Kinetics 6: Main recall

KT = Aexp(-Ea/RT) • KT = rate constant, units vary • A = A-factor / pre-exponential factor* same units & dimensions as K, since exp term is dimensionless • Ea = 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

10-200 kJ mol-1

~2.4 kJ mol-1

Fraction = exp(-Ea/RT) Recall RT = 2.4 kJ mol-1 at room temp

ĉ = √(8KBT/πm) in ms-1 KB is Boltzmann constant, m = particle mass in kg ĉ = √(8KBT/μ) in ms-1 Where reduced mass, μ = (mAmB/mA+mB) μ in AMU, atomic mass units

Steric factor p is the fraction of sufficiently energetic collisions which lead to reaction p = Aexperimental/Acoll theory normally p <1, but p >1 when molecules interact over larger distances than predicted by gas kinetic theory

ĉ = √(8KBT/πm) in ms-1 KB is Boltzmann constant, m = particle mass in kg ĉ = √(8KBT/μ) in ms-1 Where reduced mass, μ = (mAmB/mA+mB) μ in AMU, atomic mass units

r = k1st[A] d[A]/dt = -k[A]

[A]t = [A]0exp(-k1stt)

rate law d[A]/dt = -k2nd[A]2 ∫(from [A]t to [A]0) 1/[A] d[A] = k2nd ∫(from t=t to t=0) dt 1/[A]t = k2ndt + 1/[A]0

t1/2 = ln2/k1st

t1/2 = 1/(k2nd[A]0)

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

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

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

kM = (k-1 + kcat)/k1) Units of conc KM is the substrate conc which gives ha;f-maximum velocity.

V = (kcat[E]0[S]) / ([S] + (k-1 + kcat)/k1) = (kcat[E]0[S]) / ([S] + kM) where KM is the michaelis constant

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.

• 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)

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)

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

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)