Thermochemistry

Thermochemistry

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Thermochemistry is the study of the heat released or absorbed as a result of chemical reactions. It is a branch of thermodynamics and is utilized by a wide range of scientists and engineers. For example, biochemists use thermochemistry to understand bioenergetics, whereas chemical engineers apply thermochemistry to design manufacturing plants. Chemical reactions involve the conversion of a set of substances collectively referred to as "reactants" to a set of substances collectively referred to as "products." In the following balanced chemical reaction the reactants are gaseous methane, CH 4 (g), and gaseous molecular oxygen, O 2 (g), and the products are gaseous carbon dioxide, CO 2 (g), and liquid water H 2 O(l):

CH 4 (g) + 2 O 2 (g) → CO 2 (g) + 2 H 2 O(l) (1)

Reactions in which a fuel combines with oxygen to produce water and carbon dioxide are called combustion reactions. Because natural gas consists primarily of methane, it is expected that reaction (1) will liberate heat. Reactions that liberate heat are termed exothermic reactions, and reactions that absorb heat are termed endothermic reactions.

The heat associated with a chemical reaction depends on the pressure and temperature at which the reaction is carried out. All thermochemical data presented here are for reactions carried out under standard conditions, which are a temperature of 298 K (24.85°C) and an applied pressure of one bar . The quantity of heat released in a reaction depends on the amount of material undergoing reaction. The chemical formulas that appear in a reaction each represent 1 mole (see article on "Mole Concept") of material; for example, the symbol CH 4 stands for 1 mole of methane having a mass of 16 grams (0.56 ounces), and the 2 O 2 (g) tells us that 2 moles of oxygen are required. Thermochemistry also depends on the physical state of the reactants and products. For example, the heat liberated in equation (1) is 890 kilojoules (kJ); if, however, water in the gas phase is formed, H 2 O(g), the heat released is only 802 kJ. Reversing a reaction like (l), which liberates heat, yields a reaction wherein heat must be supplied for the reaction to occur. The following reaction absorbs 890 kJ.

CO 2 (g) + 2 H 2 O(l) → CH 4 (g) + 2 O 2 (g) (2)

Energy and Enthalpy

Thermochemical changes are often discussed in terms of the "system" and the "surroundings." The system is regarded as the reaction products and reactants, whereas the surroundings consist of everything else in the universe. A boundary separates the system from the surroundings. The first law of thermodynamics relates the energy change belonging to a system to the amount of work and heat crossing the boundary. A statement of the first law applied to chemical reactions in which only heat and work cross the boundary is given by the expression:

U products − U reactants = Δ U = q + w (3)

Here U products represents the energy of the products and U reactants represents the energy of the reactants. The heat associated with the reaction is given as q , and w represents work done during the transformation of reactants to products. If the volume of the system changes during the reaction and the applied pressure remains constant, the work carried out is termed pressure-volume work. For example, reaction (2) converts one mole of gas and two moles of liquid to a total of three moles of gas. The volume of the system increases during the reaction because, under standard conditions, a mole of gas occupies more volume than a mole of liquid. The work of expanding a system against atmospheric pressure is experienced when one inflates a balloon, and this work can be shown to be equal to − P Δ V . Here P represents the atmospheric pressure and Δ V represents the change in volume of the system.

The first law of thermodynamics also states that U is a state function. State functions are very important in thermodynamics; they depend only on the present state of a system and not on its past history. Neither q nor w are state functions. An understanding of the concept of state function is furthered by considering the example of one's taking a trip from San Diego, California, to Denver, Colorado. The change in altitude that one experiences during this trip does not depend on the route taken and, thus, is similar to a state function. In comparison, the distance traveled between the two cities does depend on the route one follows; similarly, q and w are path-dependent quantities.

If a process such as a chemical reaction is carried out at a constant pressure in a way that involves only pressure-volume work, then − PΔV can be substituted for the work term in equation (3). Thus, we have:

Δ U + P Δ V = q p (4)

The symbol q p represents the heat accompanying a chemical change carried out at constant pressure; in our previous example this would be equivalent to our specifying the exact route of travel between the two cities. The enthalpy of a system H is related to the energy of a system by the expression:

H = U + PV (5)

For a process or reaction carried out at constant pressure:

Δ H = Δ U + P Δ V = q p (6)

Enthalpy, like energy, is a state function. Thus, equation (6) shows that, for a reaction carried out at constant pressure, q p depends only on the reactants consumed and the products formed. The enthalpy change associated with a reaction carried out under standard conditions is termed the heat of reaction and is given the symbol Δ H 0 , with the superscript denoting standard conditions. Endothermic reactions have a positive Δ H 0 whereas exothermic reactions have a negative Δ H 0 . The change in enthalpy accompanying the conversion of reactants to products in a chemical reaction determines the amount of heat liberated or absorbed by the reaction. For a reaction carried out at constant pressure the enthalpy change depends only on the reactants and products.

Hess's Law

Because enthalpy is a state function, the heat associated with a reaction does not depend on whether the reaction proceeds from reactants to products in a series of steps or in a single step. This is the basis for Hess's law, which states that if two reactions are combined to yield a third reaction, the sum of the Δ H 0 s for the first two reactions is equal to the Δ H 0 for the third. For example, consider the conversion of gaseous methane to liquid methanol:

CH 4 (g) + 1/2 O 2 (g) → CH 3 OH (l) (7)

and the subsequent combustion reaction:

CH 3 OH(l) + 3/2 O 2 (g) → 2 H 2 O(l) + CO 2 (g) (8)

Combining reactions (7) and (8) by adding them together gives reaction (1). Thus, the Δ H 0 for combined reactions (7) and (8) must equal −890kJ. If the Δ H 0 for reaction (8) is known to be −681 kJ, then the Δ H 0 for reaction(7) can be calculated by Hess's law to equal −209 kJ. Born-Haber cycles represent an application of Hess's law to reactions associated with the formation of salts, such as potassium chloride. Born-Haber cycles can be used to determine the enthalpy change accompanying the breakup of the potassium chloride lattice into isolated potassium and chlorine ions.

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