E - Kinetics

Question 1

What is the rate of a reaction?

Answer 1

The rate at which reagents are used up and products are formed.

Question 2

What is the general rate of reaction for

aA + bB → cC + dD?

Answer 2

rate = -1/a d[A]/dt

= -1/b d[B]/dt

= -1c d[C]/dt

= -1/d d[D]/dt

Question 3

What is the general rate law?

Answer 3

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

Question 4

What is a zero-order reaction, what is its rate equation and its integrated rate equation?

Answer 4

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

Question 5

What is the rate of reaction for a zero order reaction?

Answer 5

The rate of reaction remains constant with time.

The concentration of the reactants decreases linearly with time.

Question 6

What is a first-order reaction, and what is its rate equation and integrated rate equation?

Answer 6

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

Question 7

What is half-life, and what is its equation?

Answer 7

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) = - kt_1/2

t_1/2 = ln2/k

Question 8

What is radioactivity?

Answer 8

Radioactivity is the spontaneous transformation of one nuclide into another.

It is a random process that occurs with a certain probability.

Question 9

What is the activity of a radioactive substance, and what is its equation?

Answer 9

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/t_1/2​

Question 10

What is a second order reaction, and what is its rate equation and integrated rate equation?

Answer 10

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.

Question 11

How can rates of reactions be measured?

Answer 11

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

Question 12

What are the different methods of measuring the rate of a reaction?

Answer 12

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

Question 13

How do you determine the order of a reaction using the integration method?

Answer 13

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

Question 14

How do you determine the rate of a reaction using the initial rates (differential) method?

Answer 14

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

Question 15

What is an elementary step, and what are the two different kinds?

Answer 15

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

Question 16

What is the rate law for a unimolecular step?

Answer 16

A₂ → 2A

Rate = k[A₂]

Question 17

What is the rate law for a bimolecular step?

Answer 17

Homonuclear:

2A → A₂

Rate = k[A]²

Heteronuclear:

A + B → AB

Rate = k[A][B]

Question 18

What is the rate-determining step?

Answer 18

If a reaction proceeds by a series of steps then the rate constant of the slowest step determines the rate of the reaction.

Question 19

What is the steady state approximation?

Answer 19

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.

Question 20

What is the Arrhenius equation?

Answer 20

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

Question 21

What is a catalyst and how do they work?

Answer 21

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.

Question 22

What are the 3 different kinds of catalysts?

Answer 22

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

Question 23

What are enzymes and what are their properties?

Answer 23

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)

Question 24

What is K_M, the Michaelis constant?

Answer 24

K_M 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 K_M, the stronger the binding.

Question 25

What is k_cat?

Answer 25

k_cat is the turnover number; it is how many substrate molecules can be processed per second by one mole of catalyst.

k_cat gives the efficiency of the catalyst.

k_cat = V_max / [E]₀

Question 26

What is the order of reaction with respect to substrate when [S] is very large?

Answer 26

Zeroth order.

If [S] is very large then K_M + [S] ≈ [S], so the equation:

V = (k₂[E]₀[S])/(K_M + [S])

becomes:

V = k₂[E]₀

This would be first order overall​.

Question 27

What is the order of reaction with respect to substrate with [S] is very small?

Answer 27

First order.

If [S] is very small then K_M + [S] ≈ K_M, so the equation:

V = (k₂[E]₀[S])/(K_M + [S])

becomes:

V = (kcat/K_M)[E]₀[S]

because k_cat = k₂

This would be second order overall.

Question 28

On the Lineweaver-Burke plot, what is plotted on each axis, and what are the gradient and the intercepts?

Answer 28

x-axis → 1/[S]

y-axis → 1/V

gradient → K_M/V_max

y-intercept → 1/V_max

x-intercept → -1/K_M​

Question 29

How can different inhibitors affect K_M and V_max ?

Answer 29

Competitive → binds reversibly to the active site. V_max is unchanged but K_M is reduced.

Non-competitive → binds reversibly to a remote site on the enzyme. V_max is reduced but K_M is unchanged.

Irreversible → binds to the active site and shuts down the activity, reducing [E] and [E]₀ .