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Chapter 13

Chemical Kinetics

Rate of Reaction For the reaction... aA + bB ---> cC + dD.. where A and B are reactamts, C and D are products, and a, b c, d are stoichoimetric coefficients. The rate of the reaction is... Rate = -(1/a)(Δ[A]/Δt) = -(1/b)(Δ[B]/Δt) = +(1/c)(Δ[C]/Δt) = +(1/d)(Δ[D]/Δt)
Rate Law A relationship between the rate of a reaction and the concentration of the reactants... Rate = k[A]^n... where k is a constant of proportionality called the rate constant and n is the reaction order
Reaction Order(n) A value in the rate law that determines how the rate depends on the concentration of the reactants
If Reaction Order Equal Zero(n = 0) The reaction is zero order and the rate is independent of the concentration of A
If Reaction Order Equal One(n = 1) The reaction is first order and the rate is directly proportional to the concentration of A
If Reaction Order Equal Two(n = 2) The reaction is second order and the rate is proportional to the square of the concentration of A
Rate Law Defined for Reaction for More than One Reactant aA + bB ---> cC + dD... The rate law is proportional to concentration of [A] raised to the m multiplied by concentration of [B] raised to n: Rate = k[A]^m[B]^n.. where m is reaction order with respect to A and n is reaction order with respect to B
Overall Order The sum of the exponents(m + n)
Half-Life(t(1/2)) of a Reactant The time required for the concentration of a reactant to fall to one half of its initial value
Half Life for a First-Order Reaction T(1/2) = 0.693 / k
Half Life for a Second-Order Reaction t(1/2) = 1 / (k * [A]o)... The half life depends on the initial concentration
Half Life for a Zero-Order Reaction t(1/2) = [A]o / 2k... The half life for a zero-order reaction depends on the initial concentration
1. Summarizing Basic Kinetic Relationships 1. The reaction order and rate law must be determined experimentally.. 2. The rate law relates the rate of the reaction to the concentration of the reactant(s).. 3. The integrated rate law relates the concentration of the reactant(s) to time..
2. Summarizing Basic Kinetic Relationships 4. The half life is the time it takes for the concentration of a reactant to fall to one-half of its initial value.. 5. The half life of a first order reaction is constant and independent of the initial concentration..
3. Summarizing Basic Kinetic Relationships 6. The half lives of zero order and second order reactions depend on its initial concentration
Arrhenius Equation Equation which relates rate constant of a reaction to temperature, activation energy, and frequency factor:.. K = Ae^(-Ea/RT).. where R is gas constant, A is constant called frequency factor, Ea is activation energy, and e^(-Ea/Rt) is exponential factor
Activation Energy(Ea) An energy barrier or hump that must be surmounted for the reactants to be transformed into products
Frequency Factor(A) The number of times that the reactants approach the activation barrier per unit time
Zero Order Reaction Rate Law( Rate = k[A]^0 )... Units of k( M*s^-1 )... Integrate Rate Law( [A]t = -kt + [A]o)... Half Life Expression( t(1/2) = [A]o / 2k )
First Order Reaction Rate Law( Rate = k[A]^1 )... Units of k( s^-1 )... Integrate Rate Law( ln[A]t = -kt + ln[A]o) or ( ln([A]t / [A]o) = -kt )... Half Life Expression( t(1/2) = 0.693 / k )
Second Order Reaction Rate Law( Rate = k[A]^2 )... Units of k( M^-1*s^-1 )... Integrated Rate Law( 1 / [A]t = kt + 1 / [A]o)... Half Life Expression( t(1/2) = 1 / k[A]o)
Activate Complex(Transition State) A high-energy intermediate state between reactant and prodcut
Relationship Between Activation Energy and Reaction Rate The higher the activation energy, the slower the reaction rate(at a given temperature)
Exponential Factor A number between 0 and 1 that represents the fraction of molecules that have enough energy to make it over the activation barrier on a given approach. It is the fraction of approaches that are actually successful and result in the product
1. Summarizing Temperature and Reaction Rate 1. The frequency factor is the number of times that the reactants approach the activation barrier per unit time... 2. The exponential factor is the fraction of approaches that are successful in surmounting the activation barrier and forming products
2. Summarizing Temperature and Reaction Rate 3. The exponential factor increases with increasing temperature, but decreases with increasing activation energy
Arrhenius Plot lnk = (-Ea / R)(1/T) + lnA... This equation is in the form of a straight line. A plot of the natural log of the rate constant(lnk) versus the inverse of temperature in kelvins(1/T) yields a straight line with a slope of -Ea/R and a y-intercept of lnA
Two Point Form of Arrhenius Equation ln( k1 / k2 ) = ( Ea / R ) ( (1/T1) - (1/T2) )
Collision Model A chemical reaction occurs after a sufficiently energetic collisions between two reactant molcules
Collision Model Arrhenius Equation k = Ae^(-Ea/RT) = pze^(-Ea/RT)... where p is the orientation factor and z is the collision frequency.
Reaction Mechanism A series of individual chemical steps by which an overall chemical reaction occurs
Elementary Step An individual step in a reaction mechanism
Reaction Intermediate Forms in one elementary step and is consumed in another
Molecularity The number of reactant particles involved in an elementary step. Elementary steps are characterized by their molcularity
Unimolecular Describes a reaction that involves only one particles that goes on to form products
Bimolecular An elementary step in a reaction that involves two particles, either the same species or different, that collide and go on to form products
Termolecular An elementary step of a reaction in which three particles collide and go on to form products. These are very rare
1. Rate Laws for Elementary Step 1. Elementary Step(A---products)..Molecularity(1)..Rate Law(Rate = k[A]).. 2. Elementary Step(A+A--->products)..Molecularity(2)..Rate Law(Rate = k[A]^2).. 3. Elementary Step(A+B--->products)..Molecularity(2)..Rate Law(Rate = k[A][B])..
2. Rate Law for Elementary Step 4. Elementary Step(A+A+A--->products)..Molecularity(3(rare))..Rate Law(Rate = k[A]^3).. 5. Elementary Step(A+A+B--->products)..Molecularity(3(rare))..Rate Law([B]Rate = k[A]^2)
3. Rate Law for Elementary Step 6. Elementary Step(A+B+C--->products)..Molecularity(3(rare))..Rate Law(Rate = k[A][B])[C])
Rate-Determining Step The step in a reaction mechanism that occurs much more slowly than any of the other steps
For a Proposed Reaction Mechanism To Be Valid 1. The elementary steps in the mechanism must sum to the overall reaction.. 2. The rate law predicted by the mechanism must be consistent with the experimentally observed rate law
Catalyst A substance that increases the rate of a chemical reaction but in not consumed by the reaction
Homogeneous Catalysis Catalysis in which the catalyst exists in the same phase as the reactants
Heterogeneous Catalysis Catalysis in which the catalyst exist in a different phase than the reactants
Hydrogenation The catalyzed addition of hydrogen to alkene double bonds to make single bonds
Enzymes Biological catalysts that increase the rates of biochemical reaction
Active Sites The specific area of an enzyme at which catalysis occurs
Substrate The reactant molecule of a biochemical reaction that binds to an enzyme at the active site
Created by: TimChemistry2