matriculation chemistry reaction kinetics part 2.pdf

8/12/2019 Matriculation Chemistry Reaction Kinetics part 2.pdf

1/33

Objectives:

1.Write the rate law for zero order, 1st order and

2nd order reaction2. Define half-life.3. Draw the respective graphs for the different

order reactions4. Solve quantitative prole!s.

Integrated Rate Law


2/33

Zero Order Reaction

" zero order reaction is a reaction independent ofthe concentration of reactant.

"product

#he rate law is given $

rate % k&"'(rate % k

&"' )

rate

Integrated rate equations


3/33

- d&"' % k dt

*sing calculus, - d&"' % kdt - +d &"' % k+dt - &"' % kt c

sustituting t%(, &"' % &"'( - &"'( % k(c c % - &"'(

&"'(-&"' % /t

*nit of k for zero order reaction ) s-1


4/33


5/33

Half-life (t)

alf life t is the ti!e required for the

concentration of a reactant to decrease to half of itsinitial value.

zero order reaction

Sustituting t = t1/2, and [A] = [A] into the zeroorder reaction, gives !

&"'(- &"' % /t

&"'( &"'(% /t152 2 Solving for t152 gives t"#! = [A]

!$


6/33

6ro! the rate law, rate % k&"' #o otain the units of k k % rate

&"'

unit / % ) s-1)

% s-"

%irst Order Reactions

" first order reaction is a reaction where$ itsrate depends on the concentration of reactantraised to the first power.


7/33


8/33

6or first order reaction,

- d&"'dt

% /&"'

- d&"'&"' % / dt

- d&"'&"'

% / dt+ +

- ln &"' % /t c

sustituting

t % (, &"'%&"'(

- ln &"'( % k( c c % ln&"'(

-ln &"' % /t ln&"'(

ln&"'(&"'

% /t

7ate % /&"'


9/33


10/33

#he reaction 2" 9 is first order with respect " with arate constant of 2.: 1(-2s-1at :((8. ow long will it ta/efor " to decrease fro! (.:: Mto (.14 M ;

ln&"'o ln&"' % kt

kt% ln&"'( ln&"'

t%ln&"'

( ln&"'k %


11/33

&'a()le

Deco!position of 2=2aq is first order, given that k% 3.


12/33

ln 1.4@ % 3.


13/33

Aercise,

#he conversion of c$clopropane to propene in the gas phase is a first

order reaction with a rate constant of ((C8.

82 82 82 83-8%82

a f the initial concentration of c$clopropane was (.2> ), what is theconcentration after :.: !inute. *+", .

ow long will it ta/e for the concentration of c$clopropane todecrease fro! (.2> ) to (.1> ); *"/ (in.

c ow long will it ta/e to convert @4 percent of the starting !aterial;*// (in.


14/33

#he half-life0 t10is the ti!e required for the concentration of a

reactant to decrease to half of its initial concentration.t=t when &"' % &"'( 2

ln

&"'(&"'(52

k%t

ln2k

%(.if it deco!poses with a rate

constant of >.@ 1(-4

s-1

;t

ln2k

%(..@ 1(-4s-1% % 12(( s % 2( !inutes

How do 2o3 $now deco()osition is first order4

units of ks-1

Half-life of a first-order reaction


15/33

" product

6irst-order reaction

Fo. ofhalf-lives &"'o% : )

1

2

3

4

4

2

1

152

tln2k

%


16/33

&'a()le

#he deco!position of ethane 82.3< 1(-4s-1at @((o8. 82 !in


17/33

Hrole! 2

What is the half-life of a co!pound if @>I of agiven sa!ple of the co!pound deco!poses in


18/33

Hrole! 3

#he deco!position of S=28l2is a first-orderreaction.

S=28l2g S=2g 8l2g

i Write the rate differential equation for thereaction.

ii 8alculate the value of rate constant, / at >(( J if

>.(( I S=28l2deco!posed in !in."ns @.


19/33


20/33

#o otain the units of k

/ % rate&"'2

% )5s

)2% )-1 s-1

*sing calculus, the following epression can e otained

1&"'

1-&"'(

% /t

*nit /


21/33

8haracteristic graphs for second order reaction

rate

&"'

7ate % / &"'2

rate

&"'2


22/33

0raphs for second order reaction

&"'

t

&"'1

/t% &"'o

1

15&"' )-1

15&"'o

t

15&"' 15&"'o

t


23/33

22ndnd order reaction, r % /&"'order reaction, r % /&"'22

If [A] doubles,If [A] doubles,

rr22 = k (2[A])= k (2[A])22

= k ( 4 [A]= k ( 4 [A]22

)) = 4 k [A]= 4 k [A]22

= 4 r= 4 r

R will increase b 4 ti!es if [A] doublesR will increase b 4 ti!es if [A] doubles


24/33

alf life of a second order reaction

1&"'

1&"'(% /t

Sustituting t% t152&"'% &"'o

1&"'(

1&"'(

% /t152

t152 % 1/&"'(

2

2


25/33

Dete!ination of half-life using graph forsecond order reaction&"'(

&"'(52

&"'(54

&"'(5:

t 2 4

t152 % 1/&"'(


26/33

&'a()le

odine ato!s co!ine to for! !olecular iodine in

the gaseous phase g g 2g#his reaction is a second order reaction , with the

rate constant of @.( 1(E)-1 s-1f the initial concentration of iodine was (.(:< ),i calculate itKs concentration after 2 !in.ii calculate the half life of the reaction if the

initial concentration of iodine is (.(< ) and

(.42 ) respectivel$.


27/33

Solution ?

i1&"'

1&"'(% /t

1&"'

1&(.(:


28/33

&2'% (.42 )

t152 %1/&"'(

@.( 1(E (.(42

1

%

% 3.4 1(-1( s


29/33

Aa!ple,

#he following results were otained fro! aneperi!ental investigation on dissociation ofdinitrogen pentoide at 4>o8

F2=>g 2 F=2g =2gti!e, t5!in ( 1( 2( 3( 4( >( ' 1(-4 ) 1@< 124 E3 @1 >3 3E 2E

Hlot graph of &F2=>' vs ti!e, deter!ine

i #he order of the reaction

ii the rate constant /

Using graph


30/33

Solution ?

&F2=>'

1(-45)

#i!e !in

1:(

1


31/33

9ased on the aove graph,

#i!e ta/en for concentration of F2=>to changefro! 1@< 1(-4) to :: 1(-4 ) is 2( !in#i!e ta/en for concentration of F2=>to changefro! :: 1(-4) to 44 1(-4 ) is also 2( !in

#he half life for the reaction is a constant anddoes not depend on the initial concentration ofF2=>

#hus, the aove reaction is first order

i

ii / %ln2

2( !in% (.(3 !in-1


32/33

53((ar2 of t6e 7inetics of Zero-Order0 %irst-Order

and 5econd-Order Reactions

=rder 7ate Law8oncentration-#i!e

Aquation alf-Life

(

1

2

rate % k

rate % k &"'

rate % k &"'2

ln&"' % ln&"'(- kt

1&"' % 1&"'( kt

&"' % &"'(- kt

tln2k

%

t%&"'

(2k

t% 1k&"'(

Mero order 1st order 2nd order


33/33

Mero order 1 order 2 order" product " product " productr % / &"'( r % / &"'

1r % / &"'2

&"'

r

&"'

r

&"'2

r

&"'

r*nit / % ) s-1 *nit / % s

-1 *nit / % )-1 s-1

ntegrated rate law ntegrated rate law ntegrated rate law

&"'( &"' % /t ln&"'( 5 &"' % /t 15&"' 15&"'(% /t

t

&"'

&"'(

&"'( - &"'t

&"'

t

&"'

t

ln&"'

ln&"'(

t

15&"'

15&"'(

ln&"'( 5 &"' 15&"' 15&"'(

t152 % &"'(52/

t152 %

l 25/

t152 % 15/&"'(

matriculation chemistry reaction kinetics part 2.pdf

Documents