Section E: kinetics Flashcards
what is the rate of reaction for a reaction aA —> bB ?
rate = - 1/a dA/dt = 1/b dB/dt
what is the relationship between the stoichiometry of the reaction and the order?
there is no connection between the two
what is k and what does is depend on?
k is the rate constant and it depends on temperature
zero order reaction
rate = - d[A]/dt = k
integrating, ∫d[A] = - k ∫dt
[A] - [A]0 = - kt
therefore [A] = [A]0 - kt
first order reaction
rate = - d[A]/dt = k[A] integrating, ∫1/[A] d[A] = - k ∫dt ln[A] - ln[A]0 = - kt therefore ln[A] = ln[A]0 - kt and [A] = [A]0 e^-kt
second order reaction
rate = - 1/2 d[A]/dt = k[A]^2
integrating, ∫1/[A]^2 d[A] = - 2k ∫dt
- 1/[A] + 1/[A]0 = -2kt
therefore 1/[A] = 1/[A]0 + 2kt
how would you use graphs to determine the order of reaction?
[A] versus t linear? zero order ln[A] versus t linear? first order 1/[A] versus t linear? second order if not, more complex system
what is t1/2?
t1/2 is the half life = the time required for the concentration to drop to half its original value
how can t1/2 be calculated?
t1/2 = ln2 / k
what is the equation of radioactive decay?
N = N0 e^-kt
therefore N = N0 e^-tln2/t1/2
how can you measure the rate of reaction?
- start the reaction t=0
- measure a property as a function of time
- convert the measurement into concentration
- analyse the data
which methods can be used to measure the rate of reaction?
- spectrophotometric methods
- NMR
- polarimetry
- conductivity
- electrochemical/pH detection
- changes in pressure
how can spectrophotometric methods be used to measure the rate of reaction?
- UV/vis or IR absorbance ∝ [concentration]
- fluorescence
- stopped flow method (fast reaction)
- flash photolysis (very fast reaction)
how can NMR be used to measure the rate of reaction?
NMR integration ∝ [concentration]
how can polarimetry be used to measure the rate of reaction?
- measure changes in optical rotation for chiral molecules
- circular dichroism
how can conductivity be used to measure the rate of reaction?
changes in the number of ions (concentration) result in changes in conductivity
explain the initial rates/differential method
A + B —> products
rate = [A]^a [B]^b
- isolate variation in [A]
- let [B]»_space; [A] so that [B] is effectively constant (pseudo-order conditions)
- run the reaction at several different [A]0
- determine the initial rate for each curve by drawing tangents
- the ratio of any two rates is equal to the ratio of initial concentrations to the power a:
rate1/rate2 = ( [A]01/[A]02 )^a
- in general, rate = k(obs) [A]^a
- taking logs, log(rate) = log(k(obs)) + a log( [A] )
- this will produce a straight line graph with a slope equal to the order of the reaction
what is k(obs)?
- the observed rate constant
- the real rate constant must be determined properly once the order is known
what is an elementary reaction?
a reaction at the molecular level eg. a collision between two molecules or bond breaking within a molecule
what types of elementary reactions are there?
unimolecular = a single species undergoes a change bimolecular = two species come together (homo/heteronuclear)
what is the rate-determining step?
if a reaction proceeds by a number of steps, the rate constant of the slowest step governs the rate of reaction
why must we consider elementary steps?
most reactions require several steps or events for the reaction to go to completion, progressing via intermediates
explain the steady state approximation
- if A —> B —> C , we have rates r1 and r2
- if r1 B is rate determining
- [B] remains constant and low
- we can approximate d[B]/dt = 0
what is the Arrhenius equation?
k = Ae^-Ea/RT
what does the Arrhenius equation demonstrate?
that the rate constant is dependent on temperature
what is the Boltzmann distribution?
kinetic energy is evenly distributed among molecules of a sample
what is represented by e^-Ea/RT in the Arrhenius equation?
the fraction of molecules at a temperature T with energy greater than Ea
what is represented by A in the Arrhenius equation?
the total number of collision per second
describe some properties of proteases
- group specificity - will hydrolyse only peptide bonds in a protein
- stereochemical specificity - will only hydrolyse peptides made from L-amino acids
- often associated with additional molecules eg. coenzymes, prosthetic groups, etc.
- often require metal ions
who proposed the lock and key model of enzymes?
Daniel Koschland
what is the Michaelis-Menten equation?
V = Vmax [S] / (Km + [S] )
define ‘Km’
- the substrate concentration required to achieve half-maximum velocity (Vmax)
- the enzyme is half-saturated
- a measure of the enzyme’s substrate affinity
what is demonstrated by a small Km?
the enzyme has a high affinity for the substrate
what is Vmax?
- the maximal velocity
- enzyme is fully saturated
what is the effect on the M-M equation when [S] is very large?
it cancels to V = Vmax
what is the effect on the M-M equation when [S] is very small?
it cancels to V = Vmax [S] / Km
how is Kcat calculated?
Kcat = Vmax / [E]0
what is the Kcat?
the turnover number ie. the number of substrate molecules processed per second by one mole of enzyme
how is the catalytic efficiency calculated?
catalytic efficiency = Kcat / Km
what is the equation of a Lineweaver-Burk plot and how is it plotted?
1 / [V] = Km/Vmax (1 / [S] )
plot 1/[V] against 1/[S]
what is indicated by the y-intercept of a L-B plot?
y-intercept = 1 / Vmax
what is indicated by the x-intercept of a L-B plot?
x-intercept = - 1 / Km
what is indicated by the gradient of a L-B plot?
gradient = Km / Vmax
describe competitive inhibition and its effects on Km and Vmax
- binds to the active site of the enzyme
- Vmax is unchanged
- Km is decreased since the enzyme cannot bind S if bound to an inhibitor
- Km is decreased because an increased concentration of substrate is required to reach Vmax
- gradient increases
describe non-competitive inhibition and its effects on Km and Vmax
- CHEM1603: binds to a remote site on the enzyme, affecting the activity of the enzyme but not its ability to bind substrate
- BIOC1009: binds to both the free enzyme and to the enzyme-substrate complex
- Vmax is decreased
- Km is unchanged
- gradient increases
describe uncompetitive inhibition and its effects on Km and Vmax
- binds to the enzyme-substrate complex
- Vmax is decreased
- Km is decreased
- gradient is unchanged
