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

by OC24812

School

Western UniversityDepartment

ChemistryCourse Code

CHEM 1027A/BProfessor

Paul RagognaStudy Guide

FinalThis

**preview**shows pages 1-3. to view the full**19 pages of the document.**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-

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

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)

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

- 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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