kinetics + rate theories Flashcards
define rate of a reaction
change in conc over time
or rate = d[conc]/dt
+ve for formation (product)
-ve for loss (reactant)
rate of reaction r for any species A
r = 1/v(A) * d[A]/dt
where v(A) = stoichiometric coefficient of species A in balanced eqn
first order rate law
r = k(1st) [A]^1
units of first order rate constant
time-1
k(1st) = r/[A} = conc time-1 / conc
second order rate constant units
k(2nd) = conc-1 time-1
how is the temperature related to the rate constant?
by the Arrhenius eqn
k(T) = A exp(-Ea/RT)
A: pre-exponential term
Ea: activation energy, kJmol-1
units / dimensions of R (gas constant)
energy temp-1 time-1
usually kJ K-1 s-1
bc in Arrhenius Ea (kJ/mol) must have same dimensions as RT
typical values of Ea
between 10 and 200 kJ mol-1
unit of the pre-exponential factor A in Arrhenius
A must have the same dimensions as k bc exponential term is dimensionless
Arrhenius in y=mx+c form
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
how are rate constants related to the equilibrium constant?
Keq = k(forward) / k(reverse)
bc for A + B –> C + D
k(f) [A][B] = k(r) [C][D]
what happens in a reaction? general theory behind chemical reactions
A and B far = independent
A and B approach + interact, HOMO/LUMO –> bonds break/form
fundamentally, reactions involve electronic rearrangements and orbital interactions
what does a potential energy surface (PE or PES) show?
the energy (potential) as a function of the positions of ALL the atoms in the system
visualise as a surface
where do stable molecules exist in the PES?
in wells / potential energy minima of the potential energy surface
how is the most favourable reaction pathway chosen?
the path that requires the least expenditure of energy
E = energy difference between transition state and reactants
define transition state
the point of highest energy on the reaction pathway
involves partially made and broken bonds
what fraction of molecules have enough extra energy to overcome Ea?
the Bolzmann distribution:
exp(-Ea/RT)
intermediate vs transition state
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
define reaction coordinate
the minimum energy pathway from reactants to products
define reaction profile
a plot of the reaction coordinate (x axis) against potential energy
typical value of activation energy
50 kJ/mol
Boltzmann distribution exp(-50/24) shows about 1 in 1 billion molecules have enough energy to reach TS
describe simple gas kinetic theory
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
according to gas kinetic theory, how are energies and speeds of particles distributed?
according to the Maxwell distribution: all speeds possible, but very low/high improbable
eqn for mean speed of particles by Maxwell distribution
c = (8k(B)T/pi*m)^1/2
k(B) = Boltzmann constant
m is mass of particle, kg
when considering molecular collusions by the gas kinetic theory, what must be known
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
reduced mass µ is given by
µ = m(A)m(B) / m(A) + m(B)
key shortcoming of the gas kinetic collision theory
it assumes that molecules are structureless spheres, BUT orientation matters a lot (eg. Sn2 requires rear attack)
equation for collision rate Z for two molecules A with r(A) and B with r(B)
Z(AB) = c(A)c(B) pi*(r(A)+r(B))^2 c(rel)
conc (molecules / vol) * collision cross section * c(rel)
units of Z (collision rate)
collisions per m^3 per second (makes sense intuitively, but can find from equation)
m-3 s-1
what is collision cross section?
symbol sigma
an area pi*(r(A)+r(B))^2
equation for the number of successful collisions per unit volume per unit time
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
expression for k(2nd) from collision rate Z
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
how is the Arrhenius A-factor related to collision theory?
collision rate per unit concentration of A and B
comparing to expression for k(2nd) from collision rate shows A = sigma * c(rel) * L
compare real and theoretical values of exponential factor A from collision theory
collision theory OVERESTIMATES A bc it is assumed that all collisions w sufficient energy lead to reaction, but in reality orientation is important
what is the steric factor, p?
a value comparing experimental and predi ted A factors
p = A(exp) / A(collision theory)
