Kinetics 6: Main recall

Question 1

Rate constants often vary with temp, many according to the Arhenius equation.

• Give the eq
• Define the components, giving units

Answer 1

K_T = Aexp(-E_a/RT)

• K_T = rate constant, units vary
• A = A-factor / pre-exponential factor* same units & dimensions as K, since exp term is dimensionless
• E_a = act energy in kJ mol^-1
• R = gas constant, in kJ [temp unit]^-1 mol^-1 (so that overall, exp term is dimensionless)
• T = temp, K

* A is the collision rate per unit reactant concentration. A is also the rate constant at infinite temp, since 1/T = 0 when lnK = lnA. A is independent of or weakly dependent on temp

Question 2

Range of typical values for E_a

Answer 2

10-200 kJ mol^-1

Question 3

Value of RT at room temp

Answer 3

~2.4 kJ mol^-1

Question 4

What fraction of molecules have sufficient energy to attain the transition state?

Answer 4

Fraction = exp(-E_a/RT)

Recall RT = 2.4 kJ mol-1 at room temp

Question 5

Gas kinetic theory

• Expression for mean speed, give unit
• Bimolecular collisions depend on the relative motion of the molecules. Expression for mean relative speed?

Answer 5

ĉ = √(8K_BT/πm) in ms^-1

K_B is Boltzmann constant, m = particle mass in kg

ĉ = √(8K_BT/μ) in ms^-1

Where reduced mass, μ = (m_Am_B/m_A+m_B)

μ in AMU, atomic mass units

Question 6

Define and give the eq for the steric factor.

Answer 6

Steric factor p is the fraction of sufficiently energetic collisions which lead to reaction

p = A_experimental/A_{coll theory}

normally p <1, but p >1 when molecules interact over larger distances than predicted by gas kinetic theory

Question 7

Gas kinetic theory

• Expression for mean speed, give unit
• Bimolecular collisions depend on the relative motion of the molecules. Expression for mean relative speed?

Answer 7

ĉ = √(8K_BT/πm) in ms^-1

K_B is Boltzmann constant, m = particle mass in kg

ĉ = √(8K_BT/μ) in ms^-1

Where reduced mass, μ = (m_Am_B/m_A+m_B)

μ in AMU, atomic mass units

Question 8

1st order rate law

Answer 8

r = k_1st[A]

d[A]/dt = -k[A]

Question 9

integrated 1st order rate law in terms of reactant

Answer 9

[A]_t = [A]₀exp(-k_1stt)

Question 10

Produce and solve the rate law for the second order reaction A –> products.

Answer 10

rate law

d[A]/dt = -k_2nd[A]²

∫(from [A]_t to [A]₀) 1/[A] d[A] = k_2nd ∫(from t=t to t=0) dt

1/[A]_t = k_2ndt + 1/[A]₀

Question 11

Give the expression for the half-life for a first-order reaction.

Answer 11

t_1/2 = ln2/k_1st

Question 12

Give the expression for the half-life for a second order reaction.

Answer 12

t_1/2 = 1/(k_2nd[A]₀)

Question 13

Study the reaction scheme below. What conditions are required for the pre-equilibrium hypothesis to apply?

Answer 13

Rate of process 1 >> rate of process 2, such that rates of [1] and [-1] are equal (in equilibrium), and process [2] is rate-determining.

pre-eq hypothesis is often useful for intermediates involving protonation or deprotonation, since these processes are usually faster than breaking/making bonds to atoms heavier than hydrogen

Question 14

What conditions permit using the steady state approximation? Include a graph of concentration against time.

Answer 14

Applicable when, in a complex mechanism, a reactive intermediate reacts as soon as it’s formed, such that its concentration is assumed to be constant.

Only applicable when reaction is in steady state - not in the initial or final phases.

simplifies solving differential eqs since it removes the time dependence

Question 15

Write out the Michaelis-Menten scheme.

Answer 15

Question 16

Shown is the Michaelis-Menten scheme.

Write the expression for V_max and define it.

Answer 16

V_max = k_cat[E]₀

Maximum velocity which occurs when all enzyme is saturated, i.e. 0 order in [S].

Question 17

Shown is the Michaelis-Menten scheme.

• Give the expression for K_M
• What units does it have?
• define it

Answer 17

k_M = (k_-1 + k_cat)/k₁)

Units of conc

K_M is the substrate conc which gives ha;f-maximum velocity.

Question 18

Shown is the Michaelis-Menten scheme.

Write the Michaelis-Menten equation, i.e. the expression for the velocity, V (ie rate) of reaction.

Answer 18

V = (k_cat[E]₀[S]) / ([S] + (k_-1 + k_cat)/k₁)

= (k_cat[E]₀[S]) / ([S] + k_M)

where K_M is the michaelis constant

Question 19

What is a chain reaction?

Answer 19

A reaction comprised of non-linear elementary steps, which form chains in which the output of one step may be the input of an earlier step.

Question 20

What are the general stages of a chain reaction?

Answer 20

• Initiation generates chain carriers
• Propogation maintains chain carriers
• Inhibition reduces reaction rate by destroying product (but not chain carriers)
• Termination destroys chain carriers
• Chain branching (sometimes): one chain carrier reacts to give 2+ carriers (results in explosion, eg combustion)

Question 21

The thermal chain reaction H₂ + Br₂ –> 2HBr is well-characterised. Illustrate the stages of this reaction.

Answer 21

Initiation

Br₂ + M –> 2Br + M where M is a molecule

Or photodissociation: Br₂ + hv –> 2Br

Propogation

Br + H₂ –> HBr + H

H + Br₂ –> HBr + Br

Inhibition

HBr + H –> H₂ + Br

Termination

2Br + M –> Br₂ + M (M absorbs excess energy from new Br2 molecule, such that the Br2 doesn’t immediately fall apart)

Question 22

What is a chain carrier?

Answer 22

An intermediate formed during a chain reaction, which is an input into earlier reactions, and thus propogates the reaction.

Question 23

Define chain length. Give its expression.

Answer 23

The average number of times that the closed cycle of steps producing products is repeated per chain carrier.

chain length, l = (overall reaction rate)/(rate of initiation)