Thermodynamics

Heats of Formation

Allow chemists to tabulate thermochemical data in a short, easy-to-use format. Heats of formation of the elements is always zero, whether they are molecules or atoms. Ex: O₂ → O². Heats of formation can be calculated from heats of combustion. We'll need a formation reaction for each of the reactants and products, excluding elements, since they have a heat of formation of 0. Again we manipulate the equation using Hess's Law so that the reactants are on the correct side, and all substances have the correct coefficients. Everything else naturally cancel, and we have the Heat of Combustion/Reaction.

State Functions

Describe an aspect of a chemical system (Mass, phase, temperature, pressure.). Changes in state functions depend on only the initial and final state of a system. Heat and work are not state functions, since they depend on intermediate steps.

Entropy and Second Law of Thermodynamics

Entropy is the disorderliness of the system. Increasing the number of particles, the volume, and changing state by increasing temperature increases entropy. Entropy has the units J °C⁻¹, while standard entropy is J °C⁻¹ mol⁻¹¹. Standard entropy values for elements are not zero as they are for standard heat of formation, ∆H°f, and the standard free energy, ∆G°f. At absolute 0, entropy is 0. The Boltzmann entropy equation, S = k ln w, where k is the Boltzmann constant and w is the number of microstates, describes how to determine entropy. Standard entropy is defined as S° =Qrev/T, in which T represents the temperature in Kelvins, and Q rev is the heat added to raise the temperature very slowly from absolute zero up to T. Q is not a state function; however, if heat is always added in a carefully defined manner, the results will always be the same. This carefully defined path is called a reversible process. It is defined as one that occurs in infinitesimally small steps from the initial to the final state. To calculate sign of entropy change use the following principles: 1. Solid->Liquid or Liquid -> Gas increases entropy, while Gas->Liquid or Liquid->Solid decreases entropy. The magnitude of the entropy change is affected by the number of moles undergoing a phase change. 2. An increase temperature increases entropy in a system and vice-versa. The Second Law of Thermodynamics says that any physical or chemical change must result in an increase in the entropy of the universe.

Free Energy at Temperatures Other Than 298K

For temperatures other than 298K, we cannot do ∆G°=∑∆Gfproducts - ∑∆Gfreactants. Note: Units are in kJ.

Formation reaction

Is defined as a reaction in which the reactants are elements in their standard state at 25°C and 1 atmosphere of pressure, and there is only 1 mole of product. Fractional coefficients may be used.

Work

Is the force applied to an object as it moves a certain distance: Work = Force * Distance moved. Force is pressure * area, so: Work = Pressure * Area * Distance moved. Multiplying area by distance results in volume change, so we have Work = Pressure * Volume change, thus: Work = -P∆V

Types of Energy

Law of Conservation of energy states that energy is never created or destroyed. All forms of energy can be converted into heat energy. Energy can also be categorized as either kinetic energy, KE, or potential energy, PE. Kinetic energy is the energy that matter possesses because of its motion. The equation for KE is: KE = (1/2)mv². When the mass, m, is in kilograms and the velocity, v, in meters per second, the energy units are joules. Potential energy is stored energy. Forms of potential energy include gravitational energy and electrostatic attraction between appositely charged ions. PEgrav = Kgrav (m₁m₂/r) and PEelect = Kelect (q₁q₂/r). The two masses, m, in gravitational attraction and the two charges, q, in electrostatic attraction are separated by a distance, r. K is a proportionality constant that is different for each type of potential energy. The total energy of a substance is the sum of its kinetic and potential energies. Energy (E) = potential energy (PE) + kinetic energy (KE). In chemical substances, kinetic energy is the motion of the molecules. The potential energy is the sum of all attractions.

Definition of Qp, Qv, ∆E, and ∆H

Note for Qp and Qv: These are capitalized for clarity and incompatible formatting. The Qs are normally lowercase, and p and v are subscripts. The First Law of Thermodynamics may be rewritten as ∆E = Qp - P∆V. The minus sign enters this equation because an increase in volume means that the system does work on the surroundings, and such work has been defined as a negative quantity. Q is given subscript p to indicate that pressure must be constant. If heat energy is measured in a calorimeter that does not allow volume to change, P∆V must be zero. Therefore, ∆E = Qv, where subscript v indicates that the volume is held constant. Calorimeters not allowing volume change are called bomb calorimeters. For most reactions, we use Qp, which is called the enthalpy change and given the symbol ∆H. Enthalpy is the heat content of a substance and ∆H is difference in heat content of the products and reactants. ∆H = Hproducts - Hreactants. Thus: ∆E = ∆H - P∆V. Note that for many reactions, the value of ∆H is very large, and P∆V is small, so that ∆E and ∆H are approximately equal.

R for Energy Unit Conversion

R (0.0821 L atm mol⁻¹ K⁻¹) and another R (8.31 J mol⁻¹ K⁻¹) can be used to convert between energy units such as calories, joules, and liter-atmospheres.

Dulong Petit Law

Specific Heat * Molar mass = 25 J mol⁻¹ °C⁻¹ for most metals. Specific heat is an intensive property.

First Law of Thermodynamics

States that energy is always conserved. Measurable quantities heat (q) and work (w) must add up to the total energy change in a system: ∆E = q + w. Q can be measured using a calorimeter. Q is a negative value if heat is released from the system, and w is a negative value if work is done by the system. This is true vice-versa. The change in energy of a system, at constant temperature, is the difference in potential energy between the final and initial states: ∆E = PEfinal - PEinitial. ∆E is mainly heat energy.

Hess's Law

States that whatever mathematical operations are performed on a chemical equation, the same mathematical operations are applied also to the heat of the reaction. In algebraic terms, it is the Commutative Property of Multiplication, etc. where you can't randomly add something to one side but not the other. Summarized as follows: 1. If the coefficients of a chemical equation are all multiplied by a constant, the ∆H°reaction is multiplied by that same constant. 2. If two or more equations are added together to obtain an overall reaction, the heats of the equations are also added to give the heat of the overall reaction. Another principle is that ∆H of forward reaction = -∆H of reverse reaction.

Specific Heat

The calorie is the amount of energy need to raise the temperature of 1 gram of pure water from 14.t to 15.5°C. The joule is the metric unit of energy; 1 calorie is equal to exactly 4.184 joules. 4.184 joules of energy is needed to raise the temperature of 1 gram of water by 1 degree Celsius. This quantity is the specific heat of water.

Gibbs Free-Energy, ∆G

The free-energy change is the maximum amount of energy available from any chemical reaction. The equation is ∆G° = ∆H°-T∆S°. Decrease in enthalpy and increase in entropy are spontaneous and vice-versa.

Heat Energy of a Process

The heat energy of an process is q = mst, in which q is the heat energy, s is the specific heat, m is the mass, and t is the temperature change. Q, the heat energy, is expressed in joules. Temperature is a measure of average kinetic energy, while heat is the energy produced when both the kinetic energy and the energy of attractions between the atoms in the group change in a chemical or physical process.

System

The part of the universe under study. Everything else is the surroundings. An open system can transfer both energy and matter. A closed energy is where energy can be transferred to the surroundings, but matter cannot. In an isolated system, there is not transfer of energy or matter to or from the surroundings.

Exo-, Endo-, and Sign Convention

The prefix Exo- means that energy is being lost from the system, and corresponds to a negative sign for numerical thermodynamic quantities. The heat of reaction, ∆H, is a negative number. The prefix endo- indicates that energy is gained from the surroundings.

Free Energy and Equilibrium

When a system is not at standard state, free-energy change, ∆G, is: ∆G = ∆G° + RTlnQ. ∆G° is the free-energy at standard conditions. At standard state, all concentrations are equal to 1, and equal is 1, and the natural log of 1 is zero. When ∆G is negative, the reaction will proceed in the forward direction. When ∆G is positive, the reaction proceeds in the reverse direction. When ∆G is zero, the reaction is at equilibrium. For the equilibrium condition, we find that ∆G°=-RTlnK. By setting ∆G = 0, substituting the equilibrium constant, K, for the reaction quotient Q, in ∆G = ∆G° + RTlnQ, and rearranging. The relationships between ∆G and ∆G°. At standard state, only the temperature can alter the position of equilibrium.

Standard Enthalpy Changes and Standard Heat of Reaction

∆H is the heat energy or enthalpy change produced by a chemical reaction. This is an extensive property, since reacting a larger amount of chemicals produces more heat. To make the heat produced by a reaction an intensive property, the amount of chemical that reacts must be specified. ∆H°reaction has a unit of kJ, and only when the reaction involved is a formation with one and only one mole of product, and a heat or reaction symbolized as ∆Hf° will be kJ mol⁻¹. This is called the heat of formation and the unit is necessary since the heat of formation is usually multiplied by the moles of a substance resulting in the kJ units of a heat of reaction. ∆Hf° can be determined from ∆H°reaction by dividing by the number of moles.

Standard State

∆H, ∆S, ∆G, and ∆E are extensive properties of matter, meaning that they change as the amount of sample changes. To make these quantities intensive properties of matter , we must define precisely the temperature, pressure, mass, and physical state of the substance. A system is in the standard state when the pressure is 1 atmosphere, the temperature is 25°C, and 1 mole of compound is present. All liquids and solids are pute, and all solutions have 1M concentration. The energy of formation of an element in its normal state is defined as 0. If the thermodynamic quantities are at standard state, they are intensive properties and a superscript 0 is added to their symbols as ∆H°, ∆S°, ∆G°, ∆E°. To clarify, intensive properties are those that do not change even when mass or volume change; they are characteristics of an element. Examples are melting point, viscosity, and density. Extensive properties are the opposite.