6690-7-24E
AID: 1112 | 30/08/2016
The rate law expressio is as !ollows: r = k [ A ]
x
[ "]
y
[ A]
[ "]
#here $ is the rate %ostat& a' are the %o%etratio o! the spe%ies A a' "& x "& x a' y a' y are are the partial or'ers o! a rea%tio( The rate o! a %he)i%al rea%tio is 'e!ie' as the rate o! %ha*e o! %o%etratio o! rea%tats a' pro'+%ts whi%h is *i,e . . the expressio: d [ / ] rate = − dt d [ 0]
=
dt
[ ]
[ 0]
#here& 'eotes the %o%etratio o! rea%tat a' 'eotes the %o%etratio o! pro'+%t( ate o! the rea%tio !or the rea%tio *i,e elow is represete' as !ollows: A → 2" rate3 rate =
'pro'+%t 't 1 ' '" 2 't
=−
=−
'rea%tat
'A 't
't
= k A
#here k is the rate %ostat( osi'er this rea%tio *i,e elow& 5 1 ˆ ˆˆk ˆ† 16 A 7 " ‡ ˆˆ ˆˆ A k −1
26 A5 74 → 0ro'+%t A7 " 74 → 0ro'+%t
ere ere&& i this this rea% rea%ti tio o A repres represe ets ts the the )ole )ole%+ %+le le whi% whi%h h rea%t rea%tss with with " to !or) !or) a iter)e'iate a' is i e+iliri+)( or)atio o! pro'+%t !ollows a %ertai )e%hais) *i,e ao,e as !ollows: ;tep 1 represets a e+iliri+) rea%tio( ;tep 2 represets the !+rther rea%tio o! A5 with (
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ere A5 is a stea'. ,ariale whi%h is preset i the rea%tio +t either as rea%tat or pro'+%t i the o,erall rea%tio a' th+s the rate o! rea%tio o! s+%h iter)e'iate is approximation( The %osi'ere' al)ost e+al to
The *i,e a%i' %atal.
k ( 2 ) 8A8 + + "→
2
" +8 +
8A ( slow )
I the !irst rea%tio& as the rea%tio is i e+iliri+) so& rate o! !orwar' rea%tio is e+al to rate o! a%$war' rea%tio writte as !ollows: + k1 [ 8A ] 8 + = k −1 8A8
8A8 + = k −1 [ 8A ] 8 + k 1
k
8A8 + = 1 [ 8A] 8 + k −1 8A8
+
is the iter)e'iate here a' is i,ol,e' i rapi' pre e+iliri+)( k 8A8 + = 1 [ 8A] 8 + k −1 == >1 The rate o! !or)atio o! pro'+%t is& d " + rate = dt k 2
The rate law expressio !or the !or)atio o! pro'+%t with rate %ostat r
=
+
d "8
dt
= k 8A8 + " 2 [ ]
is as !ollows:
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+
d "8
dt
= k2 k 1 8A 8 + " [ ] [ ] k −1
== >2 +
d "8
dt
= k 2 k 1 8A 8 + " [ ] [ ] k −1
e%e& the rate law expressio is
(
8 + The ao,e expressio is the rate o! !or)atio o! pro'+%t a' %otais the ter) 8 + 8 + rate law expressio %a e%o)e i'epe'et o!
i! the so+r%e o!
[ 8A]
[ 8A ]
& the aother e+iliri+) represets the ioi
& the
is the a%i' 8 + to *i,e
as
K a
The e+iliri+) %ostat 8 + A − K a = [ 8A]
is *i,e as !ollows:
It is %osi'ere' that e+al %o%etratios o! proto a ' aio is release' . the a%i' so& 8 + = A −
;o& the expressio !or e+iliri+) %ostat !or the ioi
8 + A − K a =
[ 8A]
8 + =
2
[ 8A]
8 + = K a [ 8A ]
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+
d "8
dt
= = =
k2 k 1 k −1 k2 k 1 k −1
[ 8A] 8 + [ "] [ 8A]
k2 k1 ( K a )
[
K a 8A
1/2
] [ "]
3/ 2
[ 8A] [ "] k −1
8 + e%e&
the +
d "8
dt
=
rate
k 2 k1 ( K a )
1/2
expressio 3/2
[ 8A ] [ "] k −1
(
i'epe'et
o!
the
ter)
is