Nonconventional versus conventional application of pseudo-first-order kinetics to fundamental organic reactions

Article abstract of DOI:10.1002/kin.20609

Three new analysis procedures for pseudo-first-order kinetics are introduced and applied to eight different fundamental organic reactions. The reactions belong to the following classes: nitroalkane proton transfer, formal hydride ion transfers from NADH model compounds, and S_N2 reactions of alkyl halides with ionic and neutral nucleophiles. The three methods consist of (1) half-life dependence of k_app, (2) sequential linear pseudo-first-order correlation, and (3) revised instantaneous rate constant analysis. Each of the three procedures is capable of distinguishing between one- and multistep mechanisms, and the combination of the three procedures provides a powerful strategy for differentiating between the two mechanistic possibilities. The data from the eight reactions chosen as examples clearly show how the procedures work in practice.

Full text of DOI:10.1002/kin.20609

Nonconventional versus
Conventional Application of
Pseudo-First-Order Kinetics
to Fundamental Organic
Reactions
VERNON D. PARKER, WEIFANG HAO, ZHAO LI, RUSSELL SCOW
Department of Chemistry and Biochemistry, Utah State University, Logan, UT 84322-0300
Received 28 May 2011; revised 20 July 2011; accepted 20 July 2011
DOI 10.1002/kin.20609
Published online 26 September 2011 in Wiley Online Library (wileyonlinelibrary.com).
ABSTRACT: Three new analysis procedures for pseudo-first-order kinetics are introduced and
applied to eight different fundamental organic reactions. The reactions belong to the fol-
lowing classes: nitroalkane proton transfer, formal hydride ion transfers from NADH model
compounds, and SN2 reactions of alkyl halides with ionic and neutral nucleophiles. The three
methods consist of (1) half-life dependence of kapp, (2) sequential linear pseudo-first-order
correlation, and (3) revised instantaneous rate constant analysis. Each of the three procedures
is capable of distinguishing between one- and multistep mechanisms, and the combination of
the three procedures provides a powerful strategy for differentiating between the two mecha-
nistic possibilities. The data from the eight reactions chosen as examples clearly show how the
procedures work in practice. ꢀ 2011 Wiley Periodicals, Inc. Int J Chem Kinet 44: 2–12, 2012
C
was the most important kinetic technique used by the
vast majority of physical organic chemists. Aside from
the development of very rapid kinetic techniques, es-
sentially no improvements were made in the methods
for which so many rate constants were measured for
linear free-energy relationships. This is evident from
the classic book Kinetics and Mechanism, by J. W.
Moore and R. G. Pearson, published in 1981 [3]. This
deficiency continued for the remainder of the 20th cen-
tury. The digital revolution occurred during the time
period of the development of physical organic chem-
istry. The latter had a great influence on the work of
the physical chemists studying rapid kinetics but did
not filter down to the physical organic chemists mea-
suring rate constants of slower reactions. The objective
INTRODUCTION
In 1997, Professor George S. Hammond published a
short article entitled “Physical Organic Chemistry after
50 Years: It Has Changed, but Is It Still There?” [1]. In
this article, Hammond summarized the remarkable de-
velopments in the subdiscipline since it began with the
work of Hammett [2]. No mention was made of the de-
velopment of pseudo-first-order kinetic method, which
Correspondence to: Vernon D. Parker; e-mail: vernon.parker@
usu.edu.
Contract grant sponsor: National Science Foundation.
Contract grant number: ARRA: CHE-0923654.
2011 Wiley Periodicals, Inc.
c
ꢀ

NONCONVENTIONAL VERSUS CONVENTIONAL APPLICATION PSEUDO-FIRST-ORDER KINETICS
3
Table I Changes in the Slopes and the Intercepts with
the Extent of Reaction during Conventional
Pseudo-First-Order Analysis of the Reaction of
Phenoxide Ion with Methyl Iodide in Acetonitrile at
298 K
of our work is to fill the gap by introducing work on
the fundamental reactions of organic chemistry using
new methods, which take advantage of modern digi-
tal acquisition of absorbance–time data and extensive
new data analysis of pseudo-first-order kinetics. Dur-
ing the current century, several papers have appeared
that deal with inadequacy of a simple fit of an expo-
nential curve to establish a simple one-step mechanism
[4]. The work of Korma´nyos and coworkers [4b], en-
titled “Inherent Pitfalls in the Simplified Evaluation of
Kinetic Curves,” is particularly relevant to the topic of
this paper. A more mathematical approach is presented
for the analysis of the kinetics of complex systems in
[4c]. The work of Nagy and Tura´nyi [4a] deals with the
effect of uncertainties in rate constants on the reliability
of the corresponding activation parameters.
k
app
(s−1
)
Intercept (s−1
)
Number of HL
0.0125
0.0125
0.0121
0.0117
0.0111
0.0116
0.0123
0.0223
0.0445
0.0832
0.5
1.0
2.0
3.0
4.0
ER is the extent of reaction. The latter are then sub-
jected to linear least-squares analysis on five differ-
ent segments of the data over time ranges correspond-
ing to 0–0.5 half-lives (HL), 0–1 HL, 0–2 HL, 0–3
HL, and 0–4 HL. The data for the reaction of phe-
noxide ion (0.5 mM) with MeI (51.4 mM) in ace-
tonitrile at 298 K are summarized in Table I. In this
case, the data show that the values (0.0125 s−1) of the
apparent pseudo-first-order rate constant (kapp) over
the first two data segments were identical within ex-
perimental error. Values obtained for longer segments
of the data (1.0–4.0 HL) steadily decreased with de-
gree of conversion. While the changes in kapp observed
are modest, the corresponding changes in the zero-
time intercepts are much larger and suggest that this
parameter is much more sensitive to the deviations
from first-order kinetics than kapp is. Obviously, the
response expected for the single-step mechanism is a
constant value of kapp and an intercept independent of
the number of HL taken into the linear least-squares
correlation.
The kinetic response of a wide variety of reactions
will be covered without mechanism discussions. In-
stead we will present the results of the application
of three different nonconventional pseudo-first-order
procedures on the data. The data presented for each
reaction result from a single set of stopped-flow ex-
periments carried out over the course of one day. In
all cases, the data presented are a minute fraction of
the body of data available in our laboratory for each of
these reactions, but at the same time are representative
of the latter. The purpose of this type of presentation
is to allow readers to assess the data without being
influenced by the author’s views on the mechanistic
implications of the data.
EXPERIMENTAL METHODS AND DATA
PROCESSING
The methods discussed are limited to three general pro-
cedures, and the first is a more detailed application of
the conventional pseudo-first-order kinetic relationship
in a way that in some cases clearly distinguishes be-
tween simple single-step and complex multistep mech-
anisms. When a complex mechanism is indicated, the
other two procedures provide data, which give more
details of the kinetic response and can verify that the
reaction follows a complex mechanism. The methods
are discussed using experimental data for the SN2 reac-
tion of phenoxide ion with methyl iodide in acetonitrile
at 298 K.
Sequential Pseudo-First-Order Linear
Correlation
This analysis has been described in our recent pa-
pers [5–7]. The procedure involves recording 2000-
point Abs–time profiles over about the first HL of
the reaction. Linear least-squares analysis is then car-
ried out over the following point segments: 1–11,
1–21, 1–31, 1–41, 1–51, 1–101, 1–201, . . . , 1–1901.
This gives 24 kapp values at the midpoints of the
segments.
Standard deviations (SD) of the kapp evaluated for
multiple (normally 20) stopped-flow shots are then
recorded. The analysis is illustrated in Table II for
the reaction of phenoxide ion with methyl iodide in
acetonitrile at 298 K.
Half-Life Dependence of Conventional
Pseudo-First-Order Rate Constants
The procedure involves converting absorbance–time
profiles (Abs–t) to −ln (1 – ER)–time profiles, where
International Journal of Chemical Kinetics DOI 10.1002/kin

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PARKER ET AL.
Table II Apparent Rate Constants and Standard
Deviations Obtained by the 24-Point Sequential
Analysis of the Reaction of Methyl Iodide with
Phenoxide Ion in Acetonitrile at 298 K
[MeI] = 51.4 mM in AN at 298 K
treated with 1.4 mM PO
0.04
0.03
[PO−] = 0.5 mM, 305 nm
Time (s)
k
app
(s−1
)
SD (s−1
)
Segment
−1
kapp /s
0.14
0.27
0.40
0.53
0.66
1.31
2.61
3.91
5.21
0.0444
0.0324
0.0263
0.0230
0.0207
0.0157
0.0136
0.0132
0.0130
0.0130
0.0130
0.0130
0.0130
0.0130
0.0130
0.0130
0.0130
0.0130
0.0130
0.0130
0.0130
0.0130
0.0129
0.0129
0.01016
0.00433
0.00191
0.00117
0.00081
0.00034
0.00015
0.00007
0.00006
0.00005
0.00005
0.00005
0.00005
0.00005
0.00005
0.00005
0.00005
0.00005
0.00005
0.00005
0.00006
0.00006
0.00006
0.00006
1
2
3
4
5
6
7
8
0.02
0.01
0
5
10
15
20
25
Time/s
Figure 1 Apparent rate constants (kapp)–time plot for the
reaction between phenoxide ion and methyl iodide in ace-
tonitrile at 298 K (1.0 HL = 48.6 s).
9
6.51
7.81
9.11
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
A New Procedure for the Estimation of
Instantaneous Rate Constant–Time Profiles
10.41
11.71
13.01
14.31
15.61
16.91
18.21
19.51
20.81
22.11
23.41
24.71
An obvious extension of the method discussed above
is to include additional correlations. To do this, the
points in the data segment are 1–3, 1–4, 1–5, 1–6,
. . . , 1–2000, and a 1998-point array of kapp–time data
is obtained. The procedure was applied to calculated
–ln (1 – ER)–time profiles, and the results were then
compared to instantaneous rate constant (IRC)–time
(kinst–time) profiles obtained at the midpoint between
all points, as presented earlier [8]. The comparison
showed that the kapp–time values at short times, as well
as those near the end of the 1998-point array, were
nearly identical to the corresponding kinst values. The
largest deviations (about 5%) were found in values
near the center of the correlation. It was concluded that
for all practical purposes the values obtained by the
new procedure are equivalent to kinst values, and the
term kIRC is appropriate to distinguish between the two
different IRCs. The plot in Fig. 2 shows the application
of the procedure outlined above.
The SD value for segment 1 is nearly 25% of the
kapp value, and SD falls dramatically until it stabilizes
to about 5% of the corresponding kapp from segments
8 to 24. The reason for the large SD in the early seg-
ments is related to the small number of points used in
the linear correlations of the data in these segments.
Each stopped-flow experiment is generally repeated at
least three times. The expected result (20 shots) of the
24-point procedure for the single-step mechanism is a
rate constant, independent of time and of the particular
time segment analyzed.
Although the primary purpose of this method is to
estimate the errors in kapp, the plot shown in Fig. 1 pro-
vides a convenient visual representation of the data,
showing an initial high value and the subsequent de-
cay to a plateau value as steady state is reached in about
2–3 s. The expected result of the 24-point procedure
for the single-step mechanism is a rate constant, in-
dependent of time and of the particular time segment
analyzed.
PROTON TRANSFER REACTIONS
OF NITROALKANES
Proton Transfer Reactions of the Simple
Nitroalkanes
The well-known phenomenon referred to as the ni-
troalkane anomaly was named by Kresge [9] to de-
scribe the inverse relationship between the equilibrium
and kinetic acidities of nitromethane, nitroethane, and
2-nitropropane (2-NP) in aqueous solution. Kresge,
and all others who have studied these reactions, treated
the data as arising from a simple single-step process.
International Journal of Chemical Kinetics DOI 10.1002/kin

NONCONVENTIONAL VERSUS CONVENTIONAL APPLICATION PSEUDO-FIRST-ORDER KINETICS
5
Table IV Apparent Rate Constants and Standard
Deviations Obtained by the 24-Point Sequential
Analysis of the Reaction of 2-NP (0.2 mM) with
Hydroxide Ion (100 mM) in Water at 298 K
0.060
0.045
[MeI] = 51.4 mM in AN at 298 K
treated with 1.4 mM PO
[PO−] = 0.5 mM, 305 nm
kIRC/s−1
Time (s)
k
app
(s−1
)
SD (s−1
)
Segment
0.030
0.14
0.25
0.36
0.47
0.59
1.15
2.27
3.40
4.52
5.65
6.77
7.90
9.02
10.15
11.27
12.40
13.52
14.65
15.77
16.90
18.02
19.15
20.27
21.40
0.0250
0.0223
0.0218
0.0216
0.0214
0.0209
0.0201
0.0195
0.0189
0.0185
0.0182
0.0179
0.0177
0.0175
0.0174
0.0172
0.0171
0.0170
0.0169
0.0168
0.0168
0.0167
0.0166
0.0166
0.0045
0.0013
0.0012
0.0008
0.0006
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
1
2
3
4
5
6
7
8
0.015
0
5
10
15
Time/s
20
25
Figure 2 Apparent IRC (kIRC)–time plot for the reaction
between phenoxide ion and methyl iodide in acetonitrile at
298 K (1.0 HL = 48.6 s).
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Scheme 1
We have recently [6] reinvestigated the reactions and
observed significant deviations from pseudo-first-order
behavior. Here we take 2-NP as an example and show
how detailed pseudo-first-order kinetics distinguish be-
tween single- and multistep mechanisms for the reac-
tions of the simple nitroalkanes with hydroxide ion in
water.
deviations from first-order kinetics. The deviations of
both of these quantities from that expected for first-
order kinetics are a clear indication of the operation of
a complex mechanism.
The 24-point sequential correlation of abs–time data
over 1 HL (Table IV) for the reactions of 2-NP not
only verifies the time dependence of kapp but also pro-
vides standard deviations of the latter for repetitive
stopped-flow shots. As observed before, the SD are
greatest for the initial kapp values but decrease steadily
over the first six segments and then goes to a con-
stant value equal to 1% or less of the corresponding
The HL dependence of kapp for the proton trans-
fer reaction between 2-NP and hydroxide ion in water
(Scheme 1) obtained by the application of the pseudo-
first-order linear least-squares procedure is illustrated
by the data given in Table III. Once again, the change
in kapp as a function of number of HL analyzed is
modest but the trend of decreasing rate constants with
increases in the latter is significant and reproducible.
The observed intercepts are much more sensitive to the
kapp
.
Table III Changes in the Slopes and the Intercepts
with the Extent of Reaction during Conventional
Pseudo-First-Order Analysis of the Reaction of 2-NP (0.2
mM) with Hydroxide Ion (100 mM) in Water at 298 K
The IRC–time profile for product formation dur-
ing the reaction of 2-NP (0.2 mM) with hydroxide ion
(100 mM) in water (Fig. 3) sharply decreases from
about 0.03 s−1 at short times to a more slowly decreas-
ing profile near 0.015 s−1 at 1 HL. The expected result
for the one-step mechanism is a straight line with zero
slope, while that for a complex mechanism increases
from zero at short times when only product absorbs
at the experimental wavelength. On the other hand, an
initial decreasing IRC–time profile at a wavelength the
k
(s−1
)
Intercept (s−1
)
Number of HL
app
0.0182
0.0171
0.0168
0.0165
0.0163
0.0017
0.0104
0.0178
0.0270
0.0404
0.5
1.0
2.0
3.0
4.0
International Journal of Chemical Kinetics DOI 10.1002/kin

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PARKER ET AL.
Table V Changes in the Slopes and the Intercepts with
the Extent of Reaction during Conventional
Pseudo-First-Order Analysis of the Reaction of PNM
(0.0518 mM) with Hydroxide Ion (4.0 mM) in Water at
298 K
0.0375
0.0300
[2-NP] = 0.2 mM in water at 298 K
[NaOH] = 0.10 M
240 nm
(s−1
)
Intercept (s−1
)
Number of HL
k
IRC /s−1
k
app
0.440
0.433
0.420
0.398
0.356
−0.001
0.001
0.012
0.043
0.136
0.50
1.00
2.00
3.00
4.00
0.0225
0.0150
0
5
10
15
20
25
Time/s
Figure 3 Apparent IRC (kIRC)–time plot for the reaction
of 2-NP (0.2 mM) with hydroxide ion (100 mM) in water at
298 K (1.0 HL = 40.6 s).
Table VI Apparent Rate Constants and Standard
Deviations Obtained by the 24-Point Sequential
Analysis of the Reaction of PNM (0.0518 mM) with
Hydroxide Ion (4.0 mM) in Water at 293 K
Time (s)
k
(s−1
)
SD (s−1
)
Segment
app
product but not the reactant absorbs indicates that a re-
action intermediate is responsible for the initial sharp
decrease in absorbance.
0.006
0.011
0.016
0.021
0.026
0.051
0.101
0.151
0.201
0.251
0.301
0.351
0.401
0.451
0.501
0.551
0.601
0.651
0.701
0.751
0.801
0.851
0.901
0.951
0.403
0.138
0.043
0.030
0.020
0.015
0.009
0.004
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
1
2
3
4
5
6
7
8
0.426
0.434
0.442
0.442
0.449
0.447
0.445
0.444
0.444
0.443
0.443
0.442
0.441
0.441
0.440
0.439
0.438
0.438
0.437
0.436
0.435
0.435
0.434
Proton Transfer Reactions of
Phenylnitroalkanes in Water
The proton transfer reactions of phenylnitromethane
(PNM) in water and in water–DMSO mixture have
been studied extensively by Bernasconi [10], and the
results have played a prominent role in discussion of
the principle of nonperfect synchronization [11]. A
recent paper on proton transfer reactions of PNMs
was concerned with the implications on the nitroalkane
anomaly [12].
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
The conventional pseudo-first-order study of the
reaction of PNM with hydroxide ion in water
(Scheme 2) is illustrated by the data presented in
Table V, in which kapp decreases steadily from 0.440
over 1 HL to 0.356 s−1, while the intercept increased
over the same range from −0.001 to 0.136.
The 24-point sequential analysis shows more detail
as illustrated in Table VI. The value of kapp in segment
1 was observed to be equal to 0.403, and then rises
smoothly to a maximum value of 0.449 at segment 6
and then decreases steadily to 0.434 s−1 at segment 24.
The value of SD changes from about 20% of kapp to
<1% from segments 6 to 24.
The kIRC–time profile for product formation for the
reaction of PNM under these conditions shows an ini-
tial value close to 0.6 s−1, decreases sharply to about
0.34 s−1 at about 10 ms, and then rises more slowly to
0.43 s−1 at about 60 ms and is approximately constant
for the remainder of the reaction period analyzed (see
Fig. 4).
Scheme 2
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NONCONVENTIONAL VERSUS CONVENTIONAL APPLICATION PSEUDO-FIRST-ORDER KINETICS
7
Table VIII Apparent Rate Constants and Standard
Deviations Obtained by the 24-Point Sequential
Analysis of the Reaction of BNAH (7.2 mM) with MA+
(0.3 mM) in AN at 298 K
[PNM] = 0.0518 mM
[NaOH] = 4.0 mM
in H2O at 293 K
0.6
0.5
294 nm
Time (s)
k
app
(s−1
)
SD (s−1
)
Segment
kIR C /s−1
0.008
0.012
0.016
0.019
0.023
0.041
0.077
0.113
0.150
0.186
0.222
0.258
0.294
0.331
0.367
0.403
0.439
0.475
0.512
0.548
0.584
0.620
0.656
0.693
1.553
0.574
0.225
0.122
0.118
0.100
0.022
0.015
0.016
0.014
0.011
0.008
0.006
0.005
0.004
0.004
0.004
0.004
0.004
0.004
0.005
0.005
0.006
0.006
0.006
1
2
3
4
5
6
7
8
1.393
1.236
1.106
1.002
0.795
0.679
0.626
0.599
0.584
0.573
0.567
0.561
0.557
0.555
0.553
0.551
0.549
0.548
0.546
0.545
0.543
0.542
0.541
0.4
0.3
0.00 0.05 0.10 0.15 0.20 0.25
Time/s
Figure 4 Apparent IRC (kIRC)–time plot for the reaction
of PNM (0.052 mM) with hydroxide ion (4.0 mM) in water
at 298 (1.0 HL = 1.593 s).
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
FORMAL HYDRIDE TRANSFER
REACTIONS OF NADH MODELS
The Reaction of Beta-N-acetyl
hexosaminidase (BNAH) with
N-Methylacridinium Ion (MA+) in
Acetonitrile
Detailed studies of the reactions of BNAH and analogs
with substituted isoquinolinium cations were published
by Bunting and coworkers [13a–c] in the early 1980s
and were later reviewed [13d].
Conventional pseudo-first-order analysis of the
BNAH–MA+ reaction (Scheme 3) illustrated in
Table VII reveals that kapp varies smoothly from 0.564
for 0.5 HL to 0.502 for the 4 HL analysis, approxi-
mately a change of 10% over that range. In this case,
reactant (MA+) decay was monitored at 430 nm and
kapp was equal to 1.553 for segment 1, 0.584 for seg-
ment 10, and finally 0.541 for segment 24 (Table VIII).
The SD values were large in the early segments and
were of the order of 1% of the corresponding kapp from
segment 11 onward.
The kIRC–time profile (Fig. 5) has the form expected
for reactant decay in a complex mechanism decaying
rapidly from an initial value of close to 2.0 s−1 before
approaching a very slowly descending value at times
greater than about 1.5 s.
The Reaction of
N-Methyl-9,10-dihydroacridine (MAH) with
Tropylium Ion (Tr+) in Acetonitrile
We are not aware of previous studies of the reaction be-
tween MAH and Tr+ (Scheme 4). This system has the
experimental advantage that Tr+ does not absorb above
300 nm, leaving a large wavelength range over which
to monitor product (MA+) formation in acetonitrile.
The conventional pseudo-first-order analysis in
this case follows the general pattern that is emerg-
ing, a kapp value of 0.245 s−1 (1 HL) and de-
creasing smoothly to 0.190 s−1 (4 HL). The corre-
sponding intercepts increase from 0.0064 (0.5 HL)
to 0.0973 (4 HL), a factor of about 15 indicat-
ing a great deal of curvature in the correlation
(Table IX).
Table VII Changes in the Slopes and the Intercepts
with the Extent of Reaction during Conventional
Pseudo-First-Order Analysis of the Reaction of BNAH
(7.2 mM) with MA+ (0.3 mM) in Acetonitrile at 298 K
k
app
(s−1
)
Intercept (s−1
)
Number of HL
0.564
0.536
0.522
0.513
0.502
0.013
0.020
0.029
0.039
0.056
0.50
1.00
2.00
3.00
4.00
International Journal of Chemical Kinetics DOI 10.1002/kin

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PARKER ET AL.
Scheme 3
Scheme 4
2.0
[BNAH] = 7.2 mM in AN at 298 K
[MA ClO − ] = 0.3 mM, 430 nm
+
4
1.5
IRC/s−1
k
Table X Apparent Rate Constants and Standard
Deviations Obtained by the 24-Point Sequential
Analysis of the Reaction of MAH (0.2 mM) with Tr+
(50 mM) in Acetonitrile at 298 K
1.0
0.5
Time (s)
k
app
(s−1
)
SD (s−1
)
Segment
0.0
0.2
0.4
0.6
0.8
0.014
0.026
0.039
0.051
0.064
0.126
0.251
0.376
0.501
0.626
0.751
0.876
1.001
1.126
1.251
1.376
1.501
1.626
1.751
1.876
2.001
2.126
2.251
2.376
0.699
0.027
0.014
0.009
0.008
0.007
0.005
0.003
0.002
0.002
0.002
0.002
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
1
2
3
4
5
6
7
8
Time/s
0.563
0.488
0.442
0.407
0.326
0.281
0.266
0.258
0.252
0.248
0.245
0.242
0.239
0.237
0.235
0.233
0.231
0.229
0.228
0.226
0.225
0.223
0.222
Figure 5 Apparent IRC (kIRC)–time plot for the reaction
of BNAH (7.2 mM) with MA+ (0.3 mM) in acetonitrile at
298 K.
Table IX Changes in the Slopes and the Intercepts
with the Extent of Reaction during Conventional
Pseudo-First-Order Analysis of the Reaction of MAH (0.4
mM) with Tr+ (0.05 M) in Acetonitrile at 298 K
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
k
(s−1
)
Intercept (s−1
)
Number of HL
app
0.245
0.225
0.206
0.190
0.0064
0.0199
0.0499
0.0973
0.50
1.00
2.00
3.00
The 24-point sequential analysis for product evo-
lution (MA+) in this case, once again a sharply de-
creasing kapp from 0.699 at segment 1 to a more slowly
decreasing 0.266 s−1 at segment 8 and finally at seg-
ment 24, kapp equals 0.222 s−1 (Table X).
International Journal of Chemical Kinetics DOI 10.1002/kin

NONCONVENTIONAL VERSUS CONVENTIONAL APPLICATION PSEUDO-FIRST-ORDER KINETICS
9
Table XI Changes in the Slopes and the Intercepts
with the Extent of Reaction during Conventional
Pseudo-First-Order Analysis of the Reaction of MAH
0.8
(40 mM) with BQCN+ (0.5 mM) in Acetonitrile at 298 K
[MAH] = 0.4 mM in AN at 298 K
[Tr+] = 0.05 M, 430 nm
k
app
(s−1
)
Intercept (s−1
)
Number of HL
0.6
kIRC/s−1
0.4
0.00095
0.00116
0.00148
0.00171
0.00186
−0.029
−0.066
−0.152
−0.241
−0.312
0.50
1.00
2.00
3.00
4.00
0.2
0.0
0.5
1.0
1.5
2.0
2.5
Time/s
Figure 6 Apparent IRC (kIRC)–time plot for the reaction
of MAH (0.4 mM) with Tr+ (50 mM) in acetonitrile at 298
K (1.0 HL = 2.87 s).
The kIRC–time profile (Fig. 6) allows for a more
detailed illustration of the pattern indicated above. It
should be pointed out, once again, that this general pat-
tern is obviously inconsistent with a one-step mecha-
nism and that there is an intermediate that absorbs at
the wavelength of the experiment.
The Reaction of
1-Benzyl-3-cyanoquinolinium Ion (BQCN+)
with N-Methyl-9,10-dihydroacridine in
Acetonitrile
The reaction between MAH and BQCN+ in AN
(Scheme 5) has been considered to be an authentic
example of a direct hydride transfer reaction mainly
due to the work of Kreevoy and coworkers [14]. We
presented an alternative three-step mechanism in 2003
[15], which was challenged by Perrin and Zhao in 2008
[16]. The mechanism has been found to be even more
complex than we first believed [15] and was shown to
involve an oxygen-catalyzed chain reaction even when
carried out in a glove box under a nitrogen atmosphere
[7].
Scheme 5
an initial sharp increase in kIRC from the initial to a
maximum value nearly 50% greater than the former.
From the maximum, kIRC first decreased slightly and
then began a steady increase for the remainder of the
analysis period.
The data presented here are for the reaction between
MAH (40 mM) with BQCN+ (0.5 mM) in acetoni-
trile half-saturated with air (Table XI). The latter was
achieved by mixing the MAH solution from which air
was removed from a BQCN+ solution in acetonitrile
saturated with air. The 24-point sequential analysis in
this case is distinctively different from any previously
presented. In Table XII, we see that kapp first increases
to a maximum value (0.000866 s−1) before decreasing
slowly to 0.000831 s−1 at segment 8 and then increases
smoothly for the remainder of the time period analyzed
with a value of 0.001356 s−1 at segment 24.
SN2 REACTIONS OF ALKYL HALIDES WITH
ANIONIC AND NEUTRAL NUCLEOPHILES
The Reaction of Bromoacetonitrile with
Phenoxide Ion in Acetonitrile
Bromoacetonitrile (BrCN) is not a common alkyl
halide, but ClCN has been used in recent publica-
tions concerned with the mechanism of the SN2 re-
action [17]. The advantage of studying SN2 reactions
of BrCN is that it is much more reactive than a typical
alkyl halide.
The kIRC–time profile (Fig. 7) shows an important
detail only hinted at in Table XII. In Fig. 7, we see
The data for the conventional pseudo-first-order
analysis of the reaction (Scheme 6) illustrated in
International Journal of Chemical Kinetics DOI 10.1002/kin

10
PARKER ET AL.
Table XII Apparent Rate Constants and Standard
Deviations Obtained by the 24-Point Sequential
Analysis of the Reaction of MAH (40 mM) with BQCN+
(0.5 mM) in Acetonitrile at 298 K
Table XIII Changes in the Slopes and the Intercepts
with the Extent of Reaction during Conventional
Pseudo-First-Order Analysis of the Reaction of BrAN
(5.0 mM) with PO− (0.50 mM) in Acetonitrile at 298 K
Time (s)
k
app
(s−1
)
SD (s−1
)
Segment
k
(s−1
app
)
Intercept (s−1
)
Number of HL
2.5
4.7
7.0
9.2
11.5
22.7
45.2
67.7
90.2
112.7
135.2
157.7
180.2
202.7
225.2
247.7
270.2
292.7
315.2
337.7
360.2
382.7
405.2
427.7
0.000830
0.000866
0.000865
0.000859
0.000854
0.000842
0.000834
0.000831
0.000832
0.000838
0.000856
0.000883
0.000914
0.000948
0.000983
0.001020
0.001058
0.001097
0.001138
0.001181
0.001224
0.001268
0.001312
0.001356
0.00003
0.00001
0.00001
0.00001
0.00001
0.00001
0.00001
0.00001
0.00000
0.00000
0.00000
0.00001
0.00001
0.00001
0.00001
0.00001
0.00001
0.00002
0.00002
0.00002
0.00002
0.00002
0.00003
0.00003
1
2
3
4
5
6
7
8
0.0350
0.0346
0.0336
0.0318
0.0289
0.0125
0.0134
0.0244
0.0565
0.1353
0.50
1.00
2.00
3.00
4.00
Table XIV Apparent Rate Constants and Standard
Deviations Obtained by the 24-Point Sequential
Analysis of the Reaction of BrAN (5.0 mM) with PO−
(0.50 mM) in Acetonitrile at 298 K
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Time (s)
k
app
(s−1
)
SD (s−1
)
Segment
0.059
0.113
0.167
0.220
0.274
0.543
1.080
1.618
2.156
2.693
3.231
3.768
4.306
4.844
5.381
5.919
6.456
6.994
7.532
8.069
8.607
9.144
9.682
10.220
0.1038
0.0841
0.0687
0.0598
0.0542
0.0426
0.0382
0.0369
0.0364
0.0361
0.0359
0.0358
0.0357
0.0356
0.0355
0.0355
0.0354
0.0354
0.0353
0.0352
0.0352
0.0351
0.0351
0.0350
0.0188
0.0139
0.0089
0.0059
0.0039
0.0012
0.0005
0.0005
0.0005
0.0004
0.0004
0.0004
0.0004
0.0004
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Table XIII conform to the pattern observed in
earlier tables with kapp equal to 0.0350 s−1
(0.5 HL) and decreasing smoothly to 0.0289 s−1
(4 HL).
In segment 1 of the 24-point sequential analysis
(Table XIV), kapp for reactant (PO−) decay was equal
0.0015
[MAH] = 40 mM
[BQCN+] = 0.5 mM
0.0012
IRC/s−1
in AN at 298 K
294 nm
to 0.1038 s−1 with an SD of 0.0188. Both quantities
decreased sharply to 0.0382 and 0.0005 s−1, respec-
tively, in segment 7. The trend continued but with
much smaller changes for the remainder of the reaction
period.
k
0.0009
0.0006
0
100
200
300
400
500
Time/s
Figure 7 Apparent IRC (kIRC)–time plot for the reaction
of MAH (40 mM) with BQCN+ (0.5 mM) in acetonitrile at
298 K (1.0 HL = 602 s).
Scheme 6
International Journal of Chemical Kinetics DOI 10.1002/kin

NONCONVENTIONAL VERSUS CONVENTIONAL APPLICATION PSEUDO-FIRST-ORDER KINETICS
11
Table XVI Apparent Rate Constants and Standard
0.100
0.075
Deviations Obtained by the 24-Point Sequential
Analysis of the Reaction of Pyridine (1.25 M) with Benzyl
Bromide 40.0 mM) in Acetonitrile at 298 K
[BrAN] = 6 mM in AN at 298 K
pretreated with 1 mM PO
[PO] = 1 mM, 310 nm
Time (s)
k
app
(s−1
)
SD (s−1
)
Segment
kIRC /s−1
pretreated with 0.5 mM BrAN
2.34
4.46
6.59
8.71
10.84
21.46
42.71
63.96
85.21
106.46
127.71
148.96
170.21
191.46
212.71
233.96
255.21
276.46
297.71
318.96
340.21
361.46
382.70
403.95
0.000174
0.000126
0.000117
0.000128
0.000147
0.000243
0.000381
0.000479
0.000557
0.000620
0.000674
0.000721
0.000769
0.000809
0.000840
0.000869
0.000896
0.000922
0.000947
0.000971
0.000994
0.001018
0.001042
0.001066
0.00023
0.00020
0.00014
0.00011
0.00008
0.00004
0.00002
0.00002
0.00002
0.00003
0.00003
0.00003
0.00004
0.00005
0.00006
0.00007
0.00008
0.00008
0.00009
0.00010
0.00011
0.00012
0.00013
0.00014
1
2
3
4
5
6
7
8
0.050
0.025
0
2
4
6
8
10
12
Time/s
Figure 8 Apparent IRC (kIRC)–time plot for the reaction
of BrAN (5.0 mM) with PO− (0.50 mM) in acetonitrile at
298 K (1.0 HL = 19.0 s).
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
The kIRC–time profile (Fig. 8) shows an initial steep
rise to a maximum at short times before decreasing
toward a very slightly decreasing or nearly constant
value.
The Reaction of Pyridine with Benzyl
Bromide in Acetonitrile
The pseudo-first-order analysis data of the reaction of
pyridine with benzyl bromide (Scheme 7) in Table XV
fit the pattern in correlation quantities expected for
product evolution in a complex mechanism. It would
appear from the kapp values that a steady state may be
approached late in the reaction.
0.0012
The data from the 24-point sequential analysis pre-
sented in Table XVI show some deviation from the
picture presented by the data in Table XV taken alone.
0.0008
−1
kIRC/s
Table XV Changes in the Slopes and the Intercepts
with the Extent of Reaction during Conventional
Pseudo-First-Order Analysis of the Reaction of Pyridine
(1.25 M) with Benzyl Bromide (40.0 mM) in Acetonitrile
at 298 K
0.0004
[Pyr] = 1.25 M in AN at 298 K
[BBr] = 40 mM, 345 nm
0.0000
0
100
200
300
400
500
k
app
(s−1
)
Intercept (s−1
)
Number of HL
Time/s
0.00079
0.00094
0.00104
0.00109
0.00112
0.00114
−0.024
−0.052
−0.086
−0.113
−0.134
−0.152
0.50
1.00
2.00
3.00
4.00
5.00
Figure 9 Apparent IRC (kIRC)–time plot for the reaction
of pyridine (1.25 M) with benzyl bromide in acetonitrile at
298 K (1.0 HL = 697 s).
The first three segments show that kapp first decreases
sharply before beginning the slower rise toward a pos-
sible steady-state value.
The kIRC–time profile for the SN2 reaction between
benzyl bromide and pyridine (Fig. 9) indicates a pos-
sible further complication; after the initial small value
at point 1, a maximum is observed at point 4 (kIRC
0.000188) before the kapp decay indicated in Table XVI.
=
Scheme 7
International Journal of Chemical Kinetics DOI 10.1002/kin

12
PARKER ET AL.
5. Parker, V. D.; Li, Z.; Handoo, K. L; Hao, W.; Cheng,
J.-P. J Org Chem 2011, 76, 1250–1256.
CONCLUSIONS
6. Li, Z.; Cheng, J.-P.; Parker, V. D. Org Biomol Chem
2011, 9, 4563–4569.
7. Hao, W.; Parker, V. D. Unpublished work.
Experimental absorbance time profiles obtained from
eight different fundamental organic reactions were pro-
cessed using three different nonconventional pseudo-
first-order kinetic procedures, and the results are sum-
marized. The objective of the presentation has been to
allow the readers to make their own conclusions regard-
ing the mechanistic significance of the data without the
distraction of the author’s conclusions.
The procedures include (1) HL dependence of kapp
during convention pseudo-first-order analysis, (2) se-
quential linear pseudo-first-order correlation, and (3)
revised IRC analysis. Using these procedures, the de-
termination as to whether a reaction follows a simple
one step or a more complex mechanism can be made
using a minimum of both time and materials. This, of
course, is only the first step in the investigation of the
mechanism of a reaction and should be followed by
experiments under all applicable conditions, includ-
ing changes in reactant concentrations, wavelengths
at which absorbance–time data are obtained, tempera-
ture, and isotopic composition of reactants to name the
most common variables.
8. Parker, V. D. J Phys Org Chem 2006, 19, 714–724.
9. Kresge, A. J. Can J Chem 1975, 52, 1897–1903.
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International Journal of Chemical Kinetics DOI 10.1002/kin