Thermochemistry

Standard conditions

298 K, 1 atm, 1 M concentrations; normally used for measuring enthalpy, entropy, and free energy of a reaction A substance in its most stable form under standard conditions is said to be in its standard state (H2, H20, and NaCl). The changes in enthalpy, entropy, and free energy that occur when a reaction takes place under standard conditions are called the standard enthalpy, standard entropy, and standard free energy changes and are symbolized with ΔH˚, ΔS˚, and ΔG˚. ** Not the same as conditions are standard temperature and pressure (STP) which are 273K and 1 atm and is used for gas law calculations.

Heat (q)

A form of energy that can easily transfer to or from a system due to a temperature difference between the system and its surroundings; this transfer will occur spontaneously from a warmer system to a cooler system. Heat absorbed by a system (from its surroundings) is positive, while heat lost by a system (to its surroundings) is negative. Measured in calories (cal) or joules (J) and is often expressed in kcal or kJ (1 cal = 4.184 J) Most common energy exchange in chemical processes. Reactions that absorb heat energy are endothermic, while those that release heat are said to be exothermic. The heat absorbed or released in a given process is calculated from q = cm(delta)T c= specific heat, a property of a material that describes how much energy it takes to raise its temperature

Entropy

A measure of the disorder, or randomness, of a system. The units of entropy are energy/temperature, J/K or cal/K. At any given temperature, a solid will have a lower entropy than a liquid, and a liquid will have lower entropy than a gas. Individual molecules in the gaseous state are moving randomly, whereas molecules in a liquid are less able to move freely, and molecules in a solid are constrained in place. Relative entropy changes accompanying phase changes can be estimated. For example, freezing is accompanied by a decrease in entropy, as the relatively disordered liquid becomes a well-ordered solid. Meanwhile, boiling is accompanied by a large increase in entropy, as the liquid becomes a much more highly disordered gas. For any substance, sublimation will be the phase transition with the greatest entropy change. Entropy is a state function, so a change in entropy depends only on the initial and final states: ΔS = Sfinal - Sinitial ΔS˚rxn, standard entropy change for a reaction, is calculated using the standard entropies of reactants and products: ΔS˚rxn = (sum of S˚ products) - (sum of S˚ reactants) The second law of thermodynamics states that all spontaneous processes proceed such that the entropy of the system plus its surroundings (i.e., the entropy of the universe) increases: ΔS universe = ΔS system + ΔS surroundings > 0 However, it is possible for entropy to decrease in a localized part of the system, as long as there is an accompanying increase in entropy elsewhere in the system. Water can turn to ice inside a freezer, lowering the entropy of water. However, the entropy of the air surrounding the freezer will increase as the heat pumped out the back of the freezer coils increases the randomness of movement of air molecules. A system reaches its maximum entropy at equilibrium, a state in which no observable change takes place as time goes on. For a reversible process, ΔS universe is zero: ΔS universe = ΔS system + ΔS surroundings = 0 A system will spontaneously tend toward an equilibrium state if left alone.

System

A thermodynamic system is the particular set of the universe being studied; everything outside the system is considered the surroundings/environment. A system may be: - isolated: it cannot exchange energy or matter with the surroundings, as with an insulated bomb reactor - closed: it can exchange energy but not matter with the surroundings, as with a steam radiator - open: it can exchange both matter and energy with the surroundings, as with a pot of boiling water A system undergoes a process when one or more of its properties changes, such as volume, temperature or pressure. Isothermal processes occur when systems do not change temperature, while adiabatic processes occur when there is not heat exchanged between systems and their surroundings. Isobaric processes occur in systems as constant pressure, and isochoric processes occur at constance volume.

thermochemistry

All chemical reactions are accompanied by energy changes. Thermal, chemical, potential, and kinetic energies are all interconvertible, as they must obey the law of conservation of energy. Energy changes determine whether reactions can occur and how easily they will do so. Thermodynamics helps determine whether a chemical reaction is spontaneous, meaning whether or not it will go forward without assistance. The application of thermodynamics to chemical reactions is called thermochemistry.

Bond dissociation energy

Heats of reaction can also be determined by the energy required for the breakdown and formation of chemical bonds. Bond dissociation energy is the energy required to break a specific chemical bond in one mole of gaseous molecules. Since it takes energy to pull two atoms apart, bond breaking is always endothermic and bond formation is always exothermic. Bond energies can be used to calculate enthalpies of reactions. Using the convention that bond dissociation enthalpies are always positive, whether for bond breaking or bond formation, the enthalpy change of a reaction is given by: ΔHrxn = (ΔH of bonds broken) - (ΔH of bonds formed) = total energy input - total energy released

Heats of combustion

One specific type of enthalpy of reaction is the standard heat of combustion, ΔH˚comb. Combustion of hydrocarbons follows the general unbalanced reaction: Hydrocarbon + O2 > Co2 + H2O The reactions used in enthalpy calculation for C3H8 (g) are combustion reactions, and the corresponding values of ΔHa, ΔHb, and ΔHc are thus heats of combustion (example in review notes).

Hess's Law

Since enthalpy is a state function, the enthalpy of a reaction does not depend on the path taken bot only on the initial and final states. Hess's law states that the enthalpies of reactions are additive; if a reaction is broken down into individual steps, the overall enthalpy of the reaction is the sum of enthalpies for each step.

Gibbs free energy

Spontaneity of reaction - The thermodynamic state function G, known as Gibbs free energy, combines the two factors that affect the spontaneity of a reaction: changes in enthalpy and changes in entropy. ΔG represents the maximum amount of energy released (i.e., work done) by a process occurring at constant temperature and pressure. ΔG is defined by: ΔG = ΔH - TΔS, where T is the absolute temperature in kelvin. In equilibrium state, free energy is at a minimum. A process can occur spontaneously if the Gibbs function decreases (i.e., ΔG < 0) 1. If ΔG is negative, the reaction is spontaneous and proceeds forward 2. If ΔG is positive, the reaction is not spontaneous and the reverse reaction occurs 3. If ΔG is zero, the system is in a state of equilibrium, thus ΔG =0 and ΔH = TΔS *The rate of reaction depends on the activation energy, not on ΔG. Spontaneity indicates whether or not a reaction will occur but not the rate of reaction. Gibbs free energy provides information on how both enthalpy and entropy changes affect a reaction. Enthalpy and entropy may act together to drive a reaction forward or backward, or they may oppose each other. In the latter case, the temperature will determine whether entropy or enthalpy has a greater effect on the spontaneity of a reaction, and the reaction is temperature-dependent. ΔH and ΔS both (-) > spontaneous only at low temp ΔH and ΔS both (+) > spontaneous only at high temp ΔH (-) and ΔS (+) > spontaneous at all temp ΔH (+) and ΔS (-) > not spontaneous at any temp

Enthalpy

The change in enthalpy of a process is equal to the heat absorbed or given off by the system at constant pressure. The enthalpy of a process depends only on the enthalpies of the initial and final states, NOT on the path. Thus, to find the enthalpy change of a reaction, subtract the enthalpy of the reactants from the enthalpy of the products: ΔH(rxn) = H(products) - H(reactants) A positive ΔH is an endothermic process in which enthalpy is added to the system, and a negative ΔH is an exothermic process in which the system gives off enthalpy.

Standard heat of formation

The enthalpy of formation of a compound, ΔH˚(f), is the enthalpy change that occurs if one mole of a compound is formed directly from its elements in their standard states. Note that the ΔH˚f of an element in its standard state is defined as zero, so the heat of formation of a compound gives its increase or decrease in enthalpy from zero. For example, the ΔH˚f for water is the change in enthalpy when H2 gas and O2 gas are combined to form 1 mole of water vapor: H2(g) + 1/2 O2(g) > H2O (g) ; ΔH˚f = -241.8 kJ/mol Note that the equation must be balanced for one mole of the product because ΔH˚f is defined for one mole of a substance

Standard heat of reaction

The standard heat of a reaction, ΔH˚rxn is the enthalpy change that occurs when the reaction is carried out under standard conditions (298K, 1 atm, and 1 M concentration). The equation for standard heat of reaction demonstrates the same concept as the reaction coordinate diagrams. ΔH˚rxn = (sum of ΔH˚f of products) - (sum of ΔH˚f of reactants)

States and state functions

The state of a system is described by the properties of the system, such as T, P and V. When the state of a system changes, the values of the properties also change. Properties whose magnitude depends only on the initial and final states of the system and not on the path of the change are known as state functions. P, T, and V are important state functions. Others include enthalpy (H), entropy (S), free energy (G), and internal energy (E or U). Although independent of path, state functions are not necessarily independent of one another

Standard free energy

ΔG˚ is defined as the ΔG of a process occurring with reactants in their standard states at standard conditions (298K and 1 atm pressure). Similar to standard enthalpies and are calculated by similar formulas. The standard free energy formation of a compound ΔGf is the free energy change that occurs when 1 mol of a compound in its standard state is formed by its elements in their standard states under standard conditions. The standard free energy of formation of any element in its most stable, standard state is defined as zero. The standard free energy of a reaction, ΔG˚rxn, is the free energy change that occurs when the reaction carried out under standard state conditions ΔG˚rxn = (sum of ΔG˚f products) - (sum of ΔG˚f of reactants)

Reaction quotient

ΔG˚rxn can also be derived from the equilibrium constant using the equation: ΔG˚ = -RT ln K(eq) K(eq) is the equilibrium constant, R is the gas constant, T is temp in kelvin This equation demonstrates the relationship between the equilibrium constant and Gibbs free energy. If Keq > 1, then ln Keq > 0 and ΔG˚ < 0; thus the reaction will proceed forward. If Keq < 1, then ln Keq < 0 and ΔG˚ > 0, thus the reverse reaction will occur.. Once a reaction commences, however, the standard state conditions no longer hold, Keq must be replaced by another parameter, the reaction quotient (Q). For the reaction aA + bB <> cC + dD Q= ([C]^c [D]^d)/ ([A]^a [B]^b) ΔG must be used instead of ΔG˚ : ΔG = ΔG˚ + RT ln Q Keep in mind that since ΔG˚ = - RT ln Keq, it is opposite in sign to RT ln Q in this equation. If Q < Keq, then RT ln Q is smaller in magnitude than ΔG˚ and ΔG is negative and reaction will proceed forward until Q = Keq and equilibrium is reached If Q > Keq, then RT ln Q is greater in magnitude than ΔG˚ and ΔG is positive; reverse reaction will proceed until Q = Keq and equilibrium is reached