Thermodynamics

I. What is Thermodynamics?

a. Thermodynamics is the science that deals with work, heat, and energy acting upon a system.
II. Laws of Thermodynamics
a. First Law: Energy can be converted in a chemical process, but cannot be created or destroyed. The total energy must remain constant.
b. Second Law: The spontaneity of a reaction can only occur in one direction of a chemical reaction. The entropy, or disorder, always increases within spontaneous reactions.
III. State Functions: They depend upon the initial and final states of a system, not the path by which it occurs. Enthalpy, entropy, and Gibbs free energy are all examples of state functions.
a. Enthalpy (ΔH): This is the amount of energy released or absorbed by a component of a reaction when bonds are broken or formed.
i. When ΔH is a negative value, then the reaction is exothermic (releases energy). When ΔH is positive, then the reaction is endothermic (absorbs energy).
ii. Enthalpy Change: ΔH = Hproducts – Hreactants
1. If the bonds of the products are stronger than that of the reactants then the products, being more stable, will have a lower enthalpy than that of the reactants, resulting in an exothermic reaction.
2. If the bonds of the reactants are stronger than that of the reactants then the reactants, being more stable, will have a lower enthalpy than that of the products, resulting in an endothermic reaction.
iii. Heat of Formation (ΔH°f): This is the change of energy that occurs in one mole of a compound under standard conditions at 25°C (298K).
1. The same rules apply for the strengths of the bonds in ΔH°f as ΔH.
2. ΔH°f can be calculated using a table of values.
a. ΔH° = ΣΔH°f products - ΣΔH°f reactants
iv. Bond Energy: This is the amount of energy that is required in order to break a bond.
1. ΔH° = Σ Bond energies of bonds broken – Σ Bond energies of bonds formed
a. The bond energy for bonds being broken is always endothermic, so this value is positive. The bond energy for bonds being formed is always exothermic, so this value is negative.
v. Hess’s Law: This law states that if a reaction can be described in multiple steps, then ΔH for the overall reaction is a sum of the ΔH values for the various steps.

vi. Heat Capacity (Cp): Heat Capacity is the amount of heat needed to increase the temperature of a substance by 1°C.
1. Cp = ΔH / ΔT
a. ΔH is the amount of heat that is added (J or cal).
b. ΔT (in Kelvins) represents the change in temperature.
2. The greater the heat capacity, the more heat a substance can absorb without undergoing much of a change in temperature (and vice versa).
vii. Specific Heat (q): This is the amount of energy required to raise the temperature of 1g of a substance by 1°C. The units of q are Joules or calories.
1. q= mc ΔT
a. m is the mass of the substance
b. c is the specific heat
c. ΔT is the temperature change (K or °C)
b. Entropy (S): This is the measure of disorder within a system.
i. Rules
1. Liquids have higher entropy than solids.
2. Gases have higher entropy than liquids.
3. Particles in solution have higher entropy than solids.
4. Two moles of a substance have higher entropy than one mole.
ii. Standard Entropy Change (ΔS°) can be calculated using the following equation:
1. ΔS° = ΣS° products - ΣS° reactants
2. When ΔS is positive, there has been an increase in disorder. When ΔS is negative, there has been a decrease in disorder.
c. Gibbs Free Energy (ΔG): This is the measurement of the spontaneity of a reaction, or the willingness of a reaction to occur.
i. Rules
1. If ΔG is negative, the reaction is spontaneous
2. If ΔG is positive, the reaction is not spontaneous
3. If ΔG = 0, the reaction is at equilibrium.
ii. Standard Free Energy Change can be calculated using the following equation:
1. ΔG° = Σ ΔG°f products - Σ ΔG°f reactants
d. The equation that relates enthalpy and entropy to Gibbs free energy is:
i. ΔG° = ΔH° - TΔS°
1. T is the absolute temperature (K).
ii. A spontaneous reaction favors low energy and high disorder. The following chart displays the effect the various combinations of the factors affecting ΔG:

e. Relationship between ΔG and ΔG°
i. ΔG° can be calculated when all concentrations of the reactants and products are at 1M in their standard conditions. The following equations show the relationships:
1. ΔG= ΔG° + RTlnQ or ΔG = ΔG° + 2.303RTlogQ
a. ΔG° is the standard free energy change (J).
b. ΔG is the free energy change under given initial conditions (J).
c. R is the gas constant, 8.31 J/mol-K.
d. T is absolute temperature (K).
e. Q is the reaction quotient for the given initial conditions.
f. Standard Free Energy Change and Equilibrium Constant:
i. When a reaction is at equilibrium, Q=K and ΔG=0. Using this information, ΔG= ΔG° + RTlnQ can be derived as:
1. ΔG° = -RTlnK or ΔG° = -2.303RTlogK
a. R is the gas constant, 8.31 J/mol-K
b. T is absolute temperature (K).
c. K is the equilibrium constant.
ii. If ΔG° is negative then K must be greater than 1, meaning equilibrium is product favored. If ΔG° is positive then K must be less than 1, meaning equilibrium is reactant favored.
IV. Energy Diagrams
a. Exothermic Reaction:

The reaction begins with a certain amount of energy. The reactants then
reach the transition state where they are a part of the activated complex, which
is the highest point on a graph. The activation energy (Ea) is the amount of
energy needed to reach this particular point. At this point, the reactants have
been broken and bonds have not been formed within the products. Therefore,
this point contains the highest energy and lowest stability. As the reaction
proceeds past the activated complex, bonds within the products begin to form
and the energy level of the products is eventually reached. Since the products
are at a lower energy than the reactants, this reaction is
exothermic and ΔH is negative.

b. Endothermic Reaction:
The endothermic reaction is the opposite of the exothermic reaction. The energy
of the products is greater than that of the reactants, resulting in a positive ΔH.
c. Catalysts:
A catalyst speeds up a reaction by lowering the activation energy, providing the
reactants with a different path. This does not, however, affect the energy of the
reactants, products, or ΔH of the reaction. Catalysts also have no effect on
equilibrium conditions because it lowers the activation energy for the forward and reverse reactions.