E - Kinetics Flashcards
What is the rate of a reaction?
The rate at which reagents are used up and products are formed.
What is the general rate of reaction for
aA + bB → cC + dD?
rate = -1/a d[A]/dt
= -1/b d[B]/dt
= -1c d[C]/dt
= -1/d d[D]/dt
What is the general rate law?
Rate = k [A]m [B]n
where the partial orders are m and n
and the overall order is (m + n)
→ there is no connection between the stoichiometry of the reaction and the order
→ for some reactions, no order may be determined due to it being enzyme-catalysed
What is a zero-order reaction, what is its rate equation and its integrated rate equation?
A reaction where the rate does not depend on the concentration of the reactants
Rate = -d[A]/dt = k[A]0 = k
Integrated → [A] = [A]0 - kt
What is the rate of reaction for a zero order reaction?
The rate of reaction remains constant with time.
The concentration of the reactants decreases linearly with time.
What is a first-order reaction, and what is its rate equation and integrated rate equation?
The rate of reaction is proportional to the concentration of reagent.
Rate = -d[A]/dt = k[A] = kdt
[A] = [A]0e-kt
ln[A] = ln[A]0 - kt
What is half-life, and what is its equation?
The half-life of a substance is the time required for the concentration to drop to half its original value.
The half-life is independent of concentration.
ln(([A]0/2)/[A]0) = - kt1/2
t1/2 = ln2/k
What is radioactivity?
Radioactivity is the spontaneous transformation of one nuclide into another.
It is a random process that occurs with a certain probability.
What is the activity of a radioactive substance, and what is its equation?
Activity is the number of decay events per second (Bq)
Activity = rate = -dN/dt = kN
Activity therefore follows first-order kinetics:
ln(N/N0) = - kt
N = N0 x e-kt
where k (= λ) = ln2/t1/2
What is a second order reaction, and what is its rate equation and integrated rate equation?
The rate of reaction is proportional to the square of the concentration of reagent.
Rate = -d[A]/dt = k[A]2
1/[A] = 1/[A]0 + kt
In this case, the half-life is not constant and does depend on the concentration.
How can rates of reactions be measured?
Reaction rates cannot be measured directly, but then can be measured using a proxy.
1 → start reaction at time 0
2 → measure a property as a function of time
3 → convert measurement to concentraion
4 → analyse data
What are the different methods of measuring the rate of a reaction?
Spectrophotometry → UV-vis or IR ∝ concentration
→ fluorescence
→ fast reactions = stopped flow method
→ very fast = flash photolysis (measure rate of electron transfer)
NMR integration → ∝ concentration
Polarimetry → reaction of optically active materials will dive rise to changes in optical rotation
→ circular dichroism (difference in absorption of left- and right-handed light)
Conductivity → changes in the number of ions = changes in conductance of a solution
Electrochemical or pH detection
Pressure changes
How do you determine the order of a reaction using the integration method?
1 → Run reaction at several [A]0 but keep [B] constant
2 → plot [A] vs. t
linear plot? yes = zero-order reaction
no = 3 → plot ln[A] vs. t
linear plot? yes = first-order reaction
no = 4 → plot 1/[A] vs. t
linear plot? yes = second-order reaction
no = more complex system
How do you determine the rate of a reaction using the initial rates (differential) method?
1 → Keep [B[the same but let [B] >>> A so that [B] is effectively constant (pseudo-order conditions)
2 → Run the reaction at several different [A]0 and plot [A] vs time
3 → determine the initial rate for each curve by drawing a tangent at t = 0
What is an elementary step, and what are the two different kinds?
The underlying mechanism of a reaction can be broken down into a sequence of microscopic or elementary events that lead to a particular molecular outcome.
Elementary step → a reaction at the molecular level
Unimolecular reactions → a single species undergoes a change
eg. bond cleavage, isomerization of alkenes
Bimolecular reactions → two species come together
eg. bond formation
What is the rate law for a unimolecular step?
A2 → 2A
Rate = k[A2]
What is the rate law for a bimolecular step?
Homonuclear:
2A → A2
Rate = k[A]2
Heteronuclear:
A + B → AB
Rate = k[A][B]
What is the rate-determining step?
If a reaction proceeds by a series of steps then the rate constant of the slowest step determines the rate of the reaction.
What is the steady state approximation?
A → B → C
If R1 <<< R2 then A → B is rate-determining.
[B] will very low throughout because as soon as B is made in the first step, it will be used up in the second step.
So we can make the approximation the [B] will remain constant for most of the reaction.
What is the Arrhenius equation?
It shows how the rate constant depends on temperature:
k = Ae-Ea/RT
ln(k) = lnA - Ea/RT
where A = pre-exponential factor = number of collisions
If ln(k) is plotted against 1/T, the gradient = -Ea/RT and the intercept = lnA
What is a catalyst and how do they work?
A catalyst is a substance that takes part in a reaction and changes its rate but which can be recovered unchanged at the end of the reaction.
A catalyst provides the reaction with a separate mechanism which has a lower activation energy than the unassisted pathway.
What are the 3 different kinds of catalysts?
Homogenous → the catalyst is in the same phase as the reactants
Heterogenous → the catalyst is in a different phase to the reactants
Immobilised → a molecular catalyst is tethered to a polymeric or solid support
What are enzymes and what are their properties?
Enzymes are biological catalysts.
→ usually show extreme specificity, while some are more flexible and can show group specificity
→ some can show stereochemical specificity
→ they may be associated with additional molecules which are necessary for their action, such as coenzymes, prosthetic groups
→ many enzymes require metal ions
→ they operate by the lock and key model (or induced fit)
What is KM, the Michaelis constant?
KM is the equilibrium constant for the release of substrate, and so is the concentration at which 50% of the active sites are bound to substrate.
It is, therefore, a measure of how strongly the substrate binds to the enzyme.
The smaller the KM, the stronger the binding.
What is kcat?
kcat is the turnover number; it is how many substrate molecules can be processed per second by one mole of catalyst.
kcat gives the efficiency of the catalyst.
kcat = Vmax / [E]0
What is the order of reaction with respect to substrate when [S] is very large?
Zeroth order.
If [S] is very large then KM + [S] ≈ [S], so the equation:
V = (k2[E]0[S])/(KM + [S])
becomes:
V = k2[E]0
This would be first order overall.
What is the order of reaction with respect to substrate with [S] is very small?
First order.
If [S] is very small then KM + [S] ≈ KM, so the equation:
V = (k2[E]0[S])/(KM + [S])
becomes:
V = (kcat/KM)[E]0[S]
because kcat = k2
This would be second order overall.
On the Lineweaver-Burke plot, what is plotted on each axis, and what are the gradient and the intercepts?
x-axis → 1/[S]
y-axis → 1/V
gradient → KM/Vmax
y-intercept → 1/Vmax
x-intercept → -1/KM
How can different inhibitors affect KM and Vmax ?
Competitive → binds reversibly to the active site. Vmax is unchanged but KM is reduced.
Non-competitive → binds reversibly to a remote site on the enzyme. Vmax is reduced but KM is unchanged.
Irreversible → binds to the active site and shuts down the activity, reducing [E] and [E]0 .
