Chemical kinetics

BASIC TERMS

# CHEMICAL KINETICS

FIND THE RATE OF A CHEMICAL REACTION

FIND THE RATE LAW

It INSTANTANEOUS CONCENTRATION OF THE REACTANTS / PRODUCTS

Act ) FUNCTION

# RATE OF A CHEMICAL REACTION

RATE OF CHANGE IN THE CONCENTRATION OF THE REACTANTS/ PRODUCTS

DERIVATIVE OF THE CONCENTRATION (A) WITH RESPECT TO TIME ( t )

RATE =

DAHL= V DERIVATIVE

dt

# RATE LAW

RELATES THE RATE OF A REACTION TO THE INSTANTANEOUS CONCENTRATION

OF THE REACTANTS / PRODUCTS

d Act )RATE LAW - N Alt )

,. . .

DIFFERENTIAL EQUATIONIt

- p → IRREVERSIBLE ( only A → P )

REACTANT PRODUCTT REVERSIBLE ( A - p and p - A )

-4=0Act - o ) -_ Ao -

tzAct ) LAO I [ A ]

P ( t = o ) = Po = O p ( t ) > Po T CONCENTRATION

.

.'

.

.

RATE OF THE REACTION ( v )

Alta ) - Act)= OAK ) P ( ta ) -

Pete)

=

0pct)

v =

-- soVa=

--

70AVERAGE tz - t, of tz - t

, Of

Lot -0 At Lot → o PT

v = time )=dAcow

, =othigo =EE > o

INSTANTANEOUS ot→o OtIt It

DERIVATIVE -DAHL

= t ddPft) (

←¥YN→My )dt TIME

I t r→

→ gsTOCTHOMETRY :(HOW MANY MOLECULES )

0.0061 - 0.02 -5

Nz 05 v = -

=L. TOFF 2Nz0g 2. no -5

700 -2--100.0278 - O - 5Noz v= - =

4 - to -51g 4h02 4-41=10-5700

Oz ✓ = = 10-51 -5

TooS 102 ¥= 10-5

DIFFERENT ? Ok 'O

GENERALLY

AAt BB→ c C t DD. STOCTHOMETRY

f p INSTANTANEOUS CONCENTRATION

DA

RATE = it = - at # = - f- I = tf # = the ÷

RATE LAW

= PARTIAL ORDER ORDER = [ PARTIAL ORDERd Act ) i

- n Act )dt

~ k = RATE CONSTANT

DA ( t )- = - k A ( t ) DIFFERENTIAL EQUATION

dtI

M of REACTANT CONVERTED TO PRODUCT IN 1g↳ F →

hesGENERALLY ( M )

' - r

x ( s )- 1

GOAL : A ( t ) = ?

MONOMOLECULAR

A → P v = - hat r=0

v= - KA"

r=1

Bl

MOLECULARATA - P it = - WA'

r=2

ATB → AB we = - ha'

B'

r= 1+1=2TRIMOLECULARA t At A - P v= -

has r =3

At ATB - P v= - KALB"

r=21-1=3At Btc → Pw =

- LIBI r -- 1+11-1=3

PLATINUM

a he1 Nz O - Nd g)

theOz ( g ) A - P r= O →

~ 57500

> to ( s ) Enzo ] ( M ) h( I ) CA] = Enzo ]b- - O 0.4 = Ao 2. to

-3

I k =

2.10-3140.2-3 g

2 2. to

0.1 - 3 ↳ 2. to-3

M A Is CONVERTED INTO2. to

p WITHIN ISEnzo ] t k -_ CONSTANT

RATE LAW : d%t = - he A°( t ) = - k INITIAL CONDITION : t -- O Act ) = Ao

② SEPARABLE DEGOAL i Alt ) = ?

Function dA( t ) = - kdt① m

JdA dt = ) - bolt fi.dACt)=S - kdt

DEWITTEf - gdx!- Gt to f Act )= - kdttc-

INTEGRAL f1dx=XtC GENERAL solution( t ) = - htt C

c= ?

GENERAL solution c= ?

Alt ) t

fl.dA(t ) -_ f - kdt Alt )^

Ao to -_ O

[ Act ) ]aY"

= ← ht ] !Ao -

LINEAR

V = SLOPE = - he

Act ) - Ao = - ht EL - Alt ) - t

A ( t ) = Ao - ht PARTICULAR SOLUTIONV

T> t

112

HALF LIFE ( Tye ) t = Tye Alt -- Tye ) = Aofz

A ( Tye ) = -20= Ao - kTyz

kTyz= Ae2

Ao

Tmz = -

2k

- ht Act )Act ) = Ao C PARTICULAR n

SOLUTION

AO -

EXPONENTIAL F.

112"

- tT Act ) ~ e

A ( t -_ Tye ) --

HE-

Ate-

he" '

azoµUtz = la e-

k Tk

v > t- lnz = - k T T' 12 " 12

T ln2yz=k

k3 A → P

r=2→

dA( t ) 2

RATE LAW :

y= - k A ( to ) INITIAL CONDITION it =D A ( t ) = Ao

GOAL : Act ) = ? k =

21MS

SEPARABLE DE

Alt ) t

f 1- DAH )=/ - kdtAZ C t )

[ Ao to -_ o If1dx=-

I t C f -

3dx=-

3×+0×2X

EIn?"

=L- at ] !- IT , -1at = - ht

1 AoAct ) = -

÷

-1kt=IktAo

T aAct )

112

KoHoAo -

A ( t = Tye ) =

2-= - - A ( t ) - I

1tktyzAo t

^ +ht 'll Ao = 2

,Azo µTry = -

k Ao

> tT

1/2

h4 At B → AB r= 2 →

a ) b )

.A B

-.

'

- . .

DAB ( t ) . . . .

- = th Act ) Bct )dt I I

.AB

kn .- . . . .

5 At B RT AB → . .

d. ABLE )- = t k

,Act )B( t ) - kz ABLE )

dt

ABT ABIASSOCIATION DISSOCIATION

ATB AB

ATB AB→ . . . -

→

. .

F- 2 re I

REACTIONr DIFFERENTIAL INTEGRAL The k

SCHEMEFORM FORM

A → p O DAHL= - h Act ) -_ Ao - ht ALMdt 2h S

- kt

A → p 1 dIt)= - KAH ) Act ) -_ Aoe tf Idt

A → p 2 DAHL= - halt ) Act )=÷µ Atop 1-

dt MS

ATB → AB 2

dAB#=hACt)BCt)out

ATB TAB DABA )- = -1k , Act )B( t ) - kzAB( t )

dt

Alt ) A → p r=o act ) A- → P r=1^

a

Ao

b-Ao

to-

-

52 - 5- . \Ao/4 2.5

- 2.5- .

↳ If 1.25 . 1.25 .

t I

I V V > IV N

St^ ① ② ③ i ② ③

55 7.55 8.755 35 Gs 95

Tin ① 55 ① 3s

② 7.5g - 55=2.55 ② Gs - 35=35

③ 8.755-7.55=1.255 ③ 95-65=35

Tried Tyz = A 'LL.

Act )^

Ao he-

A → p r=2

µ , §IDon-

,

Ao/8 I IAtin① ② ③ t

s 3s 75

Tyre ① Is

② 3 s - Is = 25

③ 7 s - 3s=4s

Tye T

PHARMACOKINETICS

CHANGE IN Act ) = t IN - OUT

O①

( Nfu IT

METABOLISMd Act)= +5 - 1 Act )

Act ) EXCRETION . . .

-

i IN , - Act ,dt t

singleI Out

'fgfqdacts-fdtk.net) *

O

k -_ 1h510

- luc 5- act ) ) -1 in (5-0) = t

lnc 5- Act ) ) =- ttln5

- t tln5

5- Act ) = C

- t

Act ) - 5- 5in

*

J ¥ DX = f -1 ←a) du =- t law = - in ( 5 - x )

re

5 - X = u

5- u = X

- die = DX