Kinetics Flashcards
rate of reaction (simple)
how much product forms after time,t
how much reactant consumed after time, t
extent of reaction
rate of reaction (more commonly written as)
the rate for a given reaction must be independent of the species monitored
the rate has to be a transferable number, not dependent on the system size (i.e. an intensive quantity)
nQ is an extensive quantity (depends upon the system size)
- divide nQ by volume
rate constants and reaction orders - definition
rate constants and reaction orders - experimentally
molecularity
elementary and overall reactions
if A+B → C+D
r = [A]^1[B]^1
but for an overall (multistep) reaction, we cannot make this assumption
analysis of kinetc data (initial rate method)
analysis of kinetic data (differential method)
analysis of kinetic data (integration method) - zeroth order
analysis of kinetic data (integration method) - first order
analysis of kinetic data (integration method) - second order
analysis of kinetic data (numerical integration)
COME BACK TO THIS - I DONT UNDERSTAND THIS
mechanisms - combining kinetic equations
consider three sets of two elementary reactions
combine the d[A]/dt terms from each expression = overall rate
mechanisms - concurrent reactions (competitors)
mechanisms - concurrent reactions (competitors) * integration between the limits of t and t=0 (hence [B]t and [B]0)
- integration step
mechanisms - concurrent reactions (competitors) deriving the branching ratio
Branching can be profoundly important as it dictates the effects of overall reactions
mechanisms - opposing reactions (equilibria)
Here it is evident that A is lost in reaction (1) but regenerated in reaction (-1)
mechanisms - opposing reactions (equilibria) at a point before equilibrium
mechanisms - opposing reactions (equilibria) at a point before equilibrium (continued)
mechanisms - consecutive reactions (intermediates)
mechanisms - consecutive reactions (intermediates) - assumptions
mechanisms - consecutive reactions (intermediates) - observations
-d[A]/dt ≠ +d[C]/dt
implies the existence of B
B maximises then decays
return to steady state
intermediates can be quantified through SSA
A has a straightforward first order decay
B is more complicated
return to steady state - we can get [C]t from mass balance
for k1≠ k2
return to steady state - we can get [C]t from mass balance
for k1≠ k2
(step-by-step calculation)
return to steady state - we can get [C]t from mass balance
for k1= k2 = k
return to steady state - we can get [C]t from mass balance
for k1= k2 = k
step-by-step calculation
if k1 = k2 - plot analytical solutions to [A]t, [B]t, [C]t
if k1 = 0.01k2 - plot analytical solutions to [A]t, [B]t, [C]t
time when [B] maximises and stays (approximately) constant
the induction time
the kinetic condictions under which we can apply SSA
we have a kinetic condition (k2»k1) and a temporal condition (need to be past t_max) in order to use SSA
in practice, both are met for reactive intermediates
applying SSA (general methodology)
- characterise kinetics
- conduct experiments
- summarise observed orders and rate constants - propose mechanisms
- break down overall reaction into sequence of elementary reactions involving intermediates, X - write required observation from mechanism
- what are we interested in (e.g. product formation) - use SSA for [intermediates]
- solve for X
applying SSA (part 1)
characterise kinetics:
~ reaction (monitored by formation of C) appears elementary at first
~ but slows down as products are produced
propose mechanism
~ 3 elementary reactions
write required observation from mechanism
~ d[C]/dt = k2[X][B]
X is the intermediate
~ use SSA for the intermediate X
applying SSA (part 2)
predict kinetics and compare
using SSA - consecutive reactions (intermediates)
a chain reaction
The reaction could continue until all A and B were consumed
But, competing reactions e.g. R1 + R2 → minor products gradually diminish the concentrations of the radicals
features of chain reactions
very large reactions rates are possible
The rate of a chain reaction builds up following initiation in contrast to non chain processes
A = products in diagram
Chain reactions give: high product yields/high reactant consumption for a small amount of initiation
- Also susceptible to inhibition or sensitisation with small concentrations of additives
Self-sustaining reactions (e.g. flames) or continuously
increasing reaction rates (e.g. explosions) may be observed
general mechanistic factors of chain reactions
linear chain reactions
reaction rates that build up to a steady value
examples include:
- pyrolysis of hydrocarbons
- hydrogen-halogen reactions
Bodenstein (1906): found that the rate increased (i.e. a chain process) but at longer timescales then slowed down
found experimentally that:
a proposed mechanism for linear chain reactions (H2 + Br2)
from the proposed mechanism for H2 + Br2 (part 1)
from the proposed mechanism for H2 + Br2 (part 2)
from the proposed mechanism for H2 + Br2 (part 3)
from the proposed mechanism for H2 + Br2 (part 4)
H2 + other halogens
H2 + Cl2 is really fast (explosive) as the H + Cl2 reaction is very exothermic
H2 + F2 is extremely fast (explosive) as the H + F2 reaction is extremely exothermic
- the step F + H2 produces electronically excited HF
- HF can go on to dissociate further F2 and augment the reaction rate = energy branching
H2 + I2 is slow as the H + I2 reaction is very inefficient (partly due to endothermicity)
- reaction is non – chain below T ≈ 800 K
Arrhenius equation
the effect of temperature on rate of reaction
potential energy surface of a typical reaction
energy depends on both the B-C and the A-B coordinates
- represented as a potential energy surface
energy profile of a typical reaction
contour diagram to visualise energy of a typical reaction
the transition state is a saddle point on the energy surface
theories of reaction kinetics
to predict a reaction rate theoretically, need to understand how often molecular encounters pass through a transition state
there are two theories to address this:
- simple collision theory
- transition state theory
Simple collision theory: predicts Arrhenius-like behaviour
steric factor
simple collision theory usually overestimates k
- Distribution of intramolecular energy is ignored
- Molecular orientation is not represented
the steric factor expresses this:
P provides some mechanistic info, but SCT is still limited
improved theories of reaction kinetics
represents a more realistic situation
Postulates a state of equilibrium between the reactants and the activated complex
- allows quantification of of the activated complex
transition state theory
derive values for K≠ and k2
K≠
- derived from the partition functions for the reactants and the activated complex
k2
- derived from the vibrational properties
of the bond that is breaking in X≠ (k2 is taken as a vibrational frequency)
TST improves prediction of experimental k’s as f(T)
however, we dont know the exact structure and bonding of X≠
- we need to make assumptions on its structure and energetics
- actual observation of X≠ is near impossible
unimolecular reactions (A = products)
Often show first order kinetics at high total concentrations (l) or pressures (g)
PARADOX: How does A get the energy to react (to surmount Ea)
For an initiated process, this is easy, e.g. laser photolysis
For for a thermal (non-initiated) process, A must acquire energy through collision
A + M → A* → products
But collision is an elementary second order kinetic process…
Lindemann for unimolecular reactions
Lindemann for unimolecular reactions - first order at high concentrations/pressures
Lindemann for unimolecular reactions - second order at low concentrations/pressures
Lindemann - determining elementary rate constants
Lindemann - determining elementary rate constants - fits at low pressures but breaks down at higher p
this suggests a role for energy transfer (the interaction with M)
improvements to Lindemann - Rice-Ramsperger-Kassel-Marcus (RRKM) theory
[A*] is estimated from the Boltzmann fraction of energies (as in SCT)
Ratio [A≠]/[A*] is obtained analogously to TST, assuming an equilibrium
K≠, is similarly assumed as the order of a vibrational frequency of A≠
k2(E) is then integrated over all values of E = rate of product formation
RRKM compared to standard Lindemann
the calculation of k≠ again depends on assumptions on the nature of A≠
polar ozone depletion
Polar stratospheric cloud particles act as surfaces for chlorine activation:
then in sunlight, Cl2 + hv = ozone loss
Polar ozone loss is a linear chain reaction
rate of ozone loss
rate of ozone loss, in terms of r
auto-acceleration of chain reactions after initiation
If supply of reactants can be controlled, a stationary reaction can be set up,
e.g. a bunsen burner/ gas cooker
If reactants are in excess (e.g. following a gas leak) or combustion is initiated in substances chosen to yield maximum energy in minimum time, these may act as explosives
thermal auto-acceleration
k increases with increasing T
If a reaction is exothermic (ΔH negative) and partially adiabatically confined
- Energy is released (but can’t all escape) - due to it being adiabatically confined
- T increases, k increases, rate increases
the rate of enthalpy release in thermal auto-acceleration
thermal explosions
we can calculate approximate limits for thermal explosions
For a gas at initial temperature T with surroundings at Ts
plot Q + and Q − as a function of T to find explosion limits
Plot for three different concentration (hence rate) regimes, CI, CII, CIII
for Clll, the system is explosive at all temperatures (Q+ > Q- at all T)
for Cl, at low T the system has a thermally accelerated rate but reaches a steady state at Tst
- this is where all the heat produced can be removed and the system stabilises
increasing the T of this system, system Cl eventually explodes at Tign
Cll shows a critical point at Tc, this is the lowest concentration for spontaneous thermal explosion (at all temperatures) - an explosion limit
branched chain reactions
if propagation step increases the number of chain carriers - it is branched
for a banched chain reaction, rate depends on the propagation vs termination step
hydrogen-oxygen: explosive
hydrogen-oxygen
2H2 + O2 = 2H2O
3b is far faster than 3a
3a is the rate determining step
hydrogen-oxygen ~ mechanism
mechanism must be consistent with observed behaviour
because of branching, radical concentrations may change (increase) rapidly - cannot apply SSA as there concentration does not come to a steady state
as radicals interconvert, the ratios of their concentrations are constant
this is the quasi-steady state approximation (QSSA)
allows us to consider a generalised free radical concentration [R]
applying QSSA
derivation of [R]QSSA
branching factor Φ
if Φ is negative:
[R]QSSA is small and constant - non explosive
if Φ is positive:
[R]QSSA grows exponentially with time - explosion
so Φ = 0 corresponds to the (explosion) limit
first limit
low pressures: low concentration of reagents and low concentration of third species, M
therefore, homogeneous reaction rate is low
- heterogeneous termination dominates
- H more effectively collides with walls than reagents/M
there is a fixed ratio of reagents (2:1 H2:O2)
limiting oxygen concentration corresponds to limiting the pressure
the pressure limit is proportional to exp(Ea/RT)
second limit
moderate pressures: heterogeneous termination is reduced (diffusion to vessel walls less efficient)
homogeneous termination is enhanced
(reaction 4 is termolecular and contains oxygen)
as you increases pressure, system goes from explosive to non-explosive, as Φ goes from positive to negative
third limit
high pressures:
HO2 is formed efficiently in reaction (4)
- high [M], high [O2]
another channel appears:
HO2 + H2 → H2O + OH
this adds a strong positive temperature dependence to the rate
implying explosion (from increased branching) is more likely as T increases
Hence, p (amount of total gas needed for explosion) falls as T increases
