kinetics of complex reactions Flashcards
how are rate laws for elementary reactions written?
in differential form
in terms of rate of loss of reagents (-ve) or gain of products (+ve)
assumptions for sequential (multi-step) reactions
if one rate constant is much greater than another, the slowest step is the rate determining step
the reaction can be simplified to depending only on the step w the smallest k
(only for first order - 2nd order is also concentration dependent)
what is the pre-equilibrium hypothesis?
for mechanisms where the species involved in the RDS are in equilibrium w reagents
assumes species remain in equilibrium, ie. species –> products is slow enough to not disturb equilibrium and is therefore rate determining
often used for intermediates involving simple protonation/de-protonation, fast compared to making/breaking bonds
k(eq) for pre-equilibrium hypothesis
k(eq) = k(1) / k(-1) = [eq prod]/[eq reac]
what is the steady state assumption?
for sequential reactions A–>B–>C where process 2 much greater than process 1, conc intermediate B changes very little, assume constant
d[B]/dt(SS) = 0
greatly simplifies
in what cases might the steady state assumption be appropriate?
generally appropriate for reactive intermediates (high in energy) which are slow to form but consumed at once
NOT appropriate for species that accumulate / decay during the reaction
NOTE: rate laws derived from SSA only valid when reaction is at SS (not initial/completion)
describe saturation kinetics
for a fixed quantity of enzyme, the rate of the catalysed reaction first increases linearly then levels of to a maximum value as the amount of substrate increases
overall kinetic scheme of the Michaelis-Menten equation
E + S <=> ES –> E + P
how is the Michaelis-menten equation derived?
d[ES]/dt = 0 (SSA) (construct eqn from elementary steps)
sub [E]0 = [ES] + [E] to find expression for [ES]
expression for velocity of reaction
V = k(cat) [ES]
essentially rate of catalysed reaction
Michaelis-Menten equation
V = k(cat) [E]0 [S] / [S] + K(M)
Michelis constant, K(M) expression
K(M) = (k(cat) + k(-1)) / k(1)
in terms of rate constants from the elementary steps of the Michaelis-Menten equation
expression for max velocity from Michaelis-Menten eqn
V(max) = k(cat) [E]0
what does the graph of velocity vs substrate concentration look like? (for Michaelis-Menten saturation kinetics)
from 0, very steep initial increase (approximately linear), then slowing down to flatten out (“saturation”)
Michaelis-Menten eqn for LOW substrate concentrations
[S] «_space;K(M)
hence denominator of MM eqn approximates to K(M)
resulting in expression for V(low[S]) linear in terms of [S] and [E}0
corresponds to LINEAR region of saturation kinetics graph (rate vs [substrate])
Michaelis-Menten eqn for HIGH substrate concentrations
[S]»_space; K(M)
expression approximates to
V(max) = k(cat)[E]0
which is independent of [S] and hence flattening of the graph
virtually all enzyme is present as enzyme-substrate complex
K(M) physical interpretation and derivation
what does a large value of K(M) mean?
NOT a strong affinity between enzyme and substrate, as a large conc of substrate is needed to achieve half the maximum rate
what does a small value of K(M) imply?
strong affinity between enzyme and substrate, so very little substrate is needed to reach velocity V(max)/2
units of Michaelis constant
CONCENTRATION, mol/dm^-3
it is NOT an equilibrium constant
how to plot Michaelis-menten equation as a straight line
invert both sides + rearrange
plot 1/V against 1/[S] as a straight line
aka. Lineweaver-Burke plot, USED TO FIND K(M) and k(cat) for known [E]0
what is the apparent activation energy of a reaction?
form rate law from elementary reactions
assume each elementary rate constant obeys Arrhenius
sub into rate law –> overall “Arrhenius” law for the whole reaction
Apparent acivcaiton energy is a composite of the activation energies of the three steps
rate constants can be expressed by Arrhenius eqn
k(T) = A exp(-Ea/RT)
what is a chain reaction?
cyclic reactions, the output of one elementary reaction is the input of the next
what are chain carriers?
the species which carry forward the chain reaction
they are the INTERMEDIATES written in the elementary steps
(only a small number of chain carriers needed to produce many product molecules)
examples of chain reactions
common for many reactions involving reactive species such as free radicals
combustion
polymerisation
three steps in chain reactions
+ other kinds of steps
initiation
propagation
termination
inhibition step
chain branching step
define the initiation step in a chain reaction
the reaction which generates the chain carrier
usually by collision with some unspecified molecule, or by photodissociation (absorption of sufficiently energetic photons)
define termination step in chain reactions
processes which destroy chain carriers
usually involves a third body to carry away excess energy
define inhibition step in chain reaction
consumes product, leading to a reduction in the overall rate of reaction
does NOT destroy chain carriers
define chain branching step
one chain carrier reacts to give rise to 2+ chain carriers
can lead to ever increasing rate of reaction –> explosion
what can the form of a rate law tell us about the mechanism?
fractional power often indicative that radicals are involved
[product] in denomination means that the product inhibits the reaction (ie. goes slower w buildup of product)
method of approach for analysing chain reactions
construct elementary reactions
assume that reactive intermediates are AT STEADY STATE
construct eqns using rate of change of the species = 0
construct overall equation for rate of change of product
substitute previous eqns into this one to find expression in terms of reaction species only (not intermediates)
find differential expression for product in terms of reacting species
define chain length
the number of times a reaction occurs before termination
(the number of times the closed cycle of steps which produces products is repeated per carrier)
what is the chain length in terms of rates?
l = rate of overall reaction / rate of initiation
