# Reaction mechanism and reaction order (PowerPoint) by ewghwehws

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```									Reaction mechanism and reaction order
• Chemical reaction: single or sum of many steps =>reaction mechanism
• A step: (elementary reaction)
–   one, two or three reacting molecules => molecularity
–   unimolecular: isomerization, decomposition
–   bimolecular: energy transfer, combination
–   termolecular: energy transfer + combination
• Reaction order vs. molecularity
– Reaction takes place in an elementary reaction
• unimolecular: first order
• bimolecular: second order
• termolecular: third order

– Is a first order reaction is always an unimolecular reaction?
Consecutive reaction processes
• RX + H2O = ROH + H+ + X-
– Unaffected by the PH of solution, SN1 reaction
– RX  R+ + X-
– R+ + H2O  ROH + H+

• RX + OH- = ROH + X-
– Alkaline solution
– RX  R+ + X-
– R+ + OH-  ROH

• What happen for 2nd order reaction?
Consecutive reaction processes

• A  B <k1>,                 B  C <k2>
– -d[A]/dt = k1 [A]; -d(a-x)/dt = k1 (a-x)

– d[B]/dt = k1(a-x) - k2[B] = k1 a e-k1t - k2[B]
– d[B]/dt + k2[B] = k1 a e-k1t

[ B] 
ak1
k 2  k1
              
e  k1t  e k2t , k1  k 2 , [ B]  0..t  0
Plot of concentrations of A, B, C
in consecutive process
Consecuti

1

0.8

0.6                               [A]
1/a

[B]
0.4                               [C]
0.2

0
0    20           40   60
time
Maximum [B]

d [ B]
dt

ak1
k 2  k1
                   
k 2 e  k2t  k1e  k1t  0

1        k1 
tm          ln  
k1  k 2  k 2 
 
Formation of an intermediate complex

• A + B  X (1) X  A + B(2) X  C + D(3)
• Principles of Stationary state
– 1913 Chapman: the net rate of formation of a reaction intermediate
may be put equal to zero.
– X so reactive, [X] is low

d[ X ]
 k1[ A][ B ]  k 1[ X ]  k 2 [ X ]  0
dt
k k [ A][ B ]
d [C ] / dt  k 2 [ X ]  1 2
k 1  k 2
Formation of an intermediate complex

• A + B  X .. k1; X  A + B … k-1
• X + C  P + Q … k2
d[ X ]
 k1[ A][ B ]  k 1[ X ]  k 2 [ X ][C ]
dt
d [ P]                  k k [ A][ B ][C ]
 k 2 [ X ][C ]  1 2
dt                        k 1  k 2 [C ]

Two limiting cases: k-1 > k2[C], k-1 < k2[C],
Third body effect in atomic recombination

• Two atoms molecule + lot of vibrational energy
– short life time production: needs a collision with other
molecular species to shed some excessive energy
• X + X + M  X2 + M
– before first vibration (10-13 s)  effective collision
– effective molecule=highly negative activation energy
• higher temperature: lower reaction rate
– efficiency is different depend on molecule
• large molecule
Porter’s interpretation(1961)
• I + M = I.M (K1); I.M + I  I2 + M(k2)
– I.M: spectroscopically identified for benzene
– [I.M]=K1[I][M]
– d[I2]/dt = k2[I][I.M] = K1k2[I]2[M]
• RT ln K = -G = -(H-TS)
• k = A exp[-Ea/RT]

d ln K1k 2       d ln K1     d ln k 2 
Ea   R                R            R
d (1 / T )        d (1 / T )    d (1 / T )

 H1  E2
Parallel reaction

• AB (1)                         AC (2)
– -d[A]/dt = (k1 + k2)[A]
– (a-x)=a exp[-(k1+k2)t]
– k1/k2 = Yield of B/Yield of C              B
• AC (1), A+BD (2)
– -d[A]/dt = (k1 + k2[B])[A]             A
• AB (1), A+AC (2)                            C
Reactant participating in equilibria

• H2 + I2 = 2HI
– Bodenstein 1899
– first order with respect to each reactants
– Bimolecular process, elementary reaction, four center
transition state

– Sullivan 1967: 0-200C ; non elementary reaction
– I2 + h  I2*, I2*  2 I       2 I + H2  2 HI
A probable mechanism for H2 + I2

• I2 = I + I                              …        (1)
• I + I+ H2  HI + HI                     …        (2)

• K1 = [I]2/[I2]             [I]=K11/2[I2]1/2
• d[HI]/dt = 2k2[H2][I]2 = 2k2K1[H2][I2]

– Ea(k2) = 21 kJ/mole
– Ea(k2) + Bond dissociation energy of I2 == Overall activation
energy of Bodenstein thermal experiment.
A probable mechanism for H2 + I2

• I2 = I + I                          …         (1)
• I + H2 = IH2                        …         (2)
• I + IH2  HI + HI           …       (3)

• K1 = [I]2/[I2]             [I]=K11/2[I2]1/2
• K2 = [IH2]/[I][H2] [IH2]=K2 [I][H2]
• d[HI]/dt = 2k3[IH2][I] = 2k3K1K2[H2][I2]
Hydrogen-halogen kinetics

• H2-F2, H2-Br2, H2-Cl2
– complicated experimental rate law
– interpreted in terms of free radical chain reaction
• H2-I2
– simple kinetic behavior
– the least understood system
Reactant participating in equilibria

• nA=An
– [A]=Kn-1/n [An]1/n = Kn-1/n [c/n]1/n

–   [A]: a part of aggregate,
–   [aggregate]  [normal concentration of A]/n
–   Butyl lithium initiator of anionic polymerization, rate  initiator 1/6
–   butyl lithium associate to hexamer
Reactant participating in equilibria

• A = B- + H+ (Ka)
– [B-]=Ka[A]/[H+]; [A] = [H+] [B-]/ Ka.;

– [A] + [B-] = [A]{([H+] + Ka)/[H+]}
–            = [B]{(Ka + [H+])/Ka} => a
– [B-] = a·Ka/(Ka + [H+])
– [A] = a·[H+]/(Ka + [H+])

– We can formulate rate equation by [A] & [B-]
– PH dependent
Opposing reaction

• AB        (k1)            B A               (k-1)
– dx/dt = k1(a-x) -k-1 x = k1a - k1x - k-1 x

– final equilibrium.
– k1(a-xe) = k-1 xe         k1a = (k1 + k-1)xe

– dx/dt = (k1 + k-1)(xe-x)
– ln {(xe)/(xe-x)} = (k1+k2)t
Isotope exchange reaction
• AX + BX* = AX* + BX
–   Assume      K=1  G = -RT ln K = 0
–   [AX]t=0 = a; [BX*]t=0 = b;    [AX*]t=0 = [BX]t=0 = 0
–   At equilibrium
–   x2/(a-x)(b-x) = 1  x = ab/(a+b)
–   [AX]= a-x = a2/{a+b}, [BX*]= b-x = b2/{a+b}
–   [AX*]= ab/{a+b}, [BX]= ab/{a+b}
–   [AX]t+ [AX*]t = a, [BX]t+ [BX*]t = b

dx      a  x  b  x  x 2 
                       
                    
dt      a  b  ab 
                       
dx      a  x  b  x  x 2 
                 
dt      a  b  ab 
– = {(a+b)/ab}(xe-x)
– Integration with x=0 at t=0
– ln{xe/(xe-x)} = {(a+b)/ab}t
– no information on reaction order for 
• Determined by initial rate with different a and b
•  = kn apbq
– ln{xe/(xe-x)} = kn ap-1bq-1 (a+b)t

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