reaction kineticsreaction kinetics. an introduction. 2 • a condition of equilibrium is reached in...
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![Page 1: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/1.jpg)
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Reaction Kinetics
An Introduction
![Page 2: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/2.jpg)
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• A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate.
• The rate of a chemical reaction may be defined as the # of mols of a substance which disappear or are formed by the reaction per unit volume in a unit of time.
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Example
tI
ttIIRate
CI
forward ΔΔ
=−−
=
→
][][][
12
12
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• The previous rate is for the DISAPPEARANCE of I, therefore:
""
][
oflossorngdisappearimeanssignnegativethewheretIrate
ΔΔ
−=
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Backwards Example
IstudyratesreactionbothwhengformeanssignpositivethewheretC
tC
ttCC
Ratebkward
min
][][][][
12
12
ΔΔ
+=ΔΔ
=−−
=
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More Complex Reactions
tZ
tXRate
ngdisappeariisXasfastasXappearingZtodueisthis
tZ
tXRate
ZX
ΔΔ
=ΔΔ
−=
∴
ΔΔ
≠ΔΔ
−=
→
31
3
3
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In GeneralFor the Reaction:
pP + qQ → rR + sS
tS
stR
rtQ
qtP
pRate
ΔΔ
=ΔΔ
=ΔΔ
−=ΔΔ
−=1111
![Page 8: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/8.jpg)
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Reaction Order
![Page 9: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/9.jpg)
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In GeneralFor the Reaction:
pP + qQ → rR + sS
tconsrateortconsalityproportionkwhere
QPkRateor
QPtoalproportionisand
tS
stR
rtQ
qtP
pRate
mn
mn
tantan
][][
][][
1111
=
=
ΔΔ
=ΔΔ
=ΔΔ
−=ΔΔ
−=
![Page 10: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/10.jpg)
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k
A reaction with an incredibly large rate constant is faster than a reaction with an
incredibly small rate constant.
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For the Reaction:pP + qQ → rR + sS
The reaction is “n” order in [P] and “m” order in [Q]
OR
Is OVERALL “(n + m)” order
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KEY!!!!!!
“n” and “m” DO NOT necessarily equal “p”, “q”,
“r” or “s”
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Example
][
][][41][
21
)()(4)(2
52
2252
2252
ONkor
tO
tNO
tON
Rate
gOgNOgON
=
ΔΔ
=Δ
Δ=
ΔΔ
−=
+→
![Page 14: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/14.jpg)
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• This reaction is FIRST order in N2O5, NOT SECOND order as one might intuit from the stoichiometry.
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The Order of The Reaction• = the specification of the empirical (experimentally-
determined) dependence of the rate of the reaction on CONCENTRATIONS
• The order may = 0, a whole number or a non-whole number, e.g.,– 0– 1– 1½– 2
• We’ll focus on whole numbers and 0 (zero) for reactions of the type:
fF + gG → Products• AND! The order of the reaction is defined in terms of
REACTANTS not the products, therefore, products do not need to be specified
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Zero-Order Reactions
formbmxylineStraighttatFttimeatF
ChemPherenotIntegrate
tkFarrange
ktF
and
kkftFtcoefficienaonlyisf
GFktF
fRate
o
ktoFF
+====
−−
Δ−=Δ
=ΔΔ
−
==ΔΔ
−∴
=ΔΔ
−=
−=
:0][;][
:)(
][:Re
][
'][
][]['][1
][][
00
![Page 17: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/17.jpg)
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For Zero-Order Reactions
• These reactions are relatively rare
• Occur on metal surfaces
• Reaction rate is INDEPENDENT of concentration of reactants
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First Order Reactions• Assume reaction is 1st order in F and zero order
in G:
tko
o
eFFOR
tkFF
egrateandtkFFarrange
FktFkkf
GFktF
fRate
−=
−=
Δ=Δ
=ΔΔ
∴=
=ΔΔ
−=
][][
][][ln
:int:Re
]['
][]['1 01
![Page 19: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/19.jpg)
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• Many radioactive decays fit 1st order reactions:• 226Ra88 → 222Rn86 + 4He2
• 238U92 → 234Th90 + 4He2
• The rate is proportional to [F]
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The Rate is Proportional to [F]
Double [F] k [F] k [F]2 k [F]3
Rate Change ⇑ X 2 ⇑ X 4 ⇑ X 8
][FktF
=ΔΔ
![Page 21: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/21.jpg)
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Second Order Reactions: Type 1
tkFF
egrateandarrangeGtorespectwithorderZero
FtorespectwithorderSecond
FktF
andkkf
GFktF
fRate
o
=−
=ΔΔ
−
=
=ΔΔ
−=
][1
][1
:intRe
][
'
][]['1
2
02
![Page 22: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/22.jpg)
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Second Order Reactions: Type 2
overallorderSECONDGinANDFinorderFIRSTisaction
tkGFFG
FG
partsbyegrateandarrange
GFktF
henceandkkf
GFktG
gtF
fRate
o
o
oo
∴
=−
=ΔΔ
−
=
=ΔΔ
−=ΔΔ
−=
,Re][][][][
ln][][
1)(intRe
][][
,,'
][]['11
Second order reactions are the most common reactions
The rate is proportional to [G], [G]o, [F], [F]o
![Page 23: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/23.jpg)
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Pseudo-First Order Reactions
• A special kind of 2d order reaction:• Example• 1 M acetyl chloride (AcCl) reacted with 56
M water (XSSV amount) to for HOAC and HCl
AcCl + H2O → HOAc + HCl
![Page 24: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/24.jpg)
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OrderFirstPSEUDOHenceorderfirstbetoAPPEARSaction
AcClkRatekOHk
soecttosmalltooisOHinchangeThe
OHAcClktd
AcCldRate
−
=∴=
=−=
:,""Re
][','][
,det][
][][][
2
2
2
![Page 25: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/25.jpg)
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Empirical Method in Determining Reaction Orders
studiedbeingareAinONLYdifferingreactionsdifferentWhere
AA
tt
X
StepSecondAreactionfororderunknowntheX
AA
tt
raterate
StepFirstX
][2
][][log
log
:""
][][
:
2
1
1
2
2
1
1
2
2
1
ΔΔ
=
=
⎟⎟⎠
⎞⎜⎜⎝
⎛=
ΔΔ
=
![Page 26: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/26.jpg)
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Example
AinorderondisreactionM
MAAtt
X
tMAandBAaction
tMAandBAaction
sec
2239.0477.0
734.1log3log
173.03.0log
'5'15log
][][log
log
'15;173.0][:2Re
'5;3.0][:1Re
2
1
1
2
2
1
∴
===⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
=⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛ΔΔ
=
=Δ=→
=Δ=→
![Page 27: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/27.jpg)
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Practical Application• Reaction rates are proportional to some power of
[reactant]• Determined by using “initial reaction rate method”
![Page 28: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/28.jpg)
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Compare Reaction 2 with Reaction 1
![Page 29: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/29.jpg)
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Compare Reaction 3 with Reaction 1
![Page 30: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/30.jpg)
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• Fuse both effects and the rate equation for this reaction =
Rate = k [Zn] [HCl]2• REMEMBER:• The exponent in a rate equation generally
does NOT match the chemical equation coefficients.
• The exponent MUST be determined experimentally.
![Page 31: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/31.jpg)
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Another way to do this
![Page 32: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/32.jpg)
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Compare Reaction 1 with Reaction 2
![Page 33: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/33.jpg)
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Compare Reaction 3 with Reaction 1
![Page 34: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/34.jpg)
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Reaction Order Half-Lives
![Page 35: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/35.jpg)
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11
21
21
1
21
1
21
][1
:
2ln:
2][
:
−−
−
−
==
==
==
sMkF
t
OrderSecond
IONCONCENTRATofTINDEPENDENistOrderFirst
sk
t
OrderFirst
sMk
Ft
OrderZero
o
o
![Page 36: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/36.jpg)
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Example
• For the reaction:• C → D + E,• Half of the C is used up in 60 seconds.
Calculate the fraction of C used up after 10 minutes – reaction is first order in C.
![Page 37: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/37.jpg)
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Solution
UpUsedCorUPUSEDCHenceLEFTCC
CCC
CKey
tkCC
ondskandk
t
o
o
o
%9.99999022.0000978.01:000978.0][
93.6][ln)600()01155.0(][ln][ln
1][:][][ln
sec01155.060693.02ln 1
21
−−=−=
−=−=−
=
−=
=== −
![Page 38: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/38.jpg)
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Example
• 14C is present at about 1.1*10-13 mol% naturally in living matter. A bone dug up showed 9*10-15 mol% 14C. The half life of 14C is 5720 years. How old is the bone?
![Page 39: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/39.jpg)
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Solution
oldyears
t
tkCC
yrst
k
o
45.2066210*2115.1
503.2
)10*2115.1(10*1.1
10*9ln
][][ln
10*211.15720
693.02ln
4
413
15
14
14
14
21
=−
−
−=
−=
===
−
−−
−
−−
![Page 40: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/40.jpg)
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Example
• A decomposition reaction occurs in a fixed-volume container at 460°C. Its rate constant is 4.5*10-3 seconds-1. At t = 0, P = 0.75 atm. What is the pressure (P) after 8 minutes?
![Page 41: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/41.jpg)
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Solution
atmPP
P
P
tkPP
o
0865.016.2288.0ln
)480()10*5.4(75.0lnln
)480()10*5.4(75.0
ln
ln
3
3
=−=+
−=−
−=
−=
−
−
![Page 42: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/42.jpg)
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Q10 Effect
![Page 43: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/43.jpg)
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Example
• If the rate of a chemical reaction doubles for every 10°C rise in temperature, how much faster would the reaction proceed at 55°C than at 25°C?
![Page 44: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/44.jpg)
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Q 10 EffectQ 10 Effect on Reaction Rate
0, 1 10, 2 20, 4 30, 840, 16
50, 32
60, 64
70, 128
0
20
40
60
80
100
120
0 20 40 60
Temperature (Celsius)
Rel
ativ
e R
eact
ion
Rat
e
![Page 45: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/45.jpg)
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Solution
• Temperature increased 30°C, therefore, reaction rate increases 8-fold
Example:• What if the temperature was increased to
105°C from 25°C?• Temperature increased 80°C, therefore
reaction rate increases 256-fold
![Page 46: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/46.jpg)
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Example
• How much faster would a reaction go at 100°C than at 25°C?
• For every 10°C increase in temperature, the reaction rate doubles. The change in temperature is 75°C. This is 7.5 10°C increases.
• Hence 27.5 = 181 times faster
![Page 47: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/47.jpg)
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Example
• In an experiment, a sample of NaOCl was 85% decomposed in 64 minutes. How long would it have taken if the temperature was 50°C higher?
• For every 10°C increase, the reaction rate doubles. 50°C increase is 5 10°C increases.
• Hence: 25 = 32 times faster• So: (64 minutes)/(32 times faster) = 2 minutes
![Page 48: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/48.jpg)
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There are 4 types of temperature dependence for reaction rates -- 1
• Rate increases with increasing temperature
• NORMAL
![Page 49: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/49.jpg)
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There are 4 types of temperature dependence for reaction rates -- 2
• Rate increases to a point, then reduces with increasing temperature
• E.g., enzymes being denatured
![Page 50: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/50.jpg)
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There are 4 types of temperature dependence for reaction rates -- 3
• Rate decreases with increasing temperature
• VERY RARE• Known only for a
few reactions that are multi-step reactions:– A → B Fast step– B → C Rate limiting step
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There are 4 types of temperature dependence for reaction rates -- 4
• Rate increases with increasing temperature
• Odd behavior• Explosive reaction
when temperature shoots up
• Gradual rise in temperature due to chain reactions
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• The Q 10 effect is “not entirely perfect”
• There is another way to study temperature dependence:
• Mathematically with Energy of Activation
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etemperaturabsoluteTtconsGasR
ActivationofEnergyEmoleculestreacbetweencollisionsof
frequencytotalfactorfrequencyAtconsratek
a
TRaEeAk
==
=
==
−=
tan
)tan(
tan
/
![Page 54: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/54.jpg)
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Take Natural Log (ln) of Above Equation
TRE
Ak a−= lnln
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Previous Equation Can Be Manipulated
• If you know the rate constants for reactions at 2 different temperatures you can calculate the Ea:
⎟⎟⎠
⎞⎜⎜⎝
⎛−−=
121
2 11lnTTR
Ekk a
![Page 56: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/56.jpg)
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Example
• At T1 of 308 K, k1 = 0.326 s-1; at T2 of 318 K, k2 = 1.15 s-1. R = 8.314 J/mol-K. Determine Ea
molkJ
molJE
E
E
TTRE
kk
a
a
a
a
6.1028.601,10210*021.1
)314.8()26.1(
)10*021.1(314.8
26.1
3081
3181
314.8326.015.1ln
11ln
4
4
121
2
⇔==−−
−−=
⎟⎠⎞
⎜⎝⎛ −−=
⎟⎟⎠
⎞⎜⎜⎝
⎛−−=
−
−
![Page 57: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/57.jpg)
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Ea -- Transition
• Top of Energy curve (“hump”) = transition state
• The smaller the Ea, the easier it is for the reaction “to go”
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Ea – “thermic”
Ea is related to ΔG
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Reaction Mechanisms
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Unimolecular Steps
• A single molecule or atom breaks down or rearranges itself into another species.
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Bimolecular Steps
• Collision of two molecules or atoms; relatively common
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Termolecular Steps
• 3 molecules or atoms collide simultaneously; relatively rare and SLOW
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Elementary Steps
• = each step in a mechanism; a specific occurrence in the reaction sequence– The rate of elementary steps are proportional
to the number of collisions per step– The number of collisions per step are
proportional to every reactant concentration– Hence the rate of elementary steps are
proportional to the concentration of every reactant
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The exponents of an elementary step rate equation are equal to the coefficients in the step’s equation
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E.g., Bi Elementary Steps
OrderstSOkStepforequationRate
OrderdOSOkStepforequationRate
StepOSOSOStepSOOSO
RxnOverallOSOOSO
1][:2
2][][:1
21
51
321
235
532
2332
+→→+
+→+
![Page 66: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/66.jpg)
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E.g., Termolecular Elementary Steps
OrderstClHkStepforequationRate
OrderdHClkStepforequationRate
OrderstClkStepforequationRate
StepHClClHStepClHHCl
StepClCl
RxnOverallHClHCl
1][:3
2][][:2
1][:1
3222
12
2
223
22
2
21
22
222
2
22
=
=
=
→→+
→
→+
−
−
−
![Page 67: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/67.jpg)
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Reaction MechanismsTWO requirements of postulated mechanisms:
1) MUST account for the postulated mechanism2) MUST explain the experimental rate equation
1) – INHERENT in this is the assumption that2) 1 step is incredibly SLOWER than the others,
hence, it determines the speed of the reaction.3) This step is called the rate limiting step.4) Therefore, the overall rate equation is determined
by rate equations for the rate limiting step.5) ALSO: when a catalyst is present, there MUST BE
at least 2 steps in the mechanism!
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Example
• The empirically derived rate equation for:2NO2 (g) + Cl2 (g) → 2NO2Cl ↑ is
k [NO2] [Cl2]
• Write a two-step mechanism with a slow first step
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stepslowtheisStepHenceEquationRateEmpiricalStepforEquationRate
BUTClClNOk
EquationRateStepClNOClClNO
ClNOkEquationRate
StepClClNOClNORxnOverallClNOClNO
1,1
][][
22][][
122
2
22
22
222
222
=
→+
+→+→+
![Page 70: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/70.jpg)
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Comments
• Any steps after Step 1 will NOT effect the rate because step 1 is the rate limiting step
• Add up the 2 steps (just like in thermodynamics) and you get the overall reaction
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Illustrative Example
)1,Re(2
2][][
2][][
1][][
22
2
2
2
22
purposesveillustratiforwasthisSTEPisalityInLimitingRateisStep
EquationStepEqualsEquationRateEmpiricalthatNoteHIIClk
EquationRateStepHClIHIICl
HIClkEquationRate
StepHClHIHIClEquationRateDerivedyEmpiricallHIIClkRxnOverallIHClHICl
−
+→+
+→+
+→+
![Page 72: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/72.jpg)
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Example
• The empirical rate equation for
2ClO2 + F2 → 2FClO2
Is: k [ClO2] [F2]
• Write the reaction mechanism (2-step) consistent with the rate equation.
![Page 73: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/73.jpg)
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LimitingRateisStepHenceEquationRatedDtnyEmpiricall
MatchesEquationRateStepFClOk
EquationRateStepFClOFClO
FClOkEquationRate
StepFFClOFClORxnOverallFClOFClO
1,'
1][][
2][][
122
2
22
22
222
222
→+
+→+→+
![Page 74: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/74.jpg)
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Steady State Approximation• The majority of mechanisms are NOT as easy as
previous examples.• Let’s return to our Bimolecular Reaction Step Example:
![Page 75: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/75.jpg)
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Focus• SO5• This is an “intermediate” – a “transition”• An intermediate (or transition) is a compound
that is neither reactant nor product, rather in between the two.
• Intermediates are very difficult to isolate in many cases.
• They are highly reactive and, more often than not, are used up as quickly as they are formed. It is because of this characteristic that we have the Steady State Approximation
![Page 76: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/76.jpg)
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Steady State Approximation• The concentration of intermediate is a constant• I.e., the rate of formation of the intermediate is
equal to the rate of disappearance of the intermediate:
tdtermediateind
tdtermediateind ][][
−=
![Page 77: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/77.jpg)
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Example• 2O3 → 3O2
• Empirically derived rate equation = k [O3]2/[O2]
SLOWStepOOO
clearlyreactionbackwardstheforsitthatyoudsreitaskpreferIkitcallsourcessomereactionbackwardsforkratek
FASTStepcatalystOcatalystOO
reactionforwardforkratekFASTStepcatalystOOcatalystO
MECHANISM
k
k
k
32
'min)(
2
1:
23
1
21
32
1
23
3
1
1
⎯→⎯+
=+⎯→⎯++
=++⎯→⎯+
−
−
−
![Page 78: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/78.jpg)
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• The constant of a reverse reaction is indicated by (-), e.g., k-1
• The intermediate in this mechanism is the oxygen ATOM, hence:
tdOd
tdOd ][][
−=
![Page 79: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/79.jpg)
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• Knowing this, we need to show that the empirical rate equation and mechanism are consistent with each other.
![Page 80: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/80.jpg)
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][][
][][
][][][][
][][][][][
][][][][][][][''
21
31
2131
2131
2131
OOkOk
OforSolveOOkOk
catalystoutCancelcatalystOOkcatalystOk
TwoTheEquateNow
catalystOOktdOdcatalystOk
tdOd
RxndBckwofRateRxndForofRate
=
=
=
=−=
−
−
−
−
![Page 81: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/81.jpg)
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• Stop temporarily• REMEMBER: the rate limiting step is #3;
the rate equation for this step = k3 [O] [O3]• So, substitute the solution for [O] from the
first for’d and bkw’d reactions in to the rate equation for Step 3:
![Page 82: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/82.jpg)
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equationratederivedyempiricalltoidenticalIsOO
kequation
substituteandk
kkkLet
OOkOk
k
][][
:
][*][
][*
2
23
1
13
321
313
=
=−
−
![Page 83: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/83.jpg)
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• This series of kinetic equations fulfills the 2 requirements:
• 1) Accounts for the products, and,• 2) Explains the observed rate law
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Second Example• For 2NO + O2 → 2NO2, the empirical rate equation is:
k [NO]2 [O2]
• The postulated mechanism follows:
SLOWStepNONONO
FASTStepNOONO
k
k
k
22
1
223
32
2
1
1
⎯→⎯+
⇔+−
![Page 85: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/85.jpg)
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• Show that the empirical rate equation and mechanism are consistent with each other.
• Use the methodology we used in the previous example.
![Page 86: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/86.jpg)
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tdNOd
tdNOd
andNONONO
ONONO
NOONO
k
k
k
][][
2
33
23
23
32
2
1
1
−=
⎯→⎯+
+⎯→⎯
⎯→⎯+−
![Page 87: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/87.jpg)
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ytemporarilhereStop
NOk
ONOk
NOforSolveNOkONOk
twotheEquate
NOktd
NOdONOk
tdNOd
EquationRatedBkwEquationRatedFor
][][][:][
][][][:
][][
][][][
''
31
21
3
3121
313
213
=
=
=−=
−
−
−
![Page 88: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/88.jpg)
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• The rate limiting step is step 3.• The rate equation for step 3 is: k2 [NO3]
[NO]• Substitute the solution for [NO3] into the
rate equation for step 3.
![Page 89: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/89.jpg)
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][][][][][ 22
21
21 ONOkNOONOk
kk=⎟⎟
⎠
⎞⎜⎜⎝
⎛
−
![Page 90: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/90.jpg)
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Apply This to Enzymes• Enzymes are, with a couple of exceptions,
proteins• Enzymes are biological catalysts• Enzymes speed up biological reactions
incredibly• For this discussion:
– E = enzyme, – S = substrate and – P = product
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tdESd
tdESd
ANDSLOWPEESFASTSEESFASTESSE
k
k
k
][][
2
1
1
−=
+⎯→⎯
+⎯→⎯
⎯→⎯+−
![Page 92: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/92.jpg)
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ytemporarilStop
ESSEkk
ESforSolveESkSEk
MethodShort
][][][
:][][][][
1
1
11
=
=
−
−
![Page 93: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/93.jpg)
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• Rate limiting step is step 3• Rate equation is: k2 [ES]• Substitute as before:
RxnUniUniaisThisPEESSE
reactionoveralltheWrite
SEkSEk
kk
−+→⇔+
=⎟⎟⎠
⎞⎜⎜⎝
⎛
−
:
][][][][1
21
![Page 94: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/94.jpg)
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Uni-Uni Reaction – Cleland Plot
![Page 95: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/95.jpg)
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Bi-molecular Reactions
• An enzyme catalyzed reaction may utilize 2 substrates.
• This reaction is always SEQUENTIAL, however,
• May be – ORDERED or – RANDOM
![Page 96: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/96.jpg)
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E.g., Ordered Sequential Reaction
E + X + Y → E + R + SE is still enzyme
X and Y are substratesR and S are products
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Putative MechanismE + X → EX
EX + Y → EXYEXY → ERS SLOW STEP
ERS → ER + SER → E + S
And:
tdEXYd
tdERSd ][][
−=
![Page 98: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/98.jpg)
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ytemporarilhereStop
EXYEXYXEkkk
EXYforSolve
EXYkYEXkXEk
Equate
EXYktd
EXYdYEXkXEktd
ERSd
][][][][][
][
][][][][][
][][][][][][][
3
21
321
321
=⎟⎟⎠
⎞⎜⎜⎝
⎛
=
=−=
![Page 99: Reaction KineticsReaction Kinetics. An Introduction. 2 • A condition of equilibrium is reached in a system when 2 opposing changes occur simultaneously at the same rate. • The](https://reader033.vdocuments.us/reader033/viewer/2022050304/5f6cb5dc54d04363e34f70fc/html5/thumbnails/99.jpg)
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• Rate Limiting Step is: k3 [EXY]• Substitute:
][][][][
][][][][][][][][ 213
213
EXYXEk
EXYXEkkEXYXEkkkk
=
=
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Kinetic Data Tells us:
• The following sequence MUST be taking place:
E + X + Y → EX (FIRST!) → EXY (SECOND!) → ERS → ES + R → E + S
• And is an Ordered Bi Bi Reaction
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Ordered Bi Bi Reaction –Cleland Plot
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• In the case where separate experiments about the same system give 2 different rate equations, e.g.,
k [E] [X] [Y] [EX]And
k [E] [X] [Y] [EY]
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Mechanism = Random Sequential – Cleland Plot
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• What, though, if an enzyme catalyzed a reaction that bound one substrate, released its product, then binds a SECOND substrate and releases ITS product?
Overall Reaction is: E + X + Y → E + R + S
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Mechanism
E + X → EXEX → ER 1st rate limiting step
ER → E + RE + Y → EY
EY → ES 2d rate limiting stepES → E + S
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• Note: while written unidirectionally, in many cases the reactions are reversible
• With 2 rate limiting steps, this reaction and its kinetics get ugly fast.
• This sort of reaction between 2 substrates and the 1 enzyme act like a ping pong game.
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Ping Pong Mechanism –Cleland Plot
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Function of Kinetics
• To Determine Reaction Mechanisms