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Reaction Thermodynamics Review. D G rx – indicates direction of reaction given the current distribution of reactants and products. D G ˚ rx – indicates the free energy difference between reactants and products at their standard state concentrations).

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Reaction Thermodynamics Review

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Reaction thermodynamics review

Reaction Thermodynamics Review

DGrx – indicates direction of reaction given the current

distribution of reactants and products.

DG˚rx – indicates the free energy difference between reactants and products at their standard state concentrations).

The intrinsic‘favorability’ of a reaction.

Q – indicates the current distribution of reactants and

products. DG = DG˚ + RT ln Q

K – indicates the equilibrium distribution of reactants

and products. DG˚ = -RT ln K


Reaction thermodynamics review

Reaction Kinetics

r – The rate of the reaction – M s-1

k – The rate constant for the reaction – Indicates

the ‘intrinsic’ speed of a reaction.

Ea –The activation energy for a reaction – Indicates

the free energy difference between the reactants

and the transition state.

Rate law – Indicates the dependence of r on k and the

concentrations of reactants and any other

reagentthat influences the rate of a reaction.


Reaction thermodynamics review

Reaction Kinetics

aA + bBcC + dD

Rate (r) = 1/nidci/dt

= -(1/a) (d[A]/dt) or ..... + (1/c) (d[C]/dt) etc.

rate = k [A]a [B]b [L]l

k = rate constant (if you determine k using the change in a reagent

for which the stoichiometric coefficient ≠ 1

you must also adjust for this.

A and B are reactants. L = catalyst, intermediate

a/b/l = reaction orders with respect to A, B, L, respectively.

overall order, n = a + b + l.


Reaction thermodynamics review

Elementary Reactions

A + B C + D and r = k [A] [B]

Partial orders of reactants = stoichiometric coefficient

i.e. a = a and b = b.

2. no catalysts or intermediates in rate law.

3. reverse reaction is also elementary

4. Represents the actual ‘collision’ that takes place resulting in the change in molecular arrangement.

5. Typically n will be 2 or less for an elementary reaction (and its reverse reaction).


Reaction thermodynamics review

e.g.... A + C  I + D

I + B  F + C

Mechanism – A reaction is represented as a series of

elementary steps that add up to overall

stoichiometry and represent the actual

collision order in the reaction.

slow

fast

stoichiometry: A + B  D + F

I is intermediate and C is catalyst r = k[A][C]

Experimental Goals

Determine rate law – Find n and k

e.g. r = k [A] [C], n = 2, and k = r/([A][C]).

  • Determine mechanism(s) consistent with rate expression

3. Determine Activation energy by T dependence of k.


Reaction thermodynamics review

Most Common Reaction Orders

1st order:

rate = k [A]

rate = k [A]2 or....

2nd order:

rate = k [A][B]

rate expression can include ......

orders > 2, half-integral orders,

inverse dependency – [X] in denominator


Reaction thermodynamics review

1st Order Reactions

half-life

ln([A]/[Ao]) = -kt

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

if [A] = [Ao]/2

then t = t1/2 & .....

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

[Ao][A]d[A]/[A] = -k 0tdt

ln 0.5 = -kt½

t½= ln 2/k

ln [A] - ln[Ao] = ln([A]/[Ao]) = -kt

Linear: ln [A] = -kt + ln [Ao]

t½= 0.693/k

[A] = [Ao] e(-kt)

t½is independent of [Ao]


Reaction thermodynamics review

2nd Order Reactions

half-life

r = - d[A]/dt = k[A]2

1/[A] – 1/[Ao] = kt

-d[A]/[A]2= -k dt

2/[Ao] - 1/[Ao] = kt½

1/[Ao] = kt½

[Ao][A] [A]-2 d[A] = -k 0tdt

1/[A] – 1/[A0] = kt

linear 1/[A] = kt + 1/[A0]

t½= 1/(k[Ao])

[A] = [Ao]/(1 + kt[Ao])

as [Ao]  t½


Reaction thermodynamics review

0 Order Reactions (rare – some free radical reactions)

r = -d[A]/dt = k

∫AoAd[A] = k ∫0tdt

[A] = kt + [Ao]

[Ao]

Plot [A] vs. t

slope = k

Yint = [Ao]

[A]

t


Reaction thermodynamics review

Determining Reaction Order, n

Half-life Method

1st order – t½ is constant regardless of [A]0.

2nd order – t½ doubles as [A]0↓ by ½.

plot lnt½vs. ln [Ao]  slope = 1-n

115 (115) 230 (115) 345

167(333)500

Advantage: Single experiment

Disadvantage: Requires reaction integrity over multiple half-lives

unless ‘fraction’ < ½ used.


Reaction thermodynamics review

Determining Partial Order (a)

Initial rate method ― r = k [A]a [B]b

1. vary [Ao] while holding [Bo] etc. cst.

2. find initial rate r from plot of [A] vs. t

r2/r1 = ([A0,2]/[A0,1])a

log (r2/r1) = a log ([A0,2]/[A0,1])

two data points: a = log(r2/r1)/log([A0,2]/[A0,1])

Multiple data points: plot log (ro) vs. log [Ao]: slope = a

3. repeat for other reagents in rate expression

20.4 - p726


Reaction thermodynamics review

AB*

A + B

G

C + D

Transition State theory (collision theory) A + B → C + D

Boltzmann Distribution

N2/N1 =exp(-Ea/RT)

Ea

where N2 = # collisions leading to reaction &

N1= total # collisions

DG

Eadetermines rate - DG° determines Equil.


Reaction thermodynamics review

F2(g) + 2ClO2(g) 2FClO2(g)

Determining the Rate Law

X = 1

rate = k [F2]x[ClO2]y

r2 = k•(2[F2])x•[ClO2]y = k•2x•[F2]x•[ClO2]y = 2x = 2

r1 k•[F2]x•[ClO2]y k• [F2]x•[ClO2]y

r2 = k•[F2]x•(4•[ClO2])y = k•[F2]x•4y•[ClO2]y = 4y = 4

r1 k•[F2]x•[ClO2]y k•[F2]x• [ClO2]y

y = 1

rate = k [F2][ClO2] ― Note that partial orders ≠ reaction coefficients.

Problem 13.70


Reaction thermodynamics review

Arrhenius Activation Energy

The T dependence of reaction rates is due to the dependence of k on T. This in turn is due to the dependence of Ea on T. Through empirical observation Arrhenius determined that ….

k = A exp(-Ea/RT)

ln k = (-Ea/R)(1/T) + ln A

plot ln k vs. 1/Tslope = -Ea/RYint = ln A

or .. ln (k2/k1)/(1/T2 – 1/T1) = -Ea/R


Reaction thermodynamics review

H2 + I2 2HI

ln k = (-Ea/R)(1/T) + ln A

Ea = 160 kJ mol-1


Reaction mechanism

REACTION MECHANISM

1. List of Elementary Steps

2. Must add to overall stoichiometry

3. Must be “consistent” with Rate Law

1. Rate Determining Step Method (RDS)

2. Steady State Method (SS)


Reaction thermodynamics review

A +BC + D

C+ EB+ F

A + ED + F

C is an intermediate

Product in an early step, reactant in a later step.

Doesn’t appear in stoichiometry.

May appear in rate law

B is a catalyst

Reactant in an early step, product in a later step.

Doesn’t appear in stoichiometry.

Must appear in the rate law.


Reaction thermodynamics review

H+ + HNO2 + FNH2 FN2+ + 2H2O

Rate Law: r = k [H+] [HNO2] [Br-]

Br- must be catalyst or intermediate and must

show up in mechanism.

FNH2 is reactant that is not in the rate law.

It must show up in the mechanism in a later step.

If an RDS mechanism is sufficient to explain rate

law then it must be a reactant in a step after the

rate-determining step.


Reaction thermodynamics review

k1

H+ + HNO2 H2NO2+ fast

k-1

k2

H2NO2+ + Br-  ONBr + H2O slow

k3

ONBr + FNH2 FN2+ + H2O + Br- fast

H+ + HNO2 + FNH2 FN2+ + 2H2O

Rate Law: r = k [H+] [HNO2] [Br-]

r = k2 [H2NO2+] [Br-]

[H2NO2+] = k1/k-1 [H+][HNO2]

r = k [H+][HNO2][Br-] k = (k2k1/k-1)


Reaction thermodynamics review

k1

H+ + HNO2 H2NO2+

k-1

k2

H2NO2+ + Br-  ONBr + H2O

k3

ONBr + FNH2 FN2+ + H2O + Br-

[ONBr] = k2 [H2NO2+][Br-]/(k3[NH2])

r =k3k2 [H2NO2+][Br-] [FNH2]/(k3[NH2])

apply ss assumption to H2NO2+

H+ + HNO2 + FNH2 FN2+ + 2H2O

Rate Law: r = k [H+] [HNO2] [Br-]

r = k3 [ONBr][FNH2]

d[ONBr]/dt = 0

k2 [H2NO2+][Br-] = k3 [ONBr][NH2]


Reaction thermodynamics review

k1

H+ + HNO2 H2NO2+

k-1

k2

H2NO2+ + Br-  ONBr + H2O

r = k2k1 [Br-][H+][HNO2]

k-1 + k2[Br-]

k1[H+][HNO2]

k-1 + k2[Br-]

[H2NO2+] =

r =k2[H2NO2+][Br-]/[NH2]

apply ss assumption to H2NO2+

H+ + HNO2 + FNH2 FN2+ + 2H2O

Rate Law: r = k [H+] [HNO2] [Br-]

r = k1[H+][HNO2] = k-1[H2NO2+] + k2 [H2NO2+][Br-]


Reaction thermodynamics review

r = k2k1 [Br-][H+][HNO2]

k-1 + k2[Br-]

H+ + HNO2 + FNH2 FN2+ + 2H2O

Rate Law: r = k [H+] [HNO2] [Br-]

SS

RDS r = k [H+][HNO2][Br-] k = (k2k1/k-1)

same as RDS mech. when ... k2[Br-] << k-1


Reaction thermodynamics review

D  2M

2 (M + B  P) RDS

Half Orders in Rate Law .....

D + 2B  2P

Reactant split in first step - prior to RDS

r = k2[M][B] & [M] = (k1/k-1 [D])1/2

r = k[B][D]1/2


Reaction thermodynamics review

k1

Hg22+ Hg2+ + Hg fast

k-1

k2

Hg + Tl3+ Hg2+ + Tl+ slow

Term in denominator of rate law

Hg22+ + Tl3+ 2Hg2+ + Tl+

Look for P that is co-product prior to RDS

… or I that is P in first step & R after RDS

r = k2 [Hg][Tl3+]

[Hg] = k1[Hg22+]/(k-1[Hg2+])

r = k [Hg22+][Tl3+]/[Hg2+]


Reaction thermodynamics review

Unimolecular Reactions

Still involve some type of collision.

A  B (+ C)

A + M  A* + M

A*  B (+ C)

r = k[A]


Reaction thermodynamics review

Enzyme Kinetics Mechanism:

k1

1.E + S  ES

k2

k3

2.ES  E + P

r = k3 [ES]k1[E][S] = (k2 + k3) [ES]

[ES] = k1/(k2 + k3) [E][S]

[ES] = [E][S]/KM(KM = (k2+k3)/k1

r = k3/KM [E][S]

If [S] >> KM then [ES] = [E]tot and …..

r = k3 [E]tot


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