As you work through this section, if you find that you need a bit more background material to help you understand the topics at hand, you can consult “Chemistry: The Molecular Science” (5th ed. Moore and Stanitski) Chapter 4, and/or Chapter 11.1-11.4 in the Additional Reading Materials section.

D26.1 Energy, Temperature, and Heat

Energy can be defined as the capacity to do work, that is, to move an object against a force. For example, energy provided to your body by chemical reactions enables you to climb a ladder against the force of gravity. Kinetic energy is energy that an object has because it is moving. Each molecule in a sample of argon gas is moving and therefore has kinetic energy. The gas molecules could do work by pushing against an object and moving it, so the kinetic energy of gas molecules could be converted to kinetic energy of a moving piston, for example. Potential energy is energy that an object has because of its position. When you reach the top of a ladder your potential energy is greater than it was at the bottom because Earth’s gravity attracts you downward. Should you fall off the ladder, gravitational attraction would accelerate you toward the ground, converting some of the potential energy into kinetic energy.

The Law of Conservation of Energy states that although energy can be changed from one form to another, the total quantity of energy in the universe is constant. Thus, if potential energy is converted to kinetic energy the quantity of kinetic energy at the end must equal the quantity of potential energy at the beginning. When all forms of energy are considered, whenever anything occurs the change in energy must be zero; that is, for any process, ΔE_overall = 0.

Thermal energy is kinetic energy associated with the random motion of atoms and molecules. When energy is transferred to a sample of matter, the atoms and molecules move more quickly, they have a higher average kinetic energy (KE), the object’s temperature increases, and we say that the object is “hotter.” When thermal energy is transferred out of an object, the atoms and molecules move more slowly, they have lower average KE, the object’s temperature decreases, and we say that the object is “colder”.

Heating (or heat), represented by q, is the transfer of thermal energy between two bodies at different temperatures (Figure 1).

Working (or work), represented by w, is a process that transfers kinetic energy to or from a macroscopic object. When a golf club strikes a golf ball, for example, the club does work on the ball, accelerating the ball to a high speed. Because heat and work involve transfers of energy, we will speak of heat as “a heat transfer of energy” and work as “a work transfer of energy”. Most chemists just use “heat” and “work” to mean the same thing.

The SI unit of heat, work, and energy is the joule (1 J = 1 kg m²/s²). One joule is the energy transferred to an object when a force of 1 newton acts on the object through a distance of 1 meter. It is named in honor of the English physicist James Prescott Joule.

The heat capacity (C) of a sample of matter is the heat transfer of energy required when the object’s temperature changes by one kelvin (ΔT = 1 K). (Because 1 K is the same size as 1 °C, ΔT has the same numeric value whether expressed in K or °C.)

Heat capacity depends on both the type and the quantity of substance, and therefore is an extensive property—its value is proportional to the quantity of the substance.

The specific heat capacity (c) of a substance is the heat transfer of energy required to raise the temperature of 1 g of a substance by 1 °C (or 1 kelvin):

Specific heat capacity depends only on the kind of substance and is an intensive property—the type, but not the quantity, of the substance is all that matters. It is typically reported in units of J/g °C. The molar heat capacity, also an intensive property, is the heat capacity per mole of a particular substance and typically has units of J/mol °C.

The specific heat capacity of a substance varies somewhat with temperature. However, this variation is usually small enough that we will treat specific heat capacity as constant over the range of temperatures that will be considered in this course. Specific heat capacities of some common substances are listed in Table 1.

If we know the mass of a substance and its specific heat capacity, we can calculate the heat transfer of energy, q, to or from the substance by measuring the temperature change during heating or cooling:

If a substance gains thermal energy, its temperature increases, its ΔT is positive, and the value of q is positive. If a substance loses thermal energy, its temperature decreases, its ΔT is negative, and the value of q is negative.

D26.2 Calorimetry

Calorimetry is an experimental technique used to measure quantitatively heat transfers of energy. Energy is exchanged with a calorimeter, a device whose heat capacity is known and therefore can relate temperature change to quantity of energy transferred. The calorimeter is insulated thermally so that energy does not transfer beyond its physical boundaries. In calorimetry it is useful to define a system, the substance(s) undergoing the chemical or physical change, and the surroundings, everything else that can exchange energy with the system.

Consider a simple example that illustrates the core idea behind calorimetry. Suppose we initially have a hot piece of metal (M) and cool water (W). If we place the metal in the water, there will be heat transfer of energy from M to W, until the two substances have the same temperature; that is, until they reach thermal equilibrium (Figure 3). If this occurs in a well insulated calorimeter, ideally all of this heat transfer of energy occurs between the two substances, with no heat transfer of energy either to or from the calorimeter or anything else. Under these ideal circumstances,

The magnitude of q is therefore the same for both substances. The arithmetic sign of either q value is determined by whether the matter in question loses or gains energy. In the situation described, the heat transfer of energy is from the metal (which has less energy at the end, q_M negative) to the water (which has more energy at the end, q_W positive).

Calorimetry can be applied to chemical reactions. When a chemical reaction takes place there is usually a sizable transfer of energy. That is, there is usually a significant change in temperature as reactants become products. A reaction in which there is heat transfer of energy from the reacting substances to their surroundings (a reaction that heats the surroundings) is called an exothermic reaction. For example, the combustion reaction that occurs in the flame of a lighted match is exothermic. A reaction in which there is heat transfer of energy from the surroundings to the system (a reaction that cools the surroundings) is an endothermic reaction. For example, when the substances in a cold pack (water and a salt such as ammonium nitrate) are mixed, the resulting process transfers energy from the surroundings, making the surroundings colder.

The same principles apply when we use calorimetry to determine the heat transfer of energy involved in a chemical reaction: the heat transfer of energy of the system (defined as all atoms present in reactants and products), q_reaction, plus the heat transfer of the surroundings, q_surroundings, add up to zero:

If the heat capacity of a calorimeter is too large to neglect or if we require more accurate results, then we must take into account the heat transfer of energy for the calorimeter as well as for the solution.

Coffee-cup calorimeters are designed to operate at constant (atmospheric) pressure and are convenient to measure heat transfers of energy accompanying processes that occur in solution. A different type of calorimeter that operates at constant volume, colloquially known as a bomb calorimeter, is used to measure energy transfers for reactions such as combustion reactions.

D26.3 Enthalpy

Chemical thermodynamics deals with the relationships between heat, work, and other means of energy transfer in the context of chemical and physical processes.

Substances act as reservoirs of energy. The total of all possible kinds of energy present in a substance is called the internal energy (U), sometimes symbolized as E. Energy is transferred into a system when it is heated (q) by the surroundings or when the surroundings does work (w) on the system. For example, energy can be transferred into room-temperature metal wire if it is immersed in hot water (the water heats the wire), or if you rapidly bend the wire back and forth (the wire becomes warmer because of the work done on it). Both processes increase the internal energy of the wire, which is reflected in an increase in the wire’s temperature.

The relationship between internal energy, heat, and work can be represented by the equation,

assuming there are no energy transfers other than heat and work.

This is one version of the first law of thermodynamics, the law of conservation of energy. The equation  shows that the internal energy of a system changes through heat transfer of energy into or out of the system (positive q is heat transfer in; negative q is heat transfer out) or work done on or by the system. The work, w, is positive if it is done on the system (increases internal energy) and negative if it is done by the system. Figure 4 summarizes these relationships.

Internal energy is a type of quantity known as a state function (or state variable), whereas heat and work are not state functions. The value of a state function depends only on the state that a system is in, and not on how that state is reached. If a quantity is not a state function, then its value does depend on how the state is reached. An example of a state function is altitude or elevation. If you stand on the summit of Mt. Kilimanjaro, you are at an altitude of 5895 m, and it does not matter whether you hiked there or parachuted there. The distance you traveled to the top of Kilimanjaro, however, is not a state function. You could climb to the summit by a direct route or by a more roundabout, circuitous path. Other familiar state functions are temperature, volume, and pressure.

Chemists ordinarily use a property known as enthalpy (H) to describe the thermodynamics of chemical and physical processes:

Because it is derived from three state functions (internal energy (U), pressure (P) and volume (V)), enthalpy is also a state function.

Enthalpy values for specific substances cannot be measured directly; only enthalpy changes for chemical or physical processes can be determined. For processes that take place at constant pressure (a common condition for many chemical and physical changes that take place at atmospheric pressure), the enthalpy change (ΔH) is:

(where P is factored out of Δ(PV) because P is constant). The mathematical product PΔV represents work (w), called expansion or pressure-volume work. By their definitions, the arithmetic signs of ΔV and w are always opposite:

Substituting yields:

where q_p is the heat of reaction under constant pressure. Therefore, if a chemical or physical process is carried out at constant pressure with the only work done caused by expansion or contraction, then the heat flow (q_p) equals enthalpy change (ΔH) for the process.

The heat given off when you operate a Bunsen burner is equal to the enthalpy change of the methane combustion reaction that takes place, because it occurs at the essentially constant pressure of the atmosphere. On the other hand, the heat produced by a reaction measured in a bomb calorimeter is not equal to ΔH because the closed, constant-volume metal container prevents expansion work from occurring. Chemists usually perform experiments under normal atmospheric conditions, at constant external pressure with q_p = ΔH, which makes enthalpy the most convenient choice for determining heat transfer of energy.

Heat effects of chemical reaction are summarized in thermochemical expressions. A thermochemical expression is a balanced chemical equation together with a value of Δ_rH°, the standard-state reaction enthalpy, and a temperature. The standard-state reaction enthalpy change, Δ_rH°, is the standard-state enthalpy of pure, unmixed reaction products minus the standard-state enthalpy of pure, unmixed reactants; that is, the enthalpy change for the reaction under standard-state conditions. Standard-state conditions means a pressure of 1 bar and a specified temperature. Sometimes the temperature is not specified, which usually means a temperature of 298.15 K (25.0 °C) is assumed. For example, consider this thermochemical expression:

2 H₂(g)  + O₂(g)  →  2 H₂O(g)        Δ_rH° = −483.6 kJ/mol     (25 °C)

This refers to reaction of two molecules of hydrogen with 1 molecule of oxygen to form two molecules of water, all in the gas phase. If this reaction equation took place once, the two hydrogen molecules and the one oxygen molecule would react to form two water molecules and 8.031 × 10⁻¹⁹ J would be transferred to the surroundings. Because we are interested in laboratory-scale reactions, where moles of reactants are involved, Δ_rH° is reported per mole of reaction. A mole of reaction involves a chemical reaction equation happening 6.022 × 10²³ times; in this case that is 2 mol H₂(g) reacting with 1 mol O₂(g) to give 2 mol H₂O(g). The heat transfer of energy to the surroundings is then 8.031 × 10⁻¹⁹ J × 6.022 × 10²³ mol⁻¹ = 483.6 kJ/mol. Because the energy transfer is from system to surroundings, the sign is negative and Δ_rH° = −483.6 kJ/mol.

These conventions apply to thermochemical expressions:

1. In a thermochemical expression, the listed Δ_rH° value indicates the quantity of heat transfer of energy for the coefficients in the chemical equation. If the coefficients are multiplied by some factor, Δ_rH° must be multiplied by that same factor. In other words, Δ_rH° is an extensive property. For example:
   [latex]\begin{array}{l l} \text{H}_2(g) + \frac{1}{2} \text{O}_2(g) \longrightarrow \text{H}_2 \text{O} (l) & \Delta _\text{r}H\text{°} = -286 \;\text{kJ/mol} \\[1em] (\text{two-fold increase in amounts}) \\ 2\; \text{H}_2(g) + \text{O}_2(g) \longrightarrow 2 \text{H}_2 \text{O}(l) & \Delta _\text{r}H\text{°} = 2 \times (-286 \;\text{kJ/mol}) = -572 \;\text{kJ} \\[1em] (\text{two-fold decrease in amounts}) \\ \frac{1}{2} \text{H}_2(g) + \frac{1}{4} \text{O}_2(g) \longrightarrow \frac{1}{2} \text{H}_2 \text{O}(l) & \Delta _\text{r}H\text{°} = \frac{1}{2} \times (-286 \;\text{kJ}) = -143 \;\text{kJ/mol} \end{array}[/latex]
2. Δ_rH°  of a reaction depends on the physical state of the reactants and products (whether we have gases, liquids, solids, or aqueous solutions), so these must be shown.
3. A negative Δ_rH° indicates an exothermic reaction; a positive Δ_rH° indicates an endothermic reaction. If the direction of a chemical equation is reversed, the arithmetic sign of its Δ_rH° is changed (a process that is endothermic in one direction is exothermic in the opposite direction).

Be sure to take both stoichiometry and limiting reactants into account when determining the Δ_rH° for a chemical reaction.

D26.4 Hess’s Law

Because enthalpy is a state function, the enthalpy change for a particular reaction is the same whether the reaction is carried out directly or is carried out as a series of steps. This enables calculation of the heat transfer of energy for a chemical change from other experimentally determined enthalpy changes. This type of calculation usually involves  Hess’s law: If a process can be written as the sum of several stepwise processes, the enthalpy change of the total process equals the sum of the enthalpy changes of the various steps.

For example, we can think of the following reaction as occurring directly:

or in a two-step process:

According to Hess’s law, the Δ_rH° of the direct reaction equals the sum of the Δ_rH° values of the steps. This is illustrated in Figure 5.