# The Study of Chemical Reactions. Equilibrium Constants and Free Energy l Thermodynamics: deals with the energy changes that accompany chemical and physical.

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The Study of Chemical Reactions

Equilibrium Constants and Free Energy l Thermodynamics: deals with the energy changes that accompany chemical and physical transformations.

For the general reaction Where K eq is the equilibrium constant. When K eq is > 1, the forward reaction is favored. When K eq is < 1, the reverse reaction is favored. 1. Thermodynamics

K eq is related to the Gibbs free energy by the equation: Where R = ideal gas constant T = temperature in Kelvin The equation demonstrates that reactions with negative  G values are favored.  G = free energy of the products - free energy of the reactants. But don’t forget that: 1. Thermodynamics

Enthalpy and Entropy Two factors that contribute to the Gibbs free energy are enthalpy and entropy.  G 0 =  H 0 - T  S 0  G = free energy of products - free energy of reactants.  H 0 = enthalpy of products - enthalpy of reactants  S 0 = entropy of products - entropy of reactants

Enthalpy: the amount of heat evolve or consumed in the course of a reaction. A measure of the strength of bonding in products and reactants. Reactions favor products with lowest enthalpy. l Exothermic reaction: negative value of  H 0 ; weaker bonds are broken and stronger bonds are formed.  H makes a favorable negative contribution to  G 0. l Endothermic reaction: positive value of  H 0 ; Stronger bonds are broken and weaker bonds are formed.  H makes an unfavorable positive contribution to  G 0. 2. Enthalpy and entropy

Entropy: randomness or freedom of motion. Reactions favor products with the greatest entropy. A positive entropy means that the products have more freedom of motion than the reactants. In such a case, entropy makes a favorable negative contribution to  G 0. 2. Enthalpy and entropy Usually,  S is small, and thus,  H is the driving force for the reaction.

Kinetics and Rate Equations Kinetics: the study of reaction rates. Reaction rate: how fast the products appear and the reactants disappear. Determined by measuring the increase of concentration of products or disappearance of reactants with time. Rate Equation (or Rate Law): relationship between concentration of reactants and the observed reaction rate. This is determined experimentally.

For a general reaction: Rate = k r [A] a [B] b Where k r = rate constant a and b = order with respect to each reactant. Must be determined reactant. Must be determined experimentally. experimentally. a + b = overall order of reaction. 3. Kinetics and rate equations

Example: Experiments have shown that: 1. Doubling the conc. of - OH doubles the reaction rate. 2. Doubling the conc. of CH 3 Br doubles the rate also. Therefore, the rate is proportional to the concentration of both CH 3 Br and OH -. Thus, the rate law can be written as: Rate = k r [CH 3 Br][OH - ] 3. Kinetics and rate equations The rate equation is 1st order with respect to each of the two reagents because it is proportional to the 1st power of their concentrations. The reaction is second order overall.

Example # 2: Experiments have shown that: 1. Doubling the conc. of - OH does not affect the rate. 2. Doubling the conc. of (CH 3 ) 3 CBr doubles the rate. Therefore, the rate is proportional to the concentration of (CH 3 ) 3 CBr but not OH -. Thus, the rate law can be written as: Rate = k r [(CH 3 ) 3 C-Br] 3. Kinetics and rate equations The rate equation is 1st order with respect to (CH 3 ) 3 CBr. The reaction is first order overall.

Activation Energy and Temperature Dependence of Rates Reaction rates are related to temperature by the Arrhenius equation: Arrhenius equation A = Frequency Factor Ea = Activation Energy e -Ea/RT = Fraction of collisions in which the particles have the minimum E a to react. particles have the minimum E a to react.

l Frequency Factor (A): fraction of collisions with proper orientation for reaction to occur. l Activation Energy (E a ): minimum kinetic energy molecules must possess to overcome repulsions between their electron clouds when they collide. 4. Activation Energy and Temperature Dependence of Rates The Arrhenius equation implies that the reaction rate depends upon the fraction of molecules with kinetic energy of at least E a.

4. Activation Energy and Temperature Dependence of Rates The variation in the distribution of KE in a sample depends on temperature, and can be described by the Boltzman Distribution: Number of molecules having a given E a decreases as E a increases. At higher temperatures,more collisions have the needed energy. In general, the reaction rate doubles for each 10 0 C rise in temperature.

Energy Diagrams: Graphical representation of reaction energetics in proceeding from reactants to products. l Y Axis: Represents the total potential energy of all species involved in the reaction. l X Axis: Described as the reaction coordinate or “progress of reaction”. Symbolizes the progress of the reaction in going from reactants to products. l Transition State: highest point on graph. Represents the highest energy state in a molecular collision that leads to a reaction. It is highly unstable and cannot be isolated. It is symbolized by a “double dagger” (‡). l Ea: Energy difference between the reactants and the transition state. l  H: The heat of the reaction. Represents the difference in energy between the reactants and the products.

Reaction Energy Diagram for a One Step Exothermic Reaction 5. Energy Diagrams

Reaction Energy Diagram for a Two Step Exothermic Reaction 5. Energy Diagrams In a multistep reaction, each step has its own rate, but there is only one overall rate. The overall rate is overall rate is controlled by the rate- determining step. In general, the highest energy step of a multi- step reaction represents the rate-determining step.

Introduction to Organic Reactions: Reaction Mechanisms A mechanism is a step by step description of exactly which bonds break and which bonds form in order to give observed products.

Bond Cleavage In any chemical reaction, some bonds are broken and other bonds are formed. Bond breakage or cleavage can be homolytic (to give radicals) or heterolytic (to give ions). Heterolytic Bond Cleavage: Homolytic Bond Cleavage: ions radicals

Radicals are electron deficient because they lack an octet. They readily combine with a single electron from another atom to complete the octet and form a bond. Radicals are usually represented by a structure with a single dot representing the unpaired electron. Lewis Structures: Written:

Free Radical Halogenation of Alkanes Alkanes react with molecular halogens (typically Cl 2 and Br 2 ) to form alkyl halides. Alkyl halides are hydrocarbons that contain at least one halogen atom. These reactions take place at high temperatures or in the presence of UV light (symbolized by h ). Methyl chloride ethyl bromide

Free Radical Halogenation of Alkanes The Mechanism of the reaction of CH 4 with Cl 2 is as follows: Propagationsteps Terminationsteps Initiationstep

In Free Radical Reactions: l The initiation steps generally create new free radicals l The propagation steps usually combine a free radical and a reactant to form a product and another free radical. l Termination steps generally decrease the number of free radicals, and involve the combination of two radicals to give a product. Free Radical Halogenation of Alkanes

Halogenation of Higher Alkanes Free Radical Halogenation of Alkanes In higher alkanes, the replacement of different hydrogen atoms leads to different products: The minor product was formed from substitution of a 1 0 hydrogen. The major product was formed from substitution of a 2 0 hydrogen.

Relative radical stabilities control product distribution. Free Radical Halogenation of Alkanes Methyl radical < 1 0 < 2 0 < 3 0 Increasing radical stability The more highly substituted the radical, the greater its stability.

In the analogous reaction using bromine, the product ratios are different, even though the mechanism is exactly the same. Free Radical Halogenation of Alkanes The 97:3 product ratio shows that Br abstracts a 2 0 hydrogen 97 times as fast as a 1 0 hydrogen. We say that bromine is much more selective than chlorine, and chlorine is much more reactive than bromine.

Hammond Postulate The difference in reactivity/selectivity of bromine relative to chlorine can be rationalized by the Hammond Postulate which states: Related species that are similar in energy are also similar in structure. The structure of a transition state resembles the structure of the closest stable species. Free Radical Halogenation of Alkanes

The Hammond Postulate tells us whether the transition state is more like the reactant(s) or the product(s). When the reaction is endothermic, the transition state is reached relatively late on the reaction coordinate. Bond breaking (in the reactant) and bond formation (in the product) has occurred to a large extent and the structure of the transition state is more like that of the product than the reactant. Free Radical Halogenation of Alkanes

If the reaction is exothermic, the transition state is reached relatively early on the reaction coordinate. Bond breaking and bond forming has not occurred to a large extent, and the structure of the transition state resembles the reactant more than the product. Free Radical Halogenation of Alkanes

The first propagation step is endothermic for bromine but exothermic for chlorine. The product like transition state for bromination has the C--H bond nearly broken and a great deal of radical character on the carbon atom. The energy of this transition state reflects the energy difference of the radical products. Therefore bromination is more selective. The reactant like transition state for the chlorination has the C--H bond just beginning to break, with little radical character on the C atom. This transition state reflects only a small part of the energy difference of the radical products. Therefore, chlorination is less selective. Free Radical Halogenation of Alkanes

Reactive Intermediates l Carbocations: contain carbon bearing a positive charge. They are sp 2 hybridized. Carbocations are electron deficient, so they are strong electrophiles (Lewis acids). Like radicals, they are stabilized by alkyl substituents through (a) the inductive effect, and (b) hyperconjugation. The inductive effect is donation of electron density through the sigma bonds of the molecule. The positively charged carbon atom withdraws some electron density from the alkyl groups bonded to it. Hyperconjugation refers to the weak partial overlap of filled p orbitals with empty ones. Cations are also stabilized by resonance. Methyl cation < 1 0 < 2 0 < 3 0 Increasing carbocation stability

l Free Radicals: Like carbocations, radicals are sp 2 hybridized and planar. Unlike carbocations, the p orbital perpendicular to the plane of the molecule is not empty, but contains one unpaired electron. Radicals are also stabilized by alkyl groups as well as resonance. l Carbanions: Are not electron deficient since they have an octet. They have tetrahedral geometry. Carbanions are nucleophilic and basic. They are destabilized by alkyl groups but stabilized by resonance. l Carbenes: Uncharged reactive intermediates containing a divalent carbon atom. The simplest carbene has the formula :CH 2. The carbon atom is sp 2 hybridized. An unshared electron pair occupies one of the sp 2 orbitals, and there is an empty p orbital extending above and below the plane of the molecule. Carbenes can act as electrophiles or nucleophiles since they have both a lone pair and an empty p orbital.

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