kcHEAB ( h / kH2E A + 1 + kHE A / h ) (h / kH2EAB + 1 + kHEAB / h )
h kHEA \
kcHEAB 1 + kH2EA
h kHEAB
1 + kH2EAB h
This equation can be written in terms of pH and pKs.
kcHEAB (h / kH2EA + 1 + kHEA / h)
/ . h -» 10Λ-ρΗ / . kHEA -> 10A-pKlea / . kH2EA -» 10"-pK2ea / . (h / kH2EAB + 1 + kHEAB / h)
kHEAB-» 1 0 ' - p K l e a b / . kH2EAB -» 10~-pK2eab
( l + l0PH- PK l e a + 1 0- P H+P K 2 e a j k c H E A B
1 1 QpH-pKleab i /\-pH+pK2eab
This is the same as the expression for KB in Section 3.3.1.
The third term in the denominator yields kBklA/a b.
kcHEA kcHEAB kH2EAB (h2 + h kH2E + kH2E kHE) a b kH2E (h2 + h kH2EAB + kH2EAB kHEAB) klA is given by kB a b denominator term/kB
kcHEAB ( h / kH2E A + 1 + kHE A / h ) / kcHE A kcHEAB kH2EAB (h 2 + h kH2 E + kH2 E kHE ) (h / kH2EAB + 1 + kHEAB / h ) / kH2 E (h 2 + h kH2EAB + kH2EAB kHEAB) kH2E ( 1 + — 5 — + — ) (h 2 + h kH2EA B + kH2EA B kHEABΜ
^ kH2E A h ' V /
kcHEAkH2EAB (h 2 + h kH2 E + kH2EkHE ) ( l + - ^ — + ίΞΞ^.\
i ' \ kH2EAB h I
We expect
(l + ioPH-PKle + ι0-ΡΗ+Ρκ2β) kHEA 1 + lopH"pKlea + io~pH*pK2ea
Go back to the terms in the denominator and divide the term for kB kIA/ab by the term for kB/b to get klA/a.
kcHEA kcHEAB kH2EAB (h 2 + h kH2 E + kH2 E kHE ) , kcHEAB kH2EAB (h 2 + h kH2E A + kH2E A kHEA) a b kH2 E (h 2 + h kH2EAB + kH2EAB kHEAB) ' b kH2E A (h 2 + h kH2EAB + kH2EAB kHEAB kcHEA kH2E A (h 2 + h kH2 E + kH2 E kHE Μ
a kH2 E (h 2 + h kH2E A + kH2E A kHEA )
Since this is klA/a, multiply by a and divide numerator with kH2E and denominator kH2EA.
kcHEA (h 2 / kH2 E + h + kHE ) (h2 / kH2E A + h + kHEA) kcHEA f h + -5 — + kHE ) kH2E /
h + — — + kHE A
Divide numerator and denominator by h.
kcHEA (h / kH2E + 1 + kHE / h) (h / kH2EA + 1 + kHEA / h) kcHEA
1 + ( i +
h kH2E,
h kH2E +
kHEi - + \ h
kHE v h /
\
This can be expressed in terms of pKs and pH as follows:
kcHEA ( h / kH2 E + 1 + kH E / h )
/ . h - > 10"-p H / . kHE A - > 10~-pKle a / . kH2E A - » 10~-pK2e a / . (h / kH2E A + 1 + kHE A / h )
kHE -> 1 0 ~ - p K l e / . kH2E -> 1 0 " - p K 2 e (1 + 10PH"PKle + io-PH*PK2e) kcHEA
1 + i op H _ p K l e a + io"p H*p K 2 e a This is the same as in Section 3.3.1.
■ 3.3.5 The program calckinparsordABsimp can be used to determine when a pK\s missing
Assume species EA" is missing in the mechanism; or, in other words, assume that pÄTlea and kHEA are missing. The corresponding rate equation can be derived as follows:
Solv e [{kH E = = h * e / he , kH2 E = = h * h e / h2e , kH2E A = = h * he a / h2ea , kHEAB = = h * ea b / heab , kH2EAB = = h * hea b / h2eab , kcHE A = = h e * a / hea , kcHEAB = = he a * b / heab ,
et = = e + h e + h2 e + he a + h2e a + ea b + hea b + h2eab } , {heab} , {e , he , h2e , hea , h2ea , eab , h2eab} ] {{hea b - > ( a b e t h kH2 E kH2E A kH2EAB ) /
(a b h 2 kH2 E kH2E A + a h 2 kcHEA B kH2 E kH2EA B + h 2 kcHE A kcHEA B kH2E A kH2EA B +
a b h kH2 E kH2E A kH2EA B + a h kcHEA B kH2 E kH2E A kH2EA B + h kcHE A kcHEA B kH2 E kH2E A kH2EA B + kcHEA kcHEA B kH2 E kH2E A kH2EA B kH E + a b kH2 E kH2E A kH2EA B kHEAB) } }
velordABe a = ( a b k f e t h kH2 E kH2E A kH2EAB ) /
(a b h2 kH2 E kH2E A + a h2 kcHEAB kH2 E kH2EAB + h2 kcHE A kcHEAB kH2E A kH2EA B +
a b h kH2 E kH2E A kH2EAB + a h kcHEAB kH2 E kH2E A kH2EAB + h kcHE A kcHEAB kH2 E kH2E A kH2EAB + kcHEA kcHEAB kH2 E kH2E A kH2EA B kH E ta b kH2 E kH2E A kH2EAB kHEAB)
(a b h kfe t kH2 E kH2E A kH2EAB ) /
(a b h 2 kH2 E kH2E A + a h 2 kcHEA B kH2 E kH2EA B + h 2 kcHE A kcHEA B kH2E A kH2EA B +
a b h kH2 E kH2E A kH2EA B + a h kcHEA B kH2 E kH2E A kH2EA B + h kcHE A kcHEA B kH2 E kH2E A kH2EA B + kcHEA kcHEA B kH2 E kH2E A kH2EA B kH E + a b kH2 E kH2E A kH2EA B kHEAB)
simpvelordABe a = Simplify[velordABea ]
(a b h kfe t kH2 E kH2E A kH2EAB ) / (kcHE A kcHEA B kH2E A kH2EA B (h 2 + h kH2 E + kH2 E kHE ) + a kH2 E ( h kcHEA B ( h + kH2EA ) kH2EA B + b kH2E A (h 2 + h kH2EA B + kH2EA B kHEAB) ) ) The rate equation with the arbitrarily specified kinetic parameters is
vtestordAB2e a =
simpvelordABe a / . kH E - > 1 0 A - 7 / . kH2 E - » 1 0 A - 6 / . kH2E A - > 1 0 ~ - 6. 5 / . kHEA B - 1 0 A - 8 / . kH2EAB - » 1 0 Λ - 6 / . k f e t - » 2 / . kcHE A - » 5 / . kcHEA B - > 2 0
I
6.3245 6 x 10" 1* a b h 3.1622 8 x 1 0 "
' h (3..16228xl0-'+h ) -,
a I - ! '- + 3.1622 8 x IO" 7 b
10 00 0 00 0 00 0 00 0 100 0 00 0
_ 5 _ .
h2 ^
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1000000
1000 000
This equation can be used to calculate 9 velocities under the same conditions as Table 3.3.
vtestordAB2ea / . h -» 10 Λ - 8 / . a -> 200 / . b -» 200 / / N 0.934279
vtestordAB2e a / . h - » 1 0 ~ - 8 / . a - > l / . b - > 20 0 / / N 0.26253 1
vtestordAB2e a / . h - » 1 0 " - 8 / . a - > 20 0 / . b - > 1 / / N 0.071054 4
vtestordAB2e a / . h - 1 0 ~ - 7 / . a - > 20 0 / . b - » 2 0 0 / / N 1.4960 3
vtestordAB2e a / . h - » 1 0 " - 7 / . a - » l / . b - > 20 0 / / N 0.83976 4
vtestordAB2e a / . h - » 1 0 A- 7 / . a - > 20 0 / . b - > 1 / / N 0.069992 3
vtestordAB2e a / . h - > 1 0 ~ - 6 / . a - > 20 0 / . b - > 20 0 / / N 0.82254 5
vtestordAB2e a / . h - » 1 0 " - 6 / . a - » l / . b - » 20 0 / / N 0.57533 6
vtestordAB2e a / . h - » 1 0 ~ - 6 / . a - > 20 0 / . b - » 1 / / N 0.023173 5
Estimation of kinetic parameters.
calckinparsordABsimp[0.93428 , 1 0 Λ- 8 , 200 , 200 , 0.26253 , 1 0 Λ- 8 , 1 , 200 , 0.071054 , 1 0Λ- 8 , 200 , 1 , 1.4960 , 1 0 A- 7 , 200 , 200 , 0.83976 , 1 0 Λ- 7 , 1 , 200 , 0.069992 , 1 0 Λ- 7 , 200 , 1 , 0.82255 , 1 0 ~ - 6 , 200 , 200 , 0.57534 , 1 0 Λ- 6 , 1 , 200 , 0.023174 , 1 0 Λ- 6 , 200 , 1 ] { {k f e t - > 1.99994 , kHEA B - » 9 .9993 4 x IO" 9 ,
kHEA - > -1.1132 5 x IO" 13, kH E - > 1.0000 5 x 10" 7, kcHE A - > 4.9997 , kcHEA B - » 19.9997 , kH2 E - » 9.9993 4 x 10" 7, kH2E A - > 3.1624 5 x 10" 7, kH2EA B - > 1.0000 7 x 10" 6} }
Notice that kHEA is negative, which is impossible physically. The other 8 parameters are all correct, as shown by the Grid table used before. This is the way the computer program shows that the mechanism does not include EH A = E A" + H
+.
Grid[{{kHE , kH2E , kHEA, kH2EA, kHEAB, kH2EAB, kfet , kcREA, kcHEAB} , {10~-7 , 10 A-6 , 10 Λ-7.5 , 10 A-6.5 , 10 A-8 , 10~-6 , 2 , 5 , 20}} ] / / N
kHE kH2 E kHE A kH2E A kHEA B kH2EA B kfe t kcHE A kcHEA B l.xlO" 7 l.xlO" 6 3.16228x10 s 3.16228xl0" 7 l.xlO" 8 l.xlO" 6 2 . 5 . 20 .
Calculation of the effects of 5% errors.
Iine2 1 = {kfet , kHEAB, kHEA, kHE , kcHEA, kcHEAB, kH2E , kH2EA, kH2EAB} / .
calckinparsordABsimp[0.93428 , 10~-8 , 200 , 200 , 0.26253 , 10 A-8 , 1 , 200 , 0.071054 , 10Λ-8 , 200 , 1 , 1.4960 , 10 Λ-7 , 200 , 200 , 0.83976 , 10 Λ-7 , 1 , 200 , 0.069992 , 10 Λ-7 , 200, 1 , 0.82255 , 10~-6 , 200 , 200 , 0.57534 , 10 Á-6 , 1 , 200 , 0.023174 , 10*-6 , 200 , 1 ] {{1.99994 , 9.99934χ10" 9, - 1.11325χ1 0 " , 1 . 0000 5 χ 10" 7 ,
4.9997 , 19.9997 , 9.99934χ10" 7 , 3 .1624 5 χ 10" 7 , 1.00007χ10" 6}}
calckinparsordABsimp[1.0 5 * 0.93428 , 10 Λ-8 , 200 , 200 , 0.26253 , 10 Λ-8 , 1 , 200 , 0.071054 , 10Λ-8 , 200 , 1 , 1.4960 , 10 Λ-7 , 200 , 200 , 0.83976 , 10 Λ-7 , 1 , 200 , 0.069992 , 10 Λ-7 , 200, 1 , 0.82255 , 10 Á-6 , 200 , 200 , 0.57534 , 10"-6 , 1 , 200 , 0.023174 , 10 Λ-6 , 200 , 1 ] {{kfe t - > 1.97496 , kHEA B - > 8.7390 2 χ IO" 9,
kHEA - » -1.1132 5 χ IO" 13, kH E - > 1.049 6 x IO" 7, kcHE A - > 4.87322 , kcHEA B - > 19.7499 , kH2E - > 9.527 3 x IO" 7, kH2E A - > 3.1624 5 x IO" 7, kH2EA B - > 1.024 5 x IO" 6}}
line2 2 = {kfet , kHEAB, kHEA, kHE , kcHEA, kcHEAB, kH2E , kH2EA, kH2EAB} / .
calckinparsordABsimp[1.0 5 «0.93428 , IO"-8 , 200 , 200 , 0.26253 , 10*-8 , 1 , 200 , 0.071054 , 10"-8 , 200 , 1 , 1.4960 , 10 Λ-7 , 200 , 200 , 0.83976 , 10 Λ-7 , 1 , 200 , 0.069992 , 10 Λ-7 , 200, 1 , 0.82255 , 10~-6 , 200 , 200 , 0.57534 , 10 Λ-6 , 1 , 200 , 0.023174 , 10 Λ-6 , 200 , 1 ] {{1.97496 , 8.7390 2 χ IO" 9, - 1.1132 5 x IO" 13 , 1.0496χ10" 7,
4.87322 , 19.7499 , 9.5273xl0" 7, 3 .1624 5 x IO" 7 , 1 . 024 5 x IO" 6} }
calckinparsordABsimp[0.93428 , 10 Λ-8 , 200 , 200 , 1.05*0.26253 , 10 Λ-8 , 1 , 200 , 0.071054 , 10Λ-8 , 200 , 1 , 1.4960 , 10 Λ-7 , 200 , 200 , 0.83976 , 10 Λ-7 , 1 , 200 , 0.069992 , 10 Λ-7 , 200, 1 , 0.82255 , 10 Λ-6 , 200 , 200 , 0.57534 , 10Λ-6 , 1 , 200 , 0.023174 , 10 Λ-6 , 200 , 1 ]
{{kfe t - > 1.99994 , kHEA B - » 9.9993 4 χ IO" 9, kHE A - > 2.0494 4 x IO" 10, kH E ^8.4237xl0" 8, kcHE A -»5.4621 , kcHEAB - » 19.9547 , kH2 E - > 1.187 1 x IO" 6, kH2E A - » 3.153 3 x IO" 7, kH2EA B - » 1.0000 7 x IO" 6}}
line2 3 = {kfet , kHEAB, kHEA, kHE , kcHEA, kcHEAB, kH2E , kH2EA, kH2EAB} / .
calckinparsordABsimp[0.93428 , 10 A-8 , 200 , 200 , 1.05*0.26253 , 10"-8 , 1 , 200 , 0.071054 , 10A-8 , 200 , 1 , 1.4960 , 10 Λ-7 , 200 , 200 , 0.83976 , 10 Λ-7 , 1 , 200 , 0.069992 , 10 A-7 , 200, 1 , 0.82255 , 10 A-6 , 200 , 200 , 0.57534 , 10 Λ-6 , 1 , 200 , 0.023174 , 10 Λ-6 , 200 , 1 ] {{1.99994 , 9.9993 4 x IO" 9, 2 .0494 4 x IO" 10, 8.4237xl0" 8,
5.4621 , 19.9547 , 1.1871xl0" 6, 3.1533xl0" 7, 1 . 0000 7 x IO" 6} }
calckinparsordABsimp[0.93428 , 10 Λ-8 , 200 , 200 , 0.26253 , 10'-8 , 1 , 200 , 1.05*0.071054 , 10Λ-8 , 200 , 1 , 1.4960 , 10 Λ-7 , 200 , 200 , 0.83976 , 10 A-7 , 1 , 200 , 0.069992 , 10 Λ-7 , 200, 1 , 0.82255 , 10 Λ-6 , 200 , 200 , 0.57534 , 10 Λ-6 , 1 , 200 , 0.023174 , 10 Λ-6 , 200 , 1 ] {{kfe t - > 2.0016 , kHEA B - > 1.0083 3 χ IO" 8,
kHEA - > -7.4980 9 x IO" 10, kH E - > 1.0000 5 x IO" 7, kcHE A - > 4.95847 , kcHEA B ^20.1828 , kH2E - » 9.9993 4 x 10" 7, kH2E A - » 3.1963 9 x 10" 7, kH2EA B - > 9.9848 2 x 10" 7}}
line2 4 = {kfet , kHEAB, kHEA, kBE , kcHEA, kcHEAB, kH2E , kH2EA, kH2EAB} / .
calckinparsordABsimp[0.93428 , 10 A-8 , 200 , 200 , 0.26253 , 10'-8 , 1 , 200 , 1.05*0.071054 , 10~-8 , 200 , 1 , 1.4960 , 10~-7 , 200 , 200 , 0.83976 , 10 Λ-7 , 1 , 200 , 0.069992 , 10 Λ-7 , 200, 1 , 0.82255 , 10 Λ-6 , 200 , 200 , 0.57534 , 10 Λ-6 , 1 , 200 , 0.023174 , 10 Λ-6 , 200 , 1 ] {{2.0016 , 1.00833χIO" 8, - 7.49809χ1 0 " 10, 1.00005χ10" 7,
4.95847 , 20.1828 , 9.99934χ10" 7 , 3.19639χ10" 7 , 9.98482χ10" 7 } }
calckinparsordABsimp[0.93428 , 10"-8 , 200 , 200 , 0.26253 , 10 Λ-8 , 1 , 200 , 0.071054 , 10 Λ-8 , 200, 1 , 1.05*1.4960 , 10"-7 , 200 , 200 , 0.83976 , 10 Λ-7 , 1 , 200 , 0.069992 , 10 Λ-7 ,
200, 1 , 0.82255 , 10 Λ-6 , 200 , 200 , 0.57534 , 10 Λ-6 , 1 , 200 , 0.023174 , 10 Λ-6 , 200 , 1 ] {{kfe t - > 2.17332 , kHEA B - > 1.1724 6 χ IO" 8,
kHEA -> -1.1132 5 χ IO" 13, kH E - > 8.4880 9 x IO" 8, kcHE A - > 5.79748 , kcHEA B - » 21.7336 , kH2E - » 1.3770 3 x 10" 6, kH2E A - > 3.1624 5 x IO" 7, kH2EA B - » 8.5291 2 x 10" 7}}
line2 5 = {kfet , kHEAB, kHEA, kHE , kcHEA, kcHEAB, kH2E , kH2EA, kH2EAB} / .
calckinparsordABsimp[0.93428 , 10~-8 , 200 , 200 , 0.26253 , 10"-8 , 1 , 200 , 0.071054 , 10~-8 , 200, 1 , 1.05*1.4960 , 10 Λ-7 , 200 , 200 , 0.83976 , 10 Λ-7 , 1 , 200 , 0.069992 , 10 Λ-7 ,
200, 1 , 0.82255 , 10 Λ-6 , 200 , 200 , 0.57534 , 10 Λ-6 , 1 , 200 , 0.023174 , 10 Λ-6 , 200 , 1 ] {{2.17332 , 1.1724 6 χ IO" 8, - 1.1132 5 χ IO" 13 , 8 . 4880 9 χ 10" 8 ,
5.79748 , 21.7336 , 1.37703χ10" 6 , 3.16245χ10" 7 , 8.52912χ10" 7}}
calckinparsordABsimp[0.93428 , 10~-8 , 200 , 200 , 0.26253 , 10 Á-8 , 1 , 200 , 0.071054 , 10'-8 , 200, 1 , 1.4960 , 10 Λ-7 , 200 , 200 , 1.05*0.83976 , 10 Λ-7 , 1 , 200 , 0.069992 , 10 Λ-7 ,
200, 1 , 0.82255 , 10"-6 , 200 , 200 , 0.57534 , 10~-6 , 1 , 200 , 0.023174 , 10 Á-6 , 200 , 1 ] {{kfe t - » 1.99994 , kHEA B - > 9.9993 4 χ IO" 9,
kHEA - » -6.9971 4 x IO" 11, kH E - » 1.4365 5 x IO" 7, kcHE A - > 3.55323 , kcHEA B - » 20.1419 , kH2E - » 5.5851 2 x IO" 7, kH2E A - > 3.1920 3 x IO" 7, kH2EA B - > 1.0000 7 x IO" 6}}
line2 6 = {kfet , kHEAB, kHEA, kHE , kcHEA, kcHEAB, kH2E , kH2EA, kH2EAB} / .
calckinparsordABsim p [0.93428 , 10 Λ-8 , 200 , 200 , 0.26253 , 10 Λ-8 , 1 , 200 , 0.071054 , 10~-8 , 200, 1 , 1.4960 , 10 Λ-7 , 200 , 200 , 1.05*0.83976 , 10 A-7 , 1 , 200 , 0.069992 , 10 Λ-7 ,
200, 1 , 0.82255 , 10"-6 , 200 , 200 , 0.57534 , 10A-6 , 1 , 200 , 0.023174 , 10 A-6 , 200 , 1 ] {{1.99994 , 9.99934xIO" 9, -6.99714x10" n, 1.43655xIO" 7,
3.55323 , 20.1419 , 5.58512xIO" 7, 3.19203xIO" 7, 1 . 00007xIO" 6}}
calckinparsordABsimp[0.93428 , 10 Λ-8 , 200 , 200 , 0.26253 , 10"-8 , 1 , 200 , 0.071054 , 10 A-8 , 200, 1 , 1.4960 , 10 Λ-7 , 200 , 200 , 0.83976 , 10 A-7 , 1 , 200 , 1.05*0.069992 , 10 Λ-7 ,
200, 1 , 0.82255 , 10A-6 , 200 , 200 , 0.57534 , 10 Λ-6 , 1 , 200 , 0.023174 , 10 Λ-6 , 200 , 1 ] {{kfe t - > 1.98303 , kHEA B - » 9.83111xIO" 9,
kHEA - » 9.2269 9 x IO" 10, kH E - > 1.0000 5 x IO" 7, kcHE A - » 5.4657 , kcHEA B - > 18.1399 , kH2E - » 9.9993 4 x IO" 7, kH2E A - » 2.8176 1 x IO" 7, kH2EA B - » 1.0171 8 x IO" 6}}
line2 7 = {kfet , kHEAB, kHEA, kHE , kcHEA, kcHEAB, kH2E , kH2EA, kH2EAB} / .
calckinparsordABsimp[0.93428 , 10~-8 , 200 , 200 , 0.26253 , 10 A-8 , 1 , 200 , 0.071054 , 10 Λ-8 , 200, 1 , 1.4960 , 10"-7 , 200 , 200 , 0.83976 , 10"-7 , 1 , 200 , 1.05*0.069992 , 10 Λ-7 ,
200, 1 , 0.82255 , 10~-6 , 200 , 200 , 0.57534 , 10"-6 , 1 , 200 , 0.023174 , 10 Λ-6 , 200 , 1 ] {{1.98303 , 9.8311 1 x IO" 9, 9 . 2269 9 x IO" 10 , 1 . 0000 5 x IO" 7 ,
5.4657 , 18.1399 , 9.99934xIO" 7 , 2.81761xIO" 7 , 1.01718xIO" 6}}
calcklnparsordABsim p [0.93428 , 10"-8 , 200 , 200 , 0.26253 , 10 A-8 , 1 , 200 , 0.071054 , 10"-8 , 200, 1 , 1.4960 , 10 A-7 , 200 , 200 , 0.83976 , 10 A-7 , 1 , 200 , 0.069992 , 10 A-7 , 200 , 1 , 1.05*0.82255 , 10 A-6 , 200 , 200 , 0.57534 , 10 A-6 , 1 , 200 , 0.023174 , 10 Λ-6 , 200 , 1 ] {{kfe t - * 1.97161 , kHEA B - * 9.7289 8 x10" 9,
kHEA - > -1.1132 5 x 1 0 " 13, kH E - > 1.0323 2 x 10" 7, kcHE A - > 4.85604 , kcHEA B - > 19.7165 , kH2E - » 7.7006 5 x 10" 7, kH2E A - > 3.1624 5 x 10" 7, kH2EA B - > 1.1668 3 x 10" 6}}
line2 8 = {kfet , kHEAB, kHEA, kHE , kcHEA, kcHEAB, kH2E , kH2EA, kH2EAB} / .
calcklnparsordABsimp[0.93428 , 10"-8 , 200 , 200 , 0.26253 , 10 A-8 , 1 , 200 , 0.071054 , 10 A-8 , 200, 1 , 1.4960 , 10 A-7 , 200 , 200 , 0.83976 , 10 Λ-7 , 1 , 200 , 0.069992 , 10 A-7 , 200 , 1 , 1.05*0.82255 , 10 A-6 , 200 , 200 , 0.57534 , 10 A-6 , 1 , 200 , 0.023174 , 10 A-6 , 200 , 1 ] {{1.97161 , 9.7289 8 χ IO" 9, - 1.1132 5 χ IO" 13 , 1 . 0323 2 χ IO" 7 ,
4.85604 , 19.7165 , 7.70065x1 0 7, 3 .1624 5 x 10" 7 , 1.16683x10" 6}}
calcklnparsordABsimp[0.93428 , 10'-8 , 200 , 200 , 0.26253 , 10 Á-8 , 1 , 200 , 0.071054 , 10 Á-8 , 200, 1 , 1.4960 , 10 Á-7 , 200 , 200 , 0.83976 , 10 Á-7 , 1 , 200 , 0.069992 , 10 Λ-7 , 200 , 1 , 0.82255 , 10 Á-6 , 200 , 200 , 1.05*0.57534 , 10 Λ-6 , 1 , 200 , 0.023174 , 10 Á-6 , 200 , 1 ] {{kfe t - » 1.99994 , kHEA B - » 9.9993 4 χ IO" 9,
kHEA - > 9.2338 6 x IO" 12, kH E - > 9.5700 1 x IO" 8, kcHE A - » 5.21044 , kcHEA B - » 19.9792 , kH2E - > 1.6614 3 x IO" 6, kH2E A - > 3.1499 1 x IO" 7, kH2EA B - > 1.0000 7 x IO" 6}}
line2 9 = {kfet , kHEAB, kHEA, kHE , kcHEA, kcHEAB, kH2E , kH2EA, kH2EAB} / .
calcklnparsordABsimp[0.93428 , 10 A-8 , 200 , 200 , 0.26253 , 10'-8 , 1 , 200 , 0.071054 , 10 Λ-8 , 200, 1 , 1.4960 , 10 A-7 , 200 , 200 , 0.83976 , 10 A-7 , 1 , 200 , 0.069992 , 10 A-7 , 200 , 1 , 0.82255 , 10 A-6 , 200 , 200 , 1.05*0.57534 , 10 A-6 , 1 , 200 , 0.023174 , 10 A-6 , 200 , 1 ] {{1.99994 , 9.9993 4 x IO" 9, 9 .2338 6 x IO" 12 , 9.5700 1 x IO" 8,
5.21044 , 19.9792 , 1 . 66143xIO" 6 , 3.14991xIO" 7 , 1.00007xIO" 6}}
calcklnparsordABsimp[0.93428 , 10 A-8 , 200 , 200 , 0.26253 , 10 A-8 , 1 , 200 , 0.071054 , 10'-8 , 200, 1 , 1.4960 , 10 A-7 , 200 , 200 , 0.83976 , 10 A-7 , 1 , 200 , 0.069992 , 10 A-7 , 200 , 1 , 0.82255 , 10 A-6 , 200 , 200 , 0.57534 , 10 A-6 , 1 , 200 , 1.05*0.023174 , 10 A-6 , 200 , 1 ] {{kfe t - > 2.00505 , kHEA B - > 1.00481 x IO" 8,
kHEA - > -2.2612 3 x IO" 10, kH E - > 1.0000 5 x IO" 7, kcHE A - > 4.8754 , kcHEA B - » 20.5621 , kH2E - > 9.9993 4 x IO" 7, kH2E A - » 3.499 6 x IO" 7, kH2EA B - * 9.7492 1 x IO" 7}}
line3 0 = {kfet , kHEAB, kHEA, kHE , kcHEA, kcHEAB, kH2E , kH2EA, kH2EAB} / .
calcklnparsordABsimp[0.93428 , 10"-8 , 200 , 200 , 0.26253 , 10 A-8 , 1 , 200 , 0.071054 , 10 A-8 , 200, 1 , 1.4960 , 10 A-7 , 200 , 200 , 0.83976 , 10 A-7 , 1 , 200 , 0.069992 , 10 A-7 , 200 , 1 , 0.82255 , 10 A-6 , 200 , 200 , 0.57534 , 10 A-6 , 1 , 200 , 1.05*0.023174 , 10 Λ-6 , 200 , 1 ] {{2.00505 , 1.0048 1 x IO" 8, - 2 . 2612 3 x IO" 10 , 1 . 0000 5 x IO" 7 ,
4.8754 , 20.5621 , 9 . 9993 4 x IO" 7 , 3.4996xl0" 7, 9 . 7492 1 x IO" 7 } }
Table 3.5 Application of calckinparsordABsimp to data for a mechanism without HEA = EA~ + H+, that is without kHEA or pKlea.
The following pairs of substrate concentrations have been used: {200,200}, {1,200}, and {200,1}.
TableForm[
The negative logarithms have been used as entries because it is easier to interpret pÄ"s. The imaginary terms are obtained for pKlea because
Log[10, - 1 ] i π Log[10]
There are negative values for pKlea 7 times out of 10. The pKs 9.69, 9.03, and 11.03 are outside the range that can be deter-mined when the velocity measurements are limited to the pH 6 to 8 range.
This calculation is an example of the statement earler [32] that "When a reaction is studied for the first time, there is an advan-tage in using the most general mechanism available for that type of reaction."
3.4 Effects of pH on the kinetics of ordered A + B -* products when a hydrogen ion is consumed in the rate-determining reaction
There are two different ways that hydrogen ions are involved in the thermodynamics and rapid-equilibrium kinetics of reactions at a specified pH. In addition to the effects of pKs, an integer number of hydrogen ions may be consumed in the rate-determining reaction. This is often the case for reactions involving NAD. Up to 8 hydrogen ions may be consumed in reductase reactions [23,26MathSource4]. When a single hydrogen ion is consumed, the last reaction in the mechanism in Section 3.2 is replaced with