not on how the system arrived at that state.

As mentioned above, a verbal statement of the First Law of Thermodynamics is the law of conservation of energy. A mathematical statement of the First Law of Thermodynamics is

where delta E is the change in internal energy, q is the heat exchanged between system and surroundings, and w is the work exchanged between system and surroundings. This equation means that there are two ways to change the internal energy of a system: add or remove heat, or perform or extract work from the system. The sign conventions for q and w are very important and must be learned:

• q is positive: means that the system takes in heat from the surroundings (endothermic)
• q is negative: means that the system loses heat to the surroundings (exothermic)
• w is positive: means that work is done on the system
• w is negative: means that work is done by the system

Thus, the change in internal energy for a system which takes in 500 Joules of heat from the surroundings and does 300 Joules of work on the surroundings is

Note that since delta E is positive, the net result was that energy was added to the system.

By definition, work is force applied over a distance, i.e. W = F x D. Although there are several types of work possible, the only significant source of work for most chemical processes and reactions is pressure-volume work. This type of work is defined as

where P_ext is the external pressure on the system (usually the barometric pressure) and delta V is the change in volume, defined as V_final - V_initial .

Consider a gas expanding in a cylinder with an external pressure of 1 atm. If the initial volume is 5.0 liters and the final volume is 8.0 liters, then the pressure-volume work is -(1atm)(8.0L-5.0L) = -3.0 liter-atmospheres. Notice that the negative value for the pressure-volume work is consistent with the sign convention above: a negative value for w means that the system did work on the surroundings (by pushing the piston out). The unit for the pressure-volume work may sound strange, but it should surely be an energy unit, since work has units of energy. We can derive the conversion factor between liter-atmospheres and joules by using the universal gas constant: R = 8.314 J/mol-K = 0.08206 L-atm/mol-K, so it should be clear that 8.314 J = 0.08206 L-atm, and thus

You may recognize that this is the same conversion factor as that for converting between atmospheres and kilopascals (see the Concept of the Week for Chapter 5, gases.) [This is more than mere coincidence. Can you deduce why they are the same?]

Enthalpy and Constant Pressure Processes
If a process takes place at constant pressure, then pressure-volume work results if the volume of the system changes. We can re-write the first law under these conditions as

, which can be rearranged to

.

By definition, the state function enthalpy is defined as H=E+PV. Thus, for a process which takes place at constant pressure, it follows that

This is a very useful relationship: the heat exchanged between system and surroundings at constant pressure is the enthalpy. Since almost all common chemical processes occur at constant pressure, enthalpy is a very useful function because we only need to measure the heat absorbed or evolved; we don't need to worry about the pressure-volume work.

Constant Volume Processes
It should be clear that if the volume of a system doesn't change, then there can be no pressure-volume work, since delta V is zero. Under these conditions, the first law can be written

Thus, the heat exchanged between system and surroundings at constant volume is equal to the change in internal energy.

Calorimetry
We saw above that if we can measure the heat exchanged between system and surroundings for a constant pressure process, then we have determined the change in enthalpy. As it turns out, it is very easy to measure the heat gain or loss which accompanies a process:

,

where m is the mass of whatever is gaining or losing the heat, C is the heat capacity of whatever is gaining or losing the heat, and delta T is the final temperature of whatever gained or lost the heat minus the initial temperature. Remember that heat lost by the system is gained by the surroundings, and vice-versa. For example, if aqueous solutions of acid and base are mixed with each other, the neutralization reaction is exothermic. Heat lost by the reaction is gained by the water and the container (and the rest of the universe, but usually these experiments are designed with equipment which minimizes heat loss.) Thus, to find q for the system, we use the above equation and get

The negative sign on the right side was needed because the heat lost by the system is the negative of the heat gained by the surroundings, since the process is exothermic for the system and endothermic for the surroundings.

Hess' Law
Hess' Law states that the enthalpy change for a reaction is the same whether the reaction occurs directly or in steps. This is a direct consequence of the fact that enthalpy, like internal energy, is a state function. One of the applications of Hess' Law is to determine the enthalpy change for a reaction by combining other reactions to get the desired reaction, then combining the enthalpy changes for the reactions to get delta H for the reaction under consideration. When using Hess' Law in this way, remember these two important rules:

1. If a reaction is written in reverse, change the sign of delta H. (If a reaction is endothermic in the forward reaction, it is exothermic by the same amount in the reverse reaction, and vice-versa.)
2. If the stoichiometric coefficients of a reaction are multiplied or divided by some factor, then delta H for the reaction is multiplied or divided by the same factor. (Energy changes are extensive quantities: they depend on the amount of substances reacting.)

Another application of Hess' Law is to pretend that the reactants are broken up into the elements which make them up, then these elements are combined to form the products. This results in the following useful equation:

where n represents the stoichiometric coefficient and delta H_f is the enthalpy of formation of the substance: the enthalpy change for the reaction where one mole of the substance in its standard state is formed from the constituent elements in their standard states. Remember that by definition, the enthalpy of formation of an element in its standard state is zero.

Last modified June 16, 1997