Reaction Rates in Analytical Chemistry Papers presented at the Eighth Annual Summer Symposium sponsored by Division of Analytical Chemistry and ANALYTICAL CHEMISTRY, Syracuse, N. Y., June 17 and 18, 1955
Rates, Mechanisms, and Solvent EDWARD S. AMlS Chemistry Department, University o f Arkansas, Fayetteville,
The application of kinetics to analj-tical problems is discussed with emphasis on the application of the theories of the influence of dielectric constant and ionic strength to the interpretation of rates and mechanisms for reactions in solution. The electrostatic effects of the ion atmosphere and the dielectric constant of the medium are treated with respect to ion dipolar molecule and ion-ion reactions. The electrostatic effect of the dielectric constant of the medium is discussed with respect to dipolar molecule-dipolar molecule reactions. Other factors, such as microscopic dielectric constant and selective solvation, are mentioned as perhaps being influential in rate processes.
A
LTHOUGH this paper deals for the most part with fundamental theories of rates, mechanisms, and the effect of the solvent upon kinetic processes in solution, a brief mention of the historic and current applications of reaction kinetics to analytical problems is in order. The successful kineticist must have a fundamental grasp of analytical procedures, as his determinations of the rate of disappearance of reactants or appearance oi products must in many cases depend upon chemical analysis. Kinetics, while not so essential to the analyst, nevertheless is a valuable tool for him t o learn to use, because kinetic methods and theory throw much light upon the mechanisms and natures of chemical reactions. Kinetic processes permit the determination of the actual concentrations of certain chemical species. Thus, the catalrtic activities of hydrogen and hydroxyl ions in selected reactions are the historically oldest methods for the determination of the concentrations of these ions. Of course, titrimetric deterniinations of total acid and base concentrations preceded these cntalytic methods for the determination of the concentrations of hydrogen and hydroxyl ions. In 1912 Clibbens and Francis (13) found the decomposition of nitrosotriacetonamine into nitrogcn and phorone to be a function of the catalytic activity of hydroxyl ion. The stoichiomctric equation for the reaction is:
Ark.
k , for the reaction and the hydroxyl ion concentration [OH-] v a s given by the equation k = 1.92 [OH-]
(1)
The constant k has the units of see.-' The constant 1.92 has the units of 1 X mole-' X see.-' Duboux (14) for acid-catalyzed inversion of sucrose found that the relation between the velocity constant, k , for the reaction and the concentration of hydrogen ion [Hf ] could be represented b y the equation, k = l i [H+] ~
(2)
when the acid was completely dissociated. I n this equation k~ is a proportionality constant. The equation vias used t o calculate the concentration of hydrogen ion. Both k and k~ must have the same time unite-e.g., see.-' on min.-' The quantity k has the units of time-'. For acids 11-hich were not completely dissociated the formula for the dual catalysis by hydrogen ions and undissociated acid molecules V-TIS csed. The formula is k
=
X H [H+]
+ k v ( C - [H+])
(3)
The C term represents the total acid concentration both dlssociated and undissociated, and k . is~ another proportionality
The original concentration of nitrosotriacetonamine was known and the rate of decomposition n-as found by measuring the volume of nitrogen produced as a function of time. Francis, Geake, and Roche ( 1 5 ) found that a t 30" C the relationship between the apparent first-order velocity constant,
Tmb hwrs
Figure 1. Plot of (a - x), (x - y), y and x in moles per liter vs. time in hours kl
1672
=
2 . 9 5 X 10-1,ki = 3.80 X 10-8,temperature 25.1'
c.
V O L U M E 2 7 , N O . 11, N O V E M B E R 1 9 5 5
167'3 ~~
constant. The other terms have already been defined. The k,v term was calculated for any arid in any dilution r r i t h t h e a i d of T a y l o r ' s formula by comparison with an ncid for n-hich the Taylor reLttion-nnmiciv,
Table I.
Temperature, Ester E t h y l acetate E t h y l acetate Methyl propionate E t h y l acetate E t h y l formate Methyl propionate E t h y l dichloroacetate
Solvent Water and water-ethyl alcohol Water and water-acetone TTater and water-acetone Water and water-dioxane and water and water-acetone Water and water-acetone Water a n d water-acetone Water and water-acetone
is known. The accuracy is sufficient a s k.v is very small compared with k ~ .I n this equation K is the dissociation constant of the acid. A constant k ~ indispensable , for the correct determination of hydrogen ion concentration, can be obtained onlv by preliminary measurements in completely dissociated acids for which kti =
Ester Hydrolysis
(5)
Br@nsted ( 10) suggested that the acid-catalyzed rat'e of addition of water to the nitrat'oaquotetramine cobaltic ion could be used to determine hydrogen ion concentrations. The intention here is to point out the possibilities and not t'o give an exhaustive list of applications. A second application of kinetics to analytical chemistry is to study the kinetic rate of decomposit,ion of soluble complexes, or the reagents used in forming such, under experimental conditions and, thus, to ascertain the time limit during which a test is valid. Thus, palladous salt forms a soluble colored complex wit,h acid p-fuchsin (29) which serves as a sensitive t'est for palladium. However, t,he color fades on standing. A series of kinetic measuremenk would est,ablish the period of time in tvhich the colored complex would maintain its capacity for light absorption sufficiently to give the correct concentration of palladium. Carlton, Bradbury, and Kruh ( 1 2 ) found that dithizone in molten naphthalene gave colored complexes with bismuth, ant,imony, mercury, cadmium, and tin. The reaction of bismuth wit,h dithizone in the molten solvent system was sensitive to 0.004 y of bismuth and \vas reported as a spot test for bismuth ion by Carlton and Bradbury (11). The dithizone was found by Carlt,on, Bradbury, and Kruh to decompose in molten naphthalene with specific firFt-order rate constants of 0.07, 0.14, and 0.28 niin.-l, respectively, a t 1 0 0 O . 110", and 137" C. The activation energy for the reaction at 100' C. mas 18 kcal. per mole. These data indicate that the dithizone reagent in molten naphthalene decompose? at the rates of 7 , 14, and 28% per minut'e a t the respective temIieratures loo", 110", and 137" C., and that time is therefore an important consideration in using tliip reagent in this medium. A third application of kinetics in nnalyt,ical chemistry is the determination of the concentration of a particular reactant or product from known concentrations of reactants and the rates a t which they decompose, or from the anal>-tically dekrmined concentrat,ion of a product. Broach, Rowden, and Amis (9) studied the consecut,ive firstorder reaction of tetrabromophenolsulfonphthalein with silver ion i n aqueous nitric acid solut'ion. If R represents the t,etrabromophenolsulfonphthalein molecule except for the bromine atoms, the resulting reaction for the purpose of calculation can be reprwented hy the following equations:
where a, x, and y represent the initial concentrations of the original dye, the concentration of the first substitution product, if no decomposition of this product occurred, and the concentration of the second substitution product, respectively. The
c.
Type
0 . 0 0 , 9.80, 19.10 0 . 0 0 , 1 5 . 8 7 . 19.10 25.13, 35.21, 4 5 . 4 8
Alkaline Alkaline Acid
3 6 . 0 , 45.0,55.0
Acid Acid Alkaline
35.01, 4 6 . 11, 55.02 2 5 . 0 0 , 35.03 25.00. 35.00, 45,oo
Acid
quantity (x - y ) is the net concentration of the first suhstitutlon product. The evperimental determinations of the specific velocitlconstants, ki and kz, for the first and second steps, respectively, from the rate of production of silver bromide m r e first carried out. Then the concentrations of the first and second substitution products as a function of time were calculated from the equations
x = a(1 - e+,') and
(7)
The remaining concentration (a - 2) of the reactant RBr, as a function of time was found by subtracting the calculated values of z a t the different times from the known value of a. The net concentration, (z - y ) as a function of time of the intermediate product, was calculated from the corresponding concentrations with respect to time of r and y. Plots of these concentrations as a function of time are shon-n in Figure 1. Parsons, Seaman, and Woods ( 6 5 ) have reported the spectrophotometric determination of 1-naphthol in 2-naphthol, utilizing differences in reaction rates of the two naphthols with diazotized 2-naphthylamine-5,7-disulfonicacid a t a controlled temperature and at a controlled acidity. The absorbancy of the reddish color formed was measured a t 485 mp. The standard deviation n-:is & 0.004% of 1-naphthol for samples containing 0.07 to 0.3570 I-naphthol. This is the direct application of a kinetic rate to an analytical determination of concentration. Thus, kinetic procedures allow the determination of the concentrations of reyctants and products from a few data. 11lmtrations of these methods could be multiplied, but these evamples suffice to illustrate the principle. The remainder of this discussion shows how kinetic procedures permit the identification of possible intermediates in reaction processes. This is, in a sense, a qualitative analytical adaptation of rate studies. The electrostatics of a rate process as influenced by the dielectric constant of the medium and by the ionic atmosphere in which reactant particles are located permit, under certain circumstances, an interpretation of the charge type of reactants involved in the rate controlling step of the reaction, ION DIPOLAR MOLECULE REACTIONS
The author and his coworkers have studied both the acid and the basic hydrolysis of esters. Table I summarizes their work on ester hydrolysis. The salt effect data in the case of alkaline hydrolysis were tested for obedience to theory using the Amis-Jaff6 (6)equation which is
I n this equation K is the Debye kappa, Zgc is the charge on the ion, e is the angle which the line drawn betmen the centers of
ANALYTICAL CHEMISTRY
1674 charge in the dipole makes with the line drawn from the ion to one of these centers of charge, p* is the Onsager enhanced moment, p: is the enhanced moment a t zero ionic strength, TO is the distance of approach betreen the ion and the dipole necessary for reaction to take place, D is the dielectric constant of the medium, Iz is the Boltzmann 0 gas constant, and T is the absolute temperaI1 ture. The equation was transformed for the R-C-O-R' salt effect calculations by substituting in it the dimensionless variables
z=
=
K(I
of these esters under the condition given is the reaction of n dipolar molecule with a negatively charged ion. The over-all mechanism may involve several steps. These steps could be
(10)
hTg
and
and gave
w=
2 2
(1
+ z+ '/2Z*)+
fi2
(1
+ 2)
(12)
A theoretical curve of TB versus 22 w a ~ plotted and the data for the dependrnce of the velocity constant upon ionic strength were fitted to the curve using the constants of Table 11.
Table 11. Constants Used in Fitting Ionic Strength Data to Theoretical Curve rn = 7.5
Temp..
c.
r 0.02
d x 10'8
.4. 22 a t Ionic
s'
Strength = 1
'k
= 0
The data fitted the theoretical curve well and the constants used compared favorably in magnitudes with those found in former applications of this theory. The equation (1) ln kLeD = In k ; - -
z€P + DkTrZ ~ ~ ~
- - -
(13)
has been developed for the limiting casc of the head-on approach of an ion t o a dipolar molecule from electrostatic considerations for the rate of reaction between ions and dipolar molecules. According to this equation if D is increased the rate of reaction should decrease for a positive ionic reactant and vice versa for a negative ionic reactant. If D is decreased the rate should increase for positive ions and vice versa for negative ions. I n deriving this equation, free energy and energy of activation xere assumed to be equivalent. This assumption can be verified eince, for reaction in solution, both p A V and the change of entropy of activation due to coulombic effects for rate processed carried out in solvents of constant dielectric constant (20) are each equal to zero. The directions of change are in harmony with those predicted by the Amis-Jaff6 equation. When Equation 13 is applied to the data of Potts and Amis and of Seigel and Ami3 tlie data fall on the theoretical plot of log k' versus 1 / D and the slopc, vhich is ZEP 2.303 k T r 2 , yields reasonable values of the parameter r. These values of r together with the values of T found by Quinlan and Amis ( d 7 ) , using the same approach for the alkaline hydrolysis of methyl propionate in water and water-acetone media, are recorded in Table 111. These values of T , though somevhat small for the alkaline hydrolysis of ethyl acetate in waterethyl alcohol media, are of the right order of magnitude for a molecular radius. From these correlations of empirical data and theory, one would conclude that the rate-determining step in the hydrolysis
Fiom the standpoint of the effect of the dielectric constant upon the rate, either Step 1 or some other step involving the reaction of J, dipolar molecule nith a negatively charged ion is rate deteim.ning. While Step 3 involves molecules and negatively charged ions, it involve. water as one of the reactants and there is no kinetic evidence in these data that the concentration of -rater as such is involved in the rate process. Stcps 4 and 5 are practically irreversible. Hockersmith and Amis (18)and Yair and Amis (23) found that the hydrochloric acid hydrolysis of methyl propionate and of ethyl acetate, respectively, obeyed the predictions of Equation 13 with respect to the dielectric constant effect upon the rate of a reaction, tlie rate-controlling step of which involved a dipolar molecule and a positive inn, and when the specific velocity constant was also made specific with respect to water by dividing by the concentration of water. Only the hydrolysis of ethyl acetate in water and water-acetone at the higheit temperature involved in these investigations-iinniel~~, a t 55" C.-shon s an unreasonable value of the r parameter. A summary of the r values for the various investigations is given in Table IV. From thc dielectric constant effect upon the rate, 11 appears that the mechanism for the acid hydrolysis of esters proposed by Bender (7)-namely,
Table 111. Values of Parameter r for Alkaline Hydrolysis of Esters Ester Ethyl acetate
Solvent Water and water-ethyl dcoi:ol
Ethyl acetate
Water and vater-awtonc
Methyl propionate
TTntixr no.! w-atcr-aretone
Table IV.
Temp., O
Y X
c.
19s Cm. 0.94 0.93 0.98 2.00 1.8 1.5 1.4 1.4 1.3
0.00 9.80 19.10 0.00 13,87 2 5 10 1.5 00 2.7.00 35.03
\-dues of Parameter r for Acid Hydrolysis of Certain Esters
Ester Etlij-I acetate
Solvent Water and water-dioxane
Ethyl acetate
Water and water-acrtone
3Ietliyl propionate
Water and water-acetone
Temp.,
c.
33.0 45.0 5.5. 0 35.0 45.0 55.0
x
109 9.08 9.18 0 50 5 21 G 19 Unreasonably 7
slnall ~~~~~
25.13 33.21 45.43
~~
3.43 8.42
3.01
V O L U M E 2 7 , N O . 11, N O V E M B E R 1 9 5 5 0
/I
OH:
[
+ H 2 0 +.+. R-A-0-R'
R-C-0-R'
c
9 R-
OH
0
-
]
--R'
Using the model for the acid hydrolysis, G, is 9.1 X 10-18 sq. cm. and taking bA as 1.7 X 10-8 cm., Equation 18 becomes -+
A =
AH+
+ R'-0-H
R-C(OH
8°K
1675
+ H+
(2D
- 1)(%
+ ff
-
A =
2)
(16)
Table V.
+
Ethyl acetate Methyl propionate
G
Solvent
Ionic Strength
Dioxane-water Acetone-water Acetone-water
0.05 0.05 0.02
Ethyl acc-tntc Acetone-water ?so-PrOH-~-ater tert-BuOH-7%ater n-PrOH-n ater E t OH-water MeOH-mater
Temp., O C .
4
= (18)
A model had to be constructed for the activated coniplcs in order to evaluate the b= and G,. The models for the acid and base hydrolysis of esters are given as follows: ..
-
11 34 31
3.3
35.3 25 25 25 25 25 25 25
- 24 - 32 - 50 - 61 - 74 - SF - 155
2.5 2.4 2.3 2.2 2.1 2.0 1.8
35.0 3d.O
0.05 0.05 0.05 0.05 0.05 0.05 0.05
CrHj00CHCBrCOOC?H5
I^
n/
y 3
-b',
d 7 6 A
\
R +-+'
\
/ 2 15A.
H
\
Br C2H5COOCHC(S2O3) -COOCzHs
121)
+ Br-
'H+b
\
/2' ' 5 4
\\I 7 6 A
o-
