>> Key Terms (indicated in blue within the text below):

alkane bond energy calorimetry endothermic energy enthalpy (H) exothermic first law of thermodynamics (law of conservation of energy)

formation reaction heat (q) heat capacity (cP) heat of fusion (Hfus) heat of vaporization (Hvap) Hess's law hydrocarbon kinetic energy (KE)

PV work potential energy saturated specific heat standard state state function work

Chemical and physical changes are accompanied by a change in energy. This energy can be divided into two categories. Kinetic energy (KE) is the energy of motion. It can be calculated from

KE = 1/2 mu_rms2         (Equation 11.2)

where m is the mass of the object moving and u_rms is the average (root mean square) speed of the object. Temperature reflects the movement of molecules, and heat is one type of kinetic energy. The other type of energy is potential energy, the energy of position. Chemical bonds are one example of potential energy.

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The absolute energy of any substance, is nearly impossible to measure. However, changes in energy are not. A system undergoing an energy change can transfer energy to or from its surroundings. The first law of thermodynamics says that energy is neither created nor destroyed in a chemical reaction. Therefore if the energy change of the surroundings can be measured, the energy change of the system is the same (although the direction is opposite).

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Two types of energy (both kinetic) are commonly measured, heat and work. So the change in overall energy (E) is the sum of heat (q) and work (w). Work, the force required to move an object some distance, is often in the form of a volume change at constant pressure (PV work). Since it is the volume change of the surroundings that is measured, the energy change of the system is

E = q – PV         (Equation 11.3)

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Enthalpy (H) is a more general measure of the energy of a system. It takes into account the internal energy of a system as well as its pressure and volume.

H = E + PV

A change in enthalpy at constant pressure would be equal to

H = E + PV = (q – PV) + PV = q         (Equations 11.6 and 11.7)

Therefore changes in enthalpy can be measured by changes in heat energy. Enthalpy is also defined as heat flow.

Heat (q) is a type of energy that is related to temperature but is not the same as temperature, since the energy may be used for something other than increasing temperature. For example, the heat energy required to melt 1 mole of molecules is the heat of fusion (H_fus), but no temperature change is involved in this phase change. The heat energy required to change 1 mole of liquid to 1 mole of gas is the heat of vaporization (H_vap). Similarly, no temperature change is involved in this or any other phase change.

It also requires different amounts of heat energy to change the temperature different types of molecules. The energy required to increase the temperature of 1 mole (n) of substance 1 °C is its heat capacity (c_P). Similarly, the energy required to increase the temperature of 1 g of substance 1 °C is specific heat. Therefore the heat (q) required for a temperature change (T) can be calculated from

q = nc_PT          (Equation 11.8)

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Chemical reactions also involve a change in enthalpy (H). The H_rxn is the energy per mole of reaction (q/mol). Exothermic reactions release energy into the surrounding and are designated by a negative sign on the H. Endothermic reactions take energy from the surroundings and are designated by a positive value of H.

The value of H can be determined experimentally by measuring the temperature change of the surroundings. Calorimetry is an experiment to measure q by measuring temperature change. The heat capacity of the calorimeter (the constant pressure surroundings in the experiment) is used to convert temperature change to heat energy. Since the heat capacity (C_P) refers to the whole calorimeter, heat can be calculated from

q = c_PT          (Equation 11.11)

                              >> Explore: Calorimetry Tutorial

The value of H can also be calculated theoretically. Since the energy change in a chemical reaction comes from making and breaking bonds, the value of H can be calculated from the energy of the bonds, bond energy. Energy is released (–H) when bonds are made and energy is absorbed (+H) when bonds are broken. Table 11.2 lists some bond energies. However, the values of bond energies are affected by the other bonds in a molecule. Therefore H values calculated from bond energies have a high uncertainty.

                              >> Explore: Estimating Enthalpy Changes Tutorial

The value of H can also be calculated from the H values of other reactions. Because H is a state function, the path does not affect the final result. Thus H values of a series of known reactions can be mixed to obtain the H of an unknown reaction. The H value depends on how the reaction is written. If the reaction is reversed, the sign on H is changed. If the stoichiometric coefficients of a reaction are multiplied by some factor, H is multiplied by the same factor. If reactions are added together, so are the H values. Hess's law states the H of a reaction that is the sum of other reactions is the sum of the H values of those reactions.

                              >> Explore: Hess's Law Tutorial

One type of reaction useful in Hess's law is a formation reaction. A formation reaction is a reaction that forms 1 mole of substance from its elements at standard state. An element at standard state is the most stable (lowest energy) form of an element at standard state (or standard conditions). The standard conditions for H are 298.15 K and 10⁵ Pa (about 25 °C and 1 atm). Note that these standard conditions are different from the standard conditions (STP) of gas laws. An enthalpy change under standard conditions is designated by a superscripted zero (H°).

If only formation reactions are added together with Hess's law, the elements cancel in a predictable manner. The enthalpy change of the reaction at standard state (H_rxn°) can be calculated from the H values for the formation reactions of the products (H_f,P°) and the reactants (H_f,R°) with

H_rxn° = n H_f,P° – m H_f,R°         (Equation 11.13)

where n is the stoichiometric coefficient of each product and m is the stoichiometric coefficient of each reactant. ( represents summation.)

Commercially, most energy is produced from the combustion of hydrocarbons. Hydrocarbons are substances made solely of hydrogen and carbon atoms. Combustion is the reaction of these substances with oxygen (O₂). Complete combustion produces the gases carbon dioxide and water. A simple type of hydrocarbon is an alkane. Each carbon in an alkane has four single bonds. Each bond connects that carbon to either another carbon or a hydrogen. This type of hydrocarbon is saturated; that is, it has the maximum number of hydrogens possible for that number of carbons. When n is the number of carbons, the general formula for an alkane (or any saturated hydrocarbon) is C_nH_{2n + 2}.