7.5: Thermochemistry and Enthalpy

Thermochemistry and Enthalpy

Energy, Temperature, and Heat

Thermal energy is kinetic energy associated with the random motion of atoms and molecules. When thermal energy is transferred into an object, its atoms and molecules move faster on average (higher KE_average), the object’s temperature increases, and we say that the object is “hotter”. When thermal energy is transferred out of an object, its atoms and molecules move more slowly on average (lower KE_average), 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).

The heat capacity (C) of an object is the heating required when the object’s temperature changes by 1 °C. (Because 1 K is the same size as 1 °C, ΔT has the same numeric value whether expressed in K or °C.) It typically has units of J/°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 heating required to raise the temperature of 1 g of a substance by 1 °C. It typically has units of J/g·°C. Specific heat capacity depends only on the type of substance and therefore is an intensive property. 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.

Specific heat capacities of some common substances are listed in Table 1.

If we know the mass, m, of a sample and its specific heat capacity, c, we can calculate the heat transferred to or from the sample by measuring the temperature change during heating or cooling:

q = m·c·ΔT = m·c·(T_final– T_initial)

The sign of ΔT tells us whether the substance is being heated (positive value for q) or cooled (negative q ).

Calorimetry

Calorimetry is an experimental technique used to quantitatively measure heat transfer of energy. Energy is exchanged with a calorimeter, a device with known heat capacity that therefore can relate ΔT to q. A calorimeter must be 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.

For example, if we place a piece of hot metal (M) into cool water (W), heat transfer of energy occurs from metal to water until the two substances reach the same temperature (Figure 2).

If this occurs in a well insulated calorimeter, this heat transfer would ideally occur only between the two substances. Thus, the magnitude of q is the same for both substances.

q_M + q_W = 0

The arithmetic sign of q is determined by whether the substance loses or gains energy. In our example, energy is transferred from the metal (q_M is negative) to the water (q_W is positive).

The same principles apply when we apply calorimetry to determine the heat transfer of energy involved in chemical reactions:

q_reaction + q_surroundings = 0

Here, q_reaction is defined as the change in energy of all atoms present in reactants and products.

A reaction in which there is heat transfer from the reacting substances to their surroundings (a reaction that heats the surroundings) is an exothermic reaction. For example, the combustion reaction that occurs in the flame of a lit match is exothermic. A reaction in which there is heat transfer 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.

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 energy transferred to or from the calorimeter as well as energy transfers within the the calorimeter. For example, a type of calorimeter that operates at constant volume, colloquially known as a bomb calorimeter because it involves a strong, steel container that will not explode when an exothermic reaction occurs inside it (the “bomb”). Bomb calorimetry is used to measure energy transfers for reactions such as combustion reactions. The reaction occurs inside the bomb (Figure 3), which is immersed in a water bath and the temperature change of the water bath is measured. Energy has to be transferred to the bomb so the bomb can heat the water, so you need to account for the heat capacity of the bomb as well as the water. That is,

\[q_{\text{reaction}} = -[q_{\text{water}} + q_{\text{bomb}}] \nonumber \]

Enthalpy

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

Substances act as reservoirs of energy. The total of all possible kinds of energy present in a substance is called the internal energy (U). (The symbol U, instead of E, represents a sum over several different kinds of energy within the substance.) 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:

ΔU = q + w

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 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 the system’s internal energy) and negative if it is done by the system. This is summarized in the figure below.

Chemists ordinarily use a property known as enthalpy (H) to describe the thermodynamics of chemical and physical processes. Enthalpy is defined by this equation:

H = U + PV

where P is pressure and V is volume. Enthalpy is closely related to energy, differing by the quantity PV.

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:

ΔH = ΔU + Δ(PV) = ΔU + PΔV

(where P is factored out of Δ(PV) because P is constant).

The mathematical product PΔV represents pressure-volume work, also called expansion work. For example, consider a gas (the system) confined in a cylinder by a piston, as shown in the figure. The pressure exerted by the gas results from many collisions of gas molecules with the bottom of the piston and the walls of the cylinder. If the pressure of the gas causes the piston to move upward, the gas does work on the piston (part of the surroundings). This reference shows that the work done by the system on the surroundings equals PΔV. Work done by the system is the negative of w, which is defined as work done on the system, so

PΔV = –w

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 transfer of energy (q_p) equals the enthalpy change (ΔH) for the process.

The heat transfer to the surroundings when you operate a Bunsen burner is equal to the enthalpy change of the methane combustion reaction that takes place, because the reaction occurs at the essentially constant pressure of the atmosphere. 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 as a result of a chemical reaction. The enthalpy change for a chemical reaction is symbolized Δ_rH, where the subscript r indicates that the change is for a reaction.

On the other hand, the heat transfer of energy 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. In a constant-volume system w = 0 and ΔU = q_v + w= q_v, where the subscript v indicates constant volume.

Standard-state Reaction Enthalpy Change, Δ_rH°

Heat effects of a chemical reaction are summarized in thermochemical expressions, balanced chemical equations together with values of Δ_rH°, the standard-state reaction enthalpy change, and a temperature. The standard-state reaction enthalpy change, Δ_rH°, is the standard-state enthalpy of pure, unmixed products minus the standard-state enthalpy of pure, unmixed reactants; that is, the enthalpy change for the reaction under standard-state conditions.

Δ_rH° = H°(products) – H°(reactants)

A standard state is a commonly accepted set of conditions used as a reference point. For chemists, the standard state refers to substances under a pressure of 1 bar and solutions at a concentration of 1 mol/L (1 M). (Note that some thermochemical tables may list values with a standard state of 1 atm. Because 1 bar = 0.987 atm, thermochemical values are nearly the same under both sets of standard conditions; however, for accurate work the standard state should be checked.)

The standard state does not specify a temperature. Because Δ_rH° can vary with temperature, temperature is typically specified in a thermochemical expression.