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Chemistry 1027A/B Study Guide - Final Guide: Rate-Determining Step, Rate Equation, Arrhenius Equation


Department
Chemistry
Course Code
CHEM 1027A/B
Professor
Paul Ragogna
Study Guide
Final

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Chapter 3: Chemical Kinetics
3.1 Reaction Rates and Rate Laws
- chemical kinetics is study of how quickly a reaction will proceed
- speed at which a reaction takes place depends on several factors
- nature of reactants and their concentrations
- temperature
- presence of a catalyst
- rate of chemical reaction is a positive quantity defined by comparing
chainge in product or reactant concentration over time
rate = -1/a(∆[A]/∆t) = -1/b(∆[B]/∆t) = -1/c(∆[C]/∆t) =
-1/d(∆[D]/∆t)
- rate of reaction (rate law) is equal to k[A]x[B]y
- k is specific rate constant for a reaction at a given temperature
- exponents are experimentally measured and DO NOT correlate with
the coefficients in the reaction equation
- if A products is a first order reaction, rate = k[A] = -(∆[A]/∆t)
- as the reaction proceeds, [A] decreases
- rate can be integrated into integrated rate law:
[A]t = [A]0e-kt
- [A]t is the concentration after time has elapsed
- [A]0 is the initial concentration
ln[A]t = -kt + ln[A]0
- if reaction is first-order, plot of ln[A]t as a function of time gives you a
straight line with a slope of –k and a y-intercept of ln[A]0
- half life (t1/2) is the amount of time it takes to use up half of the
reactant
t1/2 = 0.693/k
- half life of first-order reaction is exponential decay
- half life is constant length of time and only depends on the rate
constant, k
fraction remaining = (0.5)n
# of elapsed half lives (n) = time elapsed/length of half life
- if A products is zero-order, rate = -(∆[A]/∆t) = k[A]0 = k
[A]t = -kt + [A]0
- plot of [A] as a function of time gives a straight line with slope of –k
and y-intercept [A]0
- if A products is second-order, rate = -(∆[A]/∆t) = k[A]2
1/[A]t – 1/[A]0 = kt
- plot of 1/[A] as a function of time gives a straight line with positive
slope
- to determine if reaction is zero, first or second-order, plot [A], ln[A] or
1[A] as a function of time and see which one gives a straight line
- half life for second-order reaction:
t1/2 = 1/k[A]0
Order Rate Integrat Straigh Slope Units Half-

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Law ed Rate
Law
t Line
Plot of Plot of k Life
0Rate =
k
[A]t = -kt
+ [A]0
[A] vs
time (t)
Negativ
eMol/Ls [A]0/2k
1Rate =
k[A]
ln[A]t =
-kt +
ln[A]0
ln[A] vs
time (t)
Negativ
e1/s 0.693/k
2Rate =
k[A]2
1/[A]t – 1/
[A]0 = kt
1/[A] vs
time (t) positive L/mols 1/k[A}0
3.2 Reaction Mechanisms and the Arrhenius Equation
- thermodyndamis: A B, results in net energy difference (∆E)
- kinetics: speed of A B conversion, depends on size of barrier
- thermodynamics and kinetics are distinct
- reaction coordinate illustrates the energy changes that occur on route
from products to reactants
- Ea = activation energy
- collision theory explains the various factors that influence reaction
rates
- molecules must overcome activation barrier (average kinetic energy
is relative to temperature)
- energy required to overcome the activation barrier is called activation
energy
- energy needed to overcome the activation barrier comes from heat
- heat has a direct impact on kinetic energy
- temperature is a measure of average kinetic energy
- there is a distribution of kinetic energies at any given temperature
- for a chemical reaction to occur:
- reactants must collide with sufficient energy to overcome the
activation barrier
- must collide in proper orientation
- rate of reaction is affected by three factors:
- reactant concentration
- probabilities of colliding in particular geometry and continuing
to products at transition state
- Ea and temperature
- rate = number of collisions x probability (steric) factor x fraction of
collisions with enough energy to overcome Ea
- Arrhenius equation:
k = Ae-Ea/RT
- A = Arrhenius probability factor for specific reaction
- Ea = activation energy for specific reaction
- R = gas constant (8.314 J/molK)

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- T = temperature (Kelvin)
- Ea is a constant that can be determined without knowing the
probability factor by performing two experiments at different
temperatures while maintaining the same reactant concentrations
rateT2/rateT1 = k2/k1 = Ae-Ea/RT2/Ae-Ea/RT1
ln(rateT2/rateT1) = ln(k2/k1) = Ea/R(1/T1 – 1/T2)
- activation energies are usually expressed in kJ/mol
lnk = -Ea/R(1/T) + lnA
- Ea can be determined experimentally by measuring a reaction rate at
different temperatures
- then plot lnk versus 1/T, making a straight line with a slope of
Ea/R and y-intercept of lnA
- catalyst is a species that increases the rate of reaction but is not
consumed in the reaction
- provides an alternate pathway with a lower Ea, increasing k
- it has no effect on the net enthalpy change
- it does not affect the equilibrium constant but allows a system to
attain equilibrium faster
- rate enhancement factor is ratio of k values for the catalyzed and
uncatalyzed reaction
- to determine the magnitude of the Ea reduction (∆Ea):
ln(ratecat/rateuncat) = ln(kcat/kuncat) = Ea(uncat) – Ea(cat)/RT = ∆Ea/RT
- reactions occur in multiple steps
- reaction mechanisms describe the sequence of steps that occur
- each step is an elementary step, which cannot be broken down
further
- molecularity refers to how many species react together in an
elementary step
- if there is only one reactant species, it is a unimolecular process
A products; rate = k[A]
- for two reactant species, it is a bimolecular process
A + A products; rate = k[A]2
A + B products; rate = k[A][B]
- for two or more elementary steps, the steps can have different
molecularity
- ONLY in elementary steps are the coefficients of the reactants
become the exponents in the rate law
- overall rate of reaction is determined by rate of slowest or rate-
determining step (RDS)
- reaction of alkyl halides is a nucleophilic substitution
- electron-bearing nucleophile (Cl) replaces bromide on
electrophilic (electron-deficient) carbon atom
- if reaction occurs in one step, the overall reaction equation is the only
elementary step
- reaction is bimolecular
- rate law is overall second-order
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