Kinetics 1: Rate laws, theories concerning rates Flashcards
- How is rate defined?
- Example of unit?
- Express rate as a derivative
- Change in concentration per time
- eg dm-3 s-1
- dc/dt
Why is rate usually expressed as a derivative?
Rate often varies with time as well as just conc, so defining it over a very small time interval dt removes this variation.
ie on a graph of conc against time, rate becomes the gradient of a tangent at a given conc value
Define the rate in terms of A and B:
A –> B
r = -(1/VA)(d[A]/dt)
r = (1/VB)(d[B]/dt)
defining in this way means rate is consistent and always +ve. can also define rate in terms of the rate law, ie r = k[A]
H2 + Br2 –> 2HBr has rate law r = (Ka[H2][Br2]3/2)/([Br2] + Kb[HBr])
Which orders can’t be defined?
Overall order
Order wrt Br2
Rate constants often vary with temp, many according to the Arhenius equation.
- Give the eq
- Define the components, giving units
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
Range of typical values for Ea
10-200 kJ mol-1
Value of RT at room temp
~2.4 kJ mol-1
Derive the straight-line Arhenius equation rearrangement
K = Aexp(-Ea/RT)
lnK = ln(Aexp(-Ea/RT) = lnA - Ea/RT = -Ea/R x 1/T + lnA
How is Keq defined?
Rate constants of the forward reaction / that of the backward reaction
derives from the fact that, by definition of eq, Kforward x bla = Kbackward x bla
What is a potential energy surface? Where on the surface to stable molecules sit?
A plot of potential energy as a function of the positions of all atoms in a reaction system.
Stable molecules are in potential energy minima.
Multi-dimensional apart from simple molecules
The reaction pathway involving the smallest energy expenditure is favoured.
- What is this pathway called?
- What is the potential energy maximum on this pathway called?
- What fraction of molecules have at least this energy, ie the activation energy?
- Why can we assume all reactants react via the minimum energy route?
- The reaction coordinate (i.e. that 2D graph of energy against reaction progress)
- Transition state
- exp(-Ea/RT) according to Boltzmann distribution
- The fraction is an exponential function of energy, so increasing E by a small amount (as would be the caase in choosing a different pathway) would give a negligable fraction of molecules with the required energy
Define transition state.
The point of highest energy on the pathway from reactants to products, in which there are partially broken and partially formed bonds.
For a reaction with Ea = 50 kJ mol-1, what fraction of molecules have sufficient energy to attain the transition state?
Fraction = exp(-Ea/RT)
Recall RT = 2.4 kJ mol-1 at room temp
so fraction = exp(-50/2.4) ~ 1 in 109
Gas kinetic theory is based on Newtonian mechanics. What 4 assumptions does it make?
What do the assumptions mean for the distribution of particle energies and speeds in a sample?
Assumptions
- Reactions occur whenever molecules collide, since particles are spherical and orientation is irrelevant (biggest defect of this theory)
- Size of particles << distance between particles
- KE causes random movement of particles
- All collisions are elastic (energy conserved)
Implication
Energies and speeds of particles in a macroscopic sample are in a Boltmann/Maxwell distribution.
Gas kinetic theory
- Expression for mean speed, give unit
- Bimolecular collisions depend on the relative motion of the molecules. Expression for mean relative speed?
ĉ = √(8KBT/πm) in ms-1
KB is Boltzmann constant, m = particle mass in kg
ĉ = √(8KBT/πμ) in ms-1
Where reduced mass, μ = (mAmB/mA+mB)
μ in AMU, atomic mass units
Collision rate, ZAB, between molecules A and B, represented by spheres of radii rA and rB:
ZAB = CACBσĉrel
- Give the expression for σ and define it
- Given that units are all SI, derive units of ZAB
- Collision cross section, σ = π(rA + rB)2 (σ is the area around A for which B is close enough to react with it)
ZAB = CACBσĉrel = (CACB)(π(rA + rB)2)(√(8kBT/μ)
Radii in m, μ in kg, speeds in molecules m-3
So units = collisions m-3 s-1
Derive an expression for the 2nd order rate constant, assuming a bimolecular reaction: A + B –> C.
Get the first expression for r
Fraction of collisions with at least Ea = exp(-Ea/RT)
So #successful collisions per volume per time = ZABexp(-Ea/RT)
Each collision gives one product molecule, so #mol product per volume per time = LZABexp(-Ea/RT) where L = avo number
So r = (1/L)ZABexp(-Ea/RT)
= (1/L)(CACAσĉrel)
Get the 2nd expression for r
Assume 1st order in A and B, so r = k(CA x CB)/L here have divided by avo number so that concs are in moles per vol, so rate is in mol per vol per time
Combine expressions
(1/L)(CACAσĉrel) = k(CA x CB)/L
Rearrange –> k = Lσĉrelexp(-Ea/RT) = Lσ(√(8kBT/μ))exp(-Ea/RT) in m3 mol-1 s-1
bimolecular reaction: A + B –> C.
Compare the following expression for the 2nd order rate constant k to the Arhenius equation, in order to derive an expression for the A-factor.
k = Lσĉrelexp(-Ea/RT)
k = L(π(rA + rB)2)(√(8kBT/μ))exp(-Ea/RT)
Arhenius k = Aexp(-Ea/RT)
So A = L(π(rA + rB)2)(√(8kBT/μ))
this is why it’s defined as collision rate per unit reactant concentration
A = L(π(rA + rB)2)(√(8kBT/μ))
This equation predicts A to be temp-dependent. Why does this contribute negligably to the expression for r?
strong temp dependence of the exp factor overpowers that of A
A = L(π(rA + rB)2)(√(8kBT/μ))
This expression can be tested experimentally. Does collision theory generally underestimate or overestimate A, and why?
Overestimates it, because collision theory assumes all collisions with Ea give successful reaction, whereas in reality orientational effects mean the number of successful collisions is lower.
Define and give the eq for the steric factor.
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
