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Year 2 - Chem > Rate Processes > Flashcards

Rate Processes Flashcards

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1
Q

What is the Arrhenius equation?

A

kr = A exp(-Ea/RT)

Determined by gradient of plot of lnkr against 1/T

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2
Q

What is the assumption of Arrhenius equation?

A

A is independent of T

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3
Q

What is simple collision theory (SCT) based on?

A

Kinetics of bimolecular gas-phase reactions

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4
Q

What are the assumptions of SCT?

A

Frequent collisions between reactants
Fraction of collisions have E >= Ea
Steric factor

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5
Q

What is the pre-exponential factor in SCT?

A

A = N2 σ crel

where
σ = πd2, collision cross section
crel = Sqrt[8kT/πμ], mean rel speed of reactants

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6
Q

What is d in SCT calculations?

A

Mean molec diameter
d = 1/2(da + db)

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7
Q

What is the collision density in SCT?

A

p(r) = NA2 σ
crel [A][B]

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8
Q

How does A in SCT compare to experimental values?

A

Experimental A is sig larger than calculated by SCT

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9
Q

What is the steric factor in SCT?

A

Correction for exp values
P = Aexp / Acalc
Fudge factor

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10
Q

What is the dividing surface in a PE map?

A

Group of tipping points from one compound to another
TS on the surface

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11
Q

What is the thermal rate coefficient?

A

kr -> rate at thermal eqm, specified T

Includes rot, vib, and trans

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12
Q

What is the transition-state theory (TST) overview?

A

A + B <-> C‡ -> P

Assumes pre-equilibrium, fixed E, all reactive states accessible, motion classical and separable from orthoganol reaction coord

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13
Q

What is the Eyring equation?

A

kr = NA κ(kT/h) (qC‡~,0/V) / [ (qA0/V)(qB0/V)] exp(-ΔE0‡)

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14
Q

What is q and how does ~,0 effect them?

A

q is molecular partition function
~ means vib modes for motion through TS removed
0 means using energies from ground state (T=0)

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15
Q

What is κ, kappa, in Eyring eqn?

A

Transmission coefficient
Prob an activated complex will lead to product

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16
Q

What is the energy term in the Eyring equation?

A

ΔE0‡ = Ea + ZPE(C‡) - ZPE(Reactants)

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17
Q

How would you derive the Eyring equation?

A

d[P]/dt = κv[C‡]
where kappa is trans coefficient and v is freq of low vib mode for motion over saddle point

use K‡ = (pθ/RT) [C‡]/[A][B]
as assume perfect gas, then use result from stat mech and q of C‡ relation to ZPE to give values

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18
Q

What is qC‡0?

A

qC‡0 = qC‡~,0 qC^,‡0

As a harmonic oscillator, qC^,‡0 = 1 - exp(-hv/kT) ~ kT/hv
This is as hv &laquo_space;kT

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19
Q

What does q of a species consist of?

A

qtotal = qtrans x qrot x qvib x qelec

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20
Q

What is the equation for qtrans in terms of T?

A

qtrans/V = (2πmjkT/h2)3/2

For relationship, q/V α T3/2

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21
Q

What is the equation for qrot in terms of T and B?

A

qrot ~ kT/B = 8π2kTμd2/h2

this is because B = hbar2/2I and I = μd2

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22
Q

How can you estimate A in TST?

A

Find approx values of q as average mps per degree of freedom
Then put into kr

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23
Q

What is the approx value for qtrans?

A

qtrans ~ qT3

Due to 3x degrees of freedom when moving in 3D

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24
Q

What is the approx value for qrot?

A

qrot ~ qRn

Where n=2 for linear & n=3 for non-linear

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25
Q

What is the approx value for qvib?

A

qvib = qvn
n = No of vib modes
3N-5 for linear, 3N-6 is for non-linear

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26
Q

What occurs to qvib if remove vib mode at TS?

A

qvib = qvn

qvib~ = qvn-1

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27
Q

How can you estimate A in SCT?

A

SCT is equal to linear TS in TST

qA0 = qB0 = qT3
qAB‡0 = qT3 x qR2 x qV

Simplifies to qR2 / qT3
Then insert into eyring

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28
Q

Estimate A for a non-linear TS in TST
AB + CD -> ABCD‡ -> Prod

A

qAB0 = qCD0 = qT3 x qR2 x qV
qABCD‡0,~ = qT3 x qR3 x qV5

Simplifies to qV3 / [qT3 x qR]

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29
Q

What is the steric factor in terms of q for a diatomic TS?

A

ATST α qR2 / qT3

ASCT α qV3 / [qT3 qR]

P = (qV/qR)3

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30
Q

What are some typical values of qR and qV?

A

qR = 10
qV = 1

No of accessible states at T

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31
Q

What is the temp dependence of qV, qT, qR?

A

Common assumption

qV = 1
qT α Sqrt(T)
qR α Sqrt(T)

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32
Q

What is the T dependence of kr in TST?

A

kr α T-1 exp[-ΔE0‡/RT]

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33
Q

How does Ea relate to ΔE0‡ in TST?

A

Ea = ΔE0‡ + nRT

Mostly ΔE0‡&raquo_space;> RT so Ea has little T-dependence

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34
Q

When do isotopic efffects dominate?

A

Low masses
Such as H/D as largest % difference in mass

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35
Q

How do rates compare when H/D?
(in terms of ln)

A

ln[krH/krH] = ln[AH/AD] - [ΔE0,H‡ - ΔE0,D‡]/RT

2nd term dominates
ln() α 1/T

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36
Q

How does activation energy relate comparing H/D?

A

ΔE0,H‡ - ΔE0,D‡ = ZPE(D) - ZPE(H)

Assumes TS has same E, assume mH/D much smaller than other atom so μHB/D = mH/D

ΔE0,H‡ - ΔE0,D‡ = 0.5NAhbar x Sqrt[kf/mH] x (1/Sqrt2 - 1)

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37
Q

What is the comparison in rates between H and D?
(absolute values)

A

krH/krD = 8

For typical diatomics @ 298K
H transfer is faster

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38
Q

How does A change when different isotope?

A

Mass change effects:
qtrans α m3/2
qrot α I

Means A larger when lighter
AH/AD = 2.8

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39
Q

Why do curved Arrhenius plots occur?

A

3 ways which causes this:
* T-dependence of A
* kr depends on reactant quantum states
* Quantum mech tunneling at low T

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40
Q

How does kr depend on the quantum state of a reactant?

A

If the reactant is in a higher energy state then the reaction is faster

e.g. v=1 instead of v=0, then the rate is 100x faster

41
Q

What is the problem of TST?

A

Structure & vib frequency of TS may not be known so need to use a simpler equation

42
Q

How can you simplify TST?

A

Use ideal gas, Vmθ = RT/Pθ
so kr = κ(kT/h)(RT/Pθ)K~‡

Where K~‡ is partial pressure eqm const
Then relate to ΔG‡

kr = κ(kT/h)(RT/Pθ) exp(ΔS‡/R) exp(-ΔH‡/RT)

And as Ea = RT2 x dlnkr/dT, Ea = ΔH‡ + 2RT

kr = κ(kT/h)(RT/Pθ)e2 exp(ΔS‡/R) exp(-Ea/RT)

43
Q

What does the simplification of TST change dependence of A?

A

A is therefore entropy-based difference between reactants & TS

Most important is difference in no of vib modes
When greatest loss of rot energy (Δn most -ve) then smaller A

44
Q

What is the difference in vib modes (Δn) for different reactions?

A

A = atom, D = diatomic, P = Polyatomic
A + A -> TS, Δn=2
A + D -> non-linear TS, Δn=1
A + D -> linear TS, Δn=0
D + D -> non-linear TS, Δn=-1
D + D -> linear TS, Δn = -2
non-linear P x2 -> non-linear TS, Δn=-3

45
Q

How do reactions in both solution and gas occur?

A

Similar rates in both phases
Little solvent dependence

46
Q

How does separation of molecules, mean free path and more, change in gas and solution?

A

Gas - rare collisions with rel free motion, low density

Solution - frequent solvent-solute collisions with rare solute-solute encounters

47
Q

What is the cage effect for gas and solution?

A

Gas - collisions between molecules occur singly

Solutions - collisions occur in bunches with rel long intervals between them

48
Q

What are scavenging reactions evidence for?

A

R-N=N-R -> {R* R} -> RR* -> R-R

Without scavenger then recombines to form R-R
Low conc competition between scavenging and bulk recomb of free radicals

49
Q

What is diffusion or activation control?

A

Diffusion -> RDS is formation of encounter pair

Activation -> RDS is reaction pair, overall will depend on KAB (eqm const for encounter formation)

50
Q

What is flux?

A

#of moles passing through a surface area of 1m2 per second

51
Q

What is the rate in a diffusion controlled reaction dependent on?

A

Rate = total flux of B molecules diffusing towards & colliding with A molecules

[B]r = (1-R*/R) [B]
where encounter distance, R* = RA + RB
and bulk conc is [B]

52
Q

What is Fick’s 1st law for diffusion controlled reactions?

A

Jr = DB(d[B]r/dr) = DB(R*/r2)[B]

where Jr = flux of B down a conc gradient
DB = diffusion coefficient

53
Q

What is the reaction rate under Fick’s 1st law for 1x static A?

A

Rate = 4πR*2 Jr=R* = (4πR*2)(DB[B]/R*) = 4πR*[B]

54
Q

What is the reaction rate under Fick’s 1st law for A and B?

A

Rate = 4πDR* [A][B]= kd [A][B]

where kd = 4πDR* NA

55
Q

What is the Stokes-Einstein equation?

A

DA = kT/6πηRA

Where viscocity, η = η0 exp(Ea/RT)

55
Q

What is the Stokes-Einstein equation?

A

DA = kT/6πηRA

Where viscocity, η = η0 exp(Ea/RT)

so kd α η-1 α exp(-Ea/RT)

56
Q

What is the Stokes-Einstein equation when they are ions?

A

Coulomb interaction adds drift term

kd = 4πDReff NA

where Reff= Rc/[exp(Rc/R*)-1]
Rc = zazbe2 / 4πε0εkT

57
Q

What is the Onsanger distance?

A

In stokes-einstein equation and diffusion control

Rc, separation @ which Coulomb interaction = kT

58
Q

What is the rates of steps in activation controlled reactions?

A

A+B <-> {AB} -> P

ka is {AB} ->, and kd is forwards of eqm and kd’ is backwards reaction
ka &laquo_space;kd’ so kr=ka(kd/kd’) KAB

59
Q

What is influence of solvent perimittivity on ionic reactions in activation-controlled reactions?

A

Add coulomb interaction to ΔG

lnkr = lnkr0 - (1/RT)(zazbe2NA/4πεε0R*)

where lnkr0 is rate without ionic interaction

zazb > 0 then kr<kr,0

Gives lnkr vs 1/ε is linear

60
Q

How does rate change when ε changes under activation controlled reactions?

A

As ε decreases, shielding of ions by solvents decreases
Means less stable encounter complex and a slower reaction

61
Q

How does ionic effects change rate in activation controlled reactions?

A

Ionic can stabilise or destabilise the TS which effects the kr

62
Q

What is the influence of pressure on activation controlled reactions?

A

Use dG = Vdp - SdT

(dlnkr/dp)T = (-1/RT)(dΔG‡/dp)T = -ΔV‡/RT

Where ΔV‡ is molar vol of reactants and TS

63
Q

What occurs when ΔV‡ is independent of T in activation controlled reactions?

A

(dlnkr/dp)T = -ΔV‡/RT

lnkr = lnkrθ - (ΔV‡/RT)(p-pθ)

where krθ is kr at p=pθ

For bimol reactions -> ΔV‡ dominated by ΔVm of reactants & encounter pair
For ionic reactions -> dominated by ΔV occupied solvent, called electrostriction

If TS more charged than reactants, solvent around TS tighter packed & ΔV‡ -ve

64
Q

How can you use Ea for kr definition?

A

Ea = ΔH‡ + RT

kr = κNA(kT/h) exp[ΔS‡/R] exp[-Ea/RT]

65
Q

How does ΔS‡ depend on zazb?

A

zazb > 0 then ΔS‡ < 0, higher TS charge so solvent more ordered

zazb < 0, then ΔS‡ > 0

66
Q

What is ionic strength effects in an activation controlled reaction?

A

K = aAB/aAaB = [{AB}]/[A][B] * (γAB/γAγB) = KAB (γAB/γAγB)

where
aJ = activity of species J
γJ = activity of coefficient of J

67
Q

What is the Debye Huckle limiting law for activation controlled reactions?

A

log γJ = -Az2J Sqrt[I]

Where I = 0.5 ΣJ (bJ/bθ)z2J
Where bJ = molarity

68
Q

How do you derive the Debye-Huckle limiting law?

A

kr = kaKAB = ka K (γAγB/γAB) = kr0 (γAγB/γAB)

logkr = logkr0+ logγA + logγB - γAB = logkr0 - ASqrt[I](z2A + z2B - z2AB

simplifies to
logkr = logkr0 + 2AzAzBSqrt[I]

69
Q

What is an unforseen factor in electron transfer (ET) reactions?

A

No bond breaking in condensed phases but still has an Ea

70
Q

What causes Ea in electron transfer (ET) reactions?

A

Effect similar to Franck-Condon factor

e- transfer faster than change in bond length or orientation change of solvent

71
Q

What is the Franck-Condon factor?

A

Absorption of light nearly instantaneous
No time for change in position of nuclei

72
Q

What is an assumption in Marcus theory?

A

All occurs in aqueous
G is in 1D, and treats it as harmonic

73
Q

How does ET occur in Marcus theory?

A

Where () is in one solvent sphere, [] is another and {} is a third

(2+) + {3+}<-> [(2+) + {3+}] <-> [2+ 3+] <-> [3+ 2+] <->{3+} + (2+)

74
Q

What is the process of ET in Marcus theory?

A

D + A -> D+ + A-

Before: solvent reorganisation & bond reorgansiation so reactants and products have same energy

ET: Tunelling in rigid nuclear framework then relaxation

75
Q

What is the rate of tunnelling dependent on in Marcus theory?

A

Depends on overlap of donor & acceptor elec wavefn decreases wrt r
ket α exp(-βr)

r = edge-to-edge separation of D & A

76
Q

What is the Δ‡G in ET according to Marcus theory?

A

When identical PE curves and ΔGF(D+A) = ΔGF(D+ + A-)
Then

Δ‡G = ( ΔrGθ +λ)2 / 4λ
where λ = reorganisation energy

77
Q

What is λ in Marcus theory?

A

Reorganisation energy
Gibbs energy to distort eqm nuclear framework of prods to that of reactants without electron transfer

78
Q

What is the reaction rate in Marcus theory?

A

kr α exp[-βr]exp[-Δ‡G/RT]

plot of lnkr vs ΔrG gives normal on left of λ, and inverted on RHS

79
Q

What is the normal Marcus reigon?

A

-ΔrGθ < λ

More -ve ΔrGθ is the driving force, so rate increases

80
Q

What occurs when -ΔrGθ = λ in Marcus theory?

A

Activation-less ET
ΔrGθ = 0 so kr is at max

Little change in bond length or molec geometry

81
Q

What is the inverted Marcus reigon?

A

ΔrGθ > λ
More -ve ΔrGθ so larger driving force
However, k decreases

82
Q

What is potential, φ?

A

φ = potential @ point is work done in moving unit +ve charge from infinity to a point
Units of V

83
Q

What is the potential difference?

A

E = φ2 - φ1
Made by charge separation
Measure by estabilishing eqm when charged species exchanged across a surface

84
Q

What is current?

A

Rate of flow of charge
j = dQ/dT

85
Q

What is G at an electrode?

A

When charge ze & subject to φ

G = G(0) + zFφ
Where F is faraday const

86
Q

What is the faraday constant?

A

Charge on mole of e-

87
Q

How does rate of an electrode reaction change when the potential, φ, changes?

A

As φ increases, the reactant is destabilised
But destab TS by smaller amount so reaction occurs faster

88
Q

What is the Butler-Volmer eqn for current density (j)?

A

j = j0( [Red]0/[Red]∞) exp[βFη/RT] - j0( [Ox]0/[Ox]∞) exp[-αFη/RT]

Where:
[]0 is conc @ electrode surface
[]∞ is conc in bulk
η is activation overpotential

89
Q

What is η in the Butler-Volmer eqn?

A

Activation overpotential
η = E - E0

90
Q

What are α&β in the Butler-Volmer eqn?

A

β is transfer coefficient
α = 1-β

if β~1 then TS resembles reactants
if β~0 then TS resembels products

91
Q

Derive the Butler-Volmer eqn

A

for reaction in aq: Oxn+ + e- <-> OxOx(n-1)+
Forward reaction is kred & backwards is kox
φm & φs for in metal and solutions respectively

Gr = Gr(0) + (n-1)Fφs - F(φm-φs)
Gp = Gp + (n-1)Fφs
G‡ = G‡(0) + (n-1)Fφs - βF(φM-φS)

gives
ΔG‡red = G‡ - Gr
ΔG‡oxn = G‡ - Gp

j = F d[e-]/dt = F(kox[Red]0 - kred[Ox]0]

Include overpotential to give Butler-Volmer
j = j0( [Red]0/[Red]∞) exp[βFη/RT] - j0( [Ox]0/[Ox]∞) exp[-αFη/RT]

92
Q

What is the exchange current density, j0?

A

j0 = Fk0 [Red]α∞ [Ox]β∞

where k0 is rate const for forward and backwards

93
Q

How does rate of red and oxn depend on overpotential, η?

A

When η large & +ve then v slow redn but fast oxn
exp(βFη/RT)~0 j~j0exp(βFη/RT) so
lnj = lnj0 + βFη/RT

When η large & -ve then v slow oxn but fast redn
exp(-αFη/RT)~0
j~ -j0exp(-αFη/RT)
ln-j = lnj0 - αFη/RT)

94
Q

How can you find j0 & E0?

A

Tafel plot of η vs ln|j|
Get α&β from gradients
j0 from extrapolated intercept of two lines
E0 is from

95
Q

How can you find j0 & E0?

A

Tafel plot of η vs ln|j|
Get α&β from gradients
j0 from extrapolated intercept of two lines
E0 is from η-axis intercept

96
Q

What is a cyclic voltammetry plot?

A

Time vs Measured current (function of potential)
X <-> Y + e-

More +ve potential gives oxn
More -ve potential gives redn

97
Q

How does potential change rate of oxn?

A

When low, kox small so rate of reaction governed by rate of e- transfer

When high, kox higher but electrolysis laready carried out depleted surface [X]
So k determined by rate of diffusion of X to electrode

Year 2 - Chem (23 decks)

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