Chapter 7

Class Notes

1. Basics
1. Thermodynamics: studies of the energetic feasibility of reactions; the study of the transformations of energy, esp. the transformation of heat into work and work into heat
2. Kinetics: studies of the rates at which reactions occur
3. Energy
1. Potential energy: the energy a body has based on its position (gravitational potential energy)
2. Chemical potential energy: energy stored in chemical bonds, based on the strength of the attractive interactions between the bonding atoms
3. Kinetic energy: energy associated with motion - translational, rotational, vibrational, spin
4. Internal energy: total energy, sum of potential and kinetic energies
5. Conservation of energy: energy can neither be created nor destroyed in chemical reactions, although it can be transferred (heat, light) or transformed (from heat to light, etc.)
6. Measured in calories and Joules (4.184 J = 1 cal)

4. Work: a transfer of energy that can be used to the change the height of a weight somewhere in the surroundings

2. Thermodynamics 101
1. Does a chemical reaction occur spontaneously or must energy be added to make it occur?
2. It takes energy to break chemical bonds and energy is given off when chemical bonds are formed
3. Enthalpy: in a system at constant pressure the heat associated change in internal energy is called enthalpy
1. Enthalpy: from Greek "enthalpein: to warm"
2. Exothermic: (-) - heat flows from system to surroundings, the products have less chemical potential energy than the reactants; heat is a product
3. Endothermic: (+) - heat flows from surroundings to system, the products have more chemical potential energy than the reactants; heat is a reactant
4. Heat of reaction: the net change in energy that results from breaking and making chemical bonds
5. dH: change in enthalpy, essentially synonymous with "heat of reaction"
6. "d" - represents "the change in"

4. Enthalpy is a extensive property - depends on the masses involved in the reaction (as compared to intensive properties such as boiling point and melting point)
1. 2 H_{2 (g)} + O_{2 (g)} => 2 H₂O_(g); dH_rxn = -483.6 kJ
2. H_{2 (g)} + ½O_{2 (g)} => H₂O_(g); dH_rxn = -241.8 kJ
3. 20 H_{2 (g)} + 10 O_{2 (g)} => 20 H₂O_(g); dH_rxn = -4836 kJ
4. "molar" enthalpy values and fractional coefficients

5. Usually if a reaction is exothermic it is spontaneous, and usually is a reaction is endothermic it is nonspontaneous - but not always
6. Free energy
1. During chemical reactions the disorder of the system tends to increase: s-> l, l -> g transitions, etc.
2. Entropy: a measure of the disorder (chaos) in a system; dS and sign conventions
3. Spontaneity in a reaction depends on the changes in enthalpy and in entropy
4. Spontaneous reactions can do useful work, while nonspontaneous reactions require work to be done on them
5. The energy available to do useful work in a chemical reactions is called the Gibb's free energy of the reaction (dG, sign conventions)
6. dG = dH - TdS
7. Implications

3. Kinetics 101
1. The rates of chemical reactions can be expressed several ways
1. Reaction rate: how fast reactant disappears (or product appears) as a function of time
2. rate ~ d[reactant] / dt or rate ~ d[product] / dt
1. Square brackets [] represent the molar concentration of a substance, which is the number of moles of a substance per liter of solution
2. "d" - represents "the change in," so "d[reactant] / dt" represents the change in reactant concentration with the change in time
3. Given the combustion of methane, if 11 moles of methane are burned in 45 seconds, what is the average rate of the reaction (assume volume = 1.00 L)?
   rate = d[CH₄] / dt = 11 mol/L / 45 s = 0.24 mol/L·s
4. If, during the course of the 45 seconds, the [CO₂] increased from 0.5 M to 9.8 M, what is the rate of the production of carbon dioxide during this time?
   rate = d[CO₂] / dt = ( 9.8 M - 0.5 M)/ 45 s = 0.21 mol/L·s

3. Various factors affect reaction rates; all are factors that impact collisions between molecules
1. Molecules must be able to collide if they are to react
2. Reactant concentration, spatial orientation, system temperature, system pressure if in the gas phase, presence of catalysts, steric hindrance, etc.

4. Rate laws are mathematical expressions of the relationship between reaction rate, temperature, and concentration
1. For the reaction aA + bB <=> cC + dD
2. At any time: rate = k[A]^m[B]ⁿ
1. k is a rate constant that depends on the particular reaction and on temperature
2. m and n must be determined experimentally

2. Reactive collisions
1. Molecules must collide with enough energy to result in the breaking of bonds
2. Molecules must be oriented in such a way that that the collisions result in formation of a new substance when old bonds are broken and new bonds are formed
1. The formation of 1,1,1-trichloroethane from ethane and Cl₂
2. The reaction of 2-butene and HCl to form 2-chlorobutane

3. Concentration and its effect on the number of effective collisions
4. As a general rule, reaction rates double with every 10°C increase in temperature because of the effect on the fraction of molecules in an ensemble with sufficient energy to react (Arrhenius equation)
5. Rate laws - how do these describe how temperature and concentration affect reaction rate?

3. Activation energy and activated complexes

1. Mechanics of a collision: the reaction of 2-butene and HCl
2. Activation energy: the minimum amount of energy required to form an activated complex; can be thought of as an energy barrier between the reactant and product states
   
   
3. dH_rxn, exothermic and endothermic reactions
4. Catalysts: increase the rate of reaction by lowering the Ea but is not consumed during the course of the reaction
1. Catalysts provide a surface on which the reaction takes place - result in bond stretching and weakening
2. Enzymes: biological catalysts, "lock and key" analogy

4. Chemical equilibrium
1. Equilibrium: all reactions are reversible to a greater or lesser extent
1. Acetic acid + methanol <=> methyl acetate + water
2. Use of arrows to indicate reversibility, rate constants k_f = k_r are sometimes shown
3. The forward reaction proceeds at a rate the gradually slows as reactants are consumed
4. The reverse reaction proceeds at a rate the gradually increases as products are produced
5. A reaction is at eqb. when k_f = k_r

2. Equilibrium constants
1. The ratio of the rate constants at eqb. is a special constant called the equilibrium constant
1. K_eq = K_c = k_r/k_f

2. Keq can also be expressed in terms of the ratios of the reactants and products at eqb (equilibrium constant expressions)
1. For the reaction aA + bB <=> cC + dD K_eq = [C]^c [D]^d / [A]^a [B]^b
2. K_c = [methyl acetate] [water] / [acetic acid] [methanol]

3. Note: only those substances with concentrations that change during the course of the reaction appear in eqb constant expressions
4. Pure solids and liquids do not appear in eqb expressions because while they might be created or consumed their concentration remains constant
5. Other examples of equilibria constant expressions for homogeneous and heterogeneous equilibria
1. CH₄ + 2 O₂<=> CO₂ + 2 H₂O
2. N_{2 (g)} + 3 H_{2 (g)} <=> 2 NH_{3 (g)}
3. Ni_(s) + 2 HCl_(aq)<=> NiCl_{2 (aq)} + H_{2 (g)}
4. TiBr_{4 (g)} + 2 H_{2 (g)}<=> Ti_(s) + 4 HBr_(g)

3. LeChatlier's principle: a system at equilibrium is stable. If the system is disturbed the system will shift so as to minimize the effects of the disturbance and restore equilibrium
1. Example: N_{2 (g)} + 3 H_{2 (g)} <=> 2 NH_{3 (g)}
2. If a reaction is endothermic or exothermic, LeChatlier's principle explains how changes in temperature effect the reaction
1. Exothermic: heat is treated as a product
2. Endothermic: heat is treated as a reactant
3. Examples
1. CH₄ + 2 O₂ <=> CO₂ + 2 H₂O + heat
2. Heat + 2 NOCl _(g) <=> 2 NO _(g) + Cl_2(g)