kinetics + rate theories

Question 1

define rate of a reaction

Answer 1

change in conc over time
or rate = d[conc]/dt

+ve for formation (product)
-ve for loss (reactant)

Question 2

rate of reaction r for any species A

Answer 2

r = 1/v(A) * d[A]/dt

where v(A) = stoichiometric coefficient of species A in balanced eqn

Question 3

first order rate law

Answer 3

r = k(1st) [A]^1

Question 4

units of first order rate constant

Answer 4

time-1

k(1st) = r/[A} = conc time-1 / conc

Question 5

second order rate constant units

Answer 5

k(2nd) = conc-1 time-1

Question 6

how is the temperature related to the rate constant?

Answer 6

by the Arrhenius eqn

k(T) = A exp(-Ea/RT)

A: pre-exponential term
Ea: activation energy, kJmol-1

Question 7

units / dimensions of R (gas constant)

Answer 7

energy temp-1 time-1
usually kJ K-1 s-1

bc in Arrhenius Ea (kJ/mol) must have same dimensions as RT

Question 8

typical values of Ea

Answer 8

between 10 and 200 kJ mol-1

Question 9

unit of the pre-exponential factor A in Arrhenius

Answer 9

A must have the same dimensions as k bc exponential term is dimensionless

Question 10

Arrhenius in y=mx+c form

Answer 10

take logs of both sides:

ln(k(T)) = ln(A) - Ea/R * 1/T
intercept = lnA
slope = -Ea/T
on graph of ink vs 1/T

Question 11

how are rate constants related to the equilibrium constant?

Answer 11

Keq = k(forward) / k(reverse)

bc for A + B –> C + D
k(f) [A][B] = k(r) [C][D]

Question 12

what happens in a reaction? general theory behind chemical reactions

Answer 12

A and B far = independent
A and B approach + interact, HOMO/LUMO –> bonds break/form

fundamentally, reactions involve electronic rearrangements and orbital interactions

Question 13

what does a potential energy surface (PE or PES) show?

Answer 13

the energy (potential) as a function of the positions of ALL the atoms in the system

visualise as a surface

Question 14

where do stable molecules exist in the PES?

Answer 14

in wells / potential energy minima of the potential energy surface

Question 15

how is the most favourable reaction pathway chosen?

Answer 15

the path that requires the least expenditure of energy
E = energy difference between transition state and reactants

Question 16

define transition state

Answer 16

the point of highest energy on the reaction pathway
involves partially made and broken bonds

Question 17

what fraction of molecules have enough extra energy to overcome Ea?

Answer 17

the Bolzmann distribution:
exp(-Ea/RT)

Question 18

intermediate vs transition state

Answer 18

may be highly energetic compared to products and reactants, but it is still a molecule existing in a PE minimum, detectable, not unstable as a transition state is

Question 19

define reaction coordinate

Answer 19

the minimum energy pathway from reactants to products

Question 20

define reaction profile

Answer 20

a plot of the reaction coordinate (x axis) against potential energy

Question 21

typical value of activation energy

Answer 21

50 kJ/mol

Boltzmann distribution exp(-50/24) shows about 1 in 1 billion molecules have enough energy to reach TS

Question 22

describe simple gas kinetic theory

Answer 22

assumes particles are objects with size much less than the speed between them, which have kinetic energy

move RANDOMLY and collide ELASTICALLY (all energy conserved)ac

Question 23

according to gas kinetic theory, how are energies and speeds of particles distributed?

Answer 23

according to the Maxwell distribution: all speeds possible, but very low/high improbable

Question 24

eqn for mean speed of particles by Maxwell distribution

Answer 24

c = (8k(B)T/pi*m)^1/2

k(B) = Boltzmann constant
m is mass of particle, kg

Question 25

when considering molecular collusions by the gas kinetic theory, what must be known

Answer 25

c(rel): mean RELATIVE speed of two molecules A and B

c(rel) = (8k(B)T/pi*µ)^1/2
where µ is the reduced mass

Question 26

reduced mass µ is given by

Answer 26

µ = m(A)m(B) / m(A) + m(B)

Question 27

key shortcoming of the gas kinetic collision theory

Answer 27

it assumes that molecules are structureless spheres, BUT orientation matters a lot (eg. Sn2 requires rear attack)

Question 28

equation for collision rate Z for two molecules A with r(A) and B with r(B)

Answer 28

Z(AB) = c(A)c(B) pi*(r(A)+r(B))^2 c(rel)

conc (molecules / vol) * collision cross section * c(rel)

Question 29

units of Z (collision rate)

Answer 29

collisions per m^3 per second (makes sense intuitively, but can find from equation)

m-3 s-1

Question 30

what is collision cross section?

Answer 30

symbol sigma
an area pi*(r(A)+r(B))^2

Question 31

equation for the number of successful collisions per unit volume per unit time

Answer 31

Z(AB) * exp(-Ea/RT)

makes sense bc it’s the rate of collisions x the fraction of molecules with enough energy

NOTE: this is number of MOLECULES so number of moles obtained by dividing by avogadros

Question 32

expression for k(2nd) from collision rate Z

Answer 32

As r = 1/L * c(A)c(B) * sigma * c(rel) * exp(-Ea/RT)
and r = k(2nd) * (c(A)/L)*(c(B)/L)

k(2nd) = sigma * c(rel) * exp(-Ea/RT) * L

Question 33

how is the Arrhenius A-factor related to collision theory?

Answer 33

collision rate per unit concentration of A and B

comparing to expression for k(2nd) from collision rate shows A = sigma * c(rel) * L

Question 34

compare real and theoretical values of exponential factor A from collision theory

Answer 34

collision theory OVERESTIMATES A bc it is assumed that all collisions w sufficient energy lead to reaction, but in reality orientation is important

Question 35

what is the steric factor, p?

Answer 35

a value comparing experimental and predi ted A factors

p = A(exp) / A(collision theory)