Ian Horrnan
university Chemistry Laboratory Cambridge, England and Michael J. Straurr University of Vermont Burlington, 05401
I I
I
Determination of the Rate of So~volysis of Benzhydryl Bromide An nmr experiment
The rate of a chemical reaction in solution is determined by measuring the change of reactant or product concentration with time (1). Concentration may be determined directly by chemical analysis, e.g., volumetric methods, or by measurement of some physical property of the reaction mixture which varies with concentration as the reaction proceeds. For reactions in solution, "physical" determinations involve measurement of such properties as optical rotation, refractive index, optical density, conductivity, etc., which for dilute solutions are proportional to concentration. The limitation on the physical property measured for a particular system is that there must be a substantial variation in this property between the reactants and products. During the past decade the use of nmr analytical techniques has become standard procedure,' and the rates of many reactions have been studied by observing the change in integrated peak heights for reaction components relative to time (3). I n these determinations the integrated peak heights are assumed to he directly proportional to the concentration of the reactants and/ or products. I n 1956, Bhar and Forsling reported the application of nmr spectroscopy to the investigation of the rate of reaction of acetic anhydride with water using a different approach (4). The proton of the carboxyl group of acetic acid and the protons of water give a single absorption by virtue of rapid exchange. The position of this absorption shifts downfield, relative to the absorption due to the protons of the CH, group, as the concentration of acetic acid increases. The separation of the absorption due to -COOH/HzO from that due to the CHa group is related to the acetic acid concentration, and hence a rate constant for the reaction could be determined. We have recently used a method similar to the latter procedure described above to estimate the rate of solvolysis of certain substituted benzyl and henzhydryl bromides in 80 volume % aqueous dioxane (5). Because of the simplicity of the procedure, and the interesting application of nmr as an analytical tool, we considered that this method could be readily adapted to a class laboratory experiment. Results obtained by this method compare favorably with those obtained for the same systems by volumetric methods (5). The advantages of the nmr method compared to the volumetric method are: (a) accurate rate constants may be obtained when the reactant is in scarce supply; (b) reactions with half-lives of -1 min For a short introduction to nrnr theory and a useful hibliography, see Reference (8). 1
114 / Journal o f Chemical Education
may by conveniently studied; ( e ) in general, it is easier to make the measurcments. A limitation of the nmr method is that the reactant must dissolve to give a minimum concentration of 0.1 M. At lower concentrations, the shift of the H20/Ha0+ absorption is too small to be measured accurately. Benzhydryl bromide has been chosen as the model reactant because of its relatively short half-life (-6 min at 39.5'C in 80 volume % aqueous dioxane) and because it is readily available. It can be purchased from Aldrich Chemical Co., Inc., or easily prepared (see Appendix). Theory
Benzhydryl bromide (BHB) undergoes solvolysis in aqueous dioxane to produce benzhydryl alcohol (BHA) and hydrogen bromide (eqn. (1)). The hydrogen ion which is generated protonates H 2 0 to give H,O+, and also protonates the dioxane to a lesser extent (eqns. (2a) and (2b)).
I n acidic aqueous media, the rate of proton exchange (eqn. (3)) is more rapid than the nmr time scale HzO
+ H30+ == H$O++ H10
(3)
and thus only a single proton resonance is observed rather than separate absorptions for the protonated and unprotonated solvent molecules. This point is discussed in most textbooks dealing with high resolution nmr spectrometry. The position of this absorption will be a weighted mean between the position for pure H,O and pure HaO+, as expressed by eqn. (4) where A is the chemical shift from a reference standard (see the section on the capillary standard). X H ~and O XE,o+are the mole fractions of total water present in
the form of Hz0 or H80+. Since X H =~ 1 - Xa,ot, eqn. (4) becomes A~amlo*= Aa9o - Xnm+ (Amo
- Anat)
(5)
indicating that a linear relationship exists between Aa,oia,o+, the position of the H,0/H30+ absorption, and XE.O+. The quantity XHI0+is, however, proportional to the hydrogen ion concentration of the medium, and thus there is a linear relationship between the hydrogen ion concentration of the medium and the position of the HzO/H30+ab~orption.~Figure 1shows that for solutions of HBr in 80 volume % aqueous dioxane a linear relationship exists between 6~,o,n,a+ (measured relative to TMS) and hydrogen ion concentration up to 0.5 M, and an approximately linear relationship exists up to 1 M. Increasing [HBr] from 0.00
Figure 2. The changes in the nmr rpedrum of 0 0.360 M rolvtion of 8H8 in 8 0 volume % aqueous dioxone of 3 9 S 9 C as the solvolyris reaction pmcoeds. The spechum is shown os it appeared ot 4-min intervals. The time is indicated by the number on the baseline of eoch spectrum. The chomicol shift, A lin cprl, is recorded relative to H a 0 in the copillory stondard for whish, b y definition, A = 0.
MOLAR CONCENTRATION
OF
HBr
Figvre 1. Plot of 8 n , o , ~ ~ othe + , shift of tho H10/H30C absorption rolativa to TMS, versus the molar concentration of HBr in 80 volume % aqueous dioxono at 39.5-C.
Figure 2 shows a stylized diagram of the nmr spectrum of a solution of BHB (0.360 M ) in 80 volume % aqueous dioxane at 39.5'C. It can be seen that as the reaction proceeds, the H20/H30+ absorption moves downfield. If one lets Ao, A,, and A, be the position of the HzO/HaO+ absorption a t to, t, and t , relative to HzO in the capillary standard, it follows that, in the solvolysis of BHB, the initial organic halide concentration is related to values of A at times zero and infinity by eqn. (8) [BHBIi
= a(Ao - A,)
(8)
where the term a is a proportionality constant (given by the slope of the line in Fig. 1). At time t, therefore to 0.50 M causes a downfield shift of the HzO/H,O+ absorption of -60 cps. The rate of solvolysis of BHB is equal to the rate of formationof HaO+,i.e.,
and since the chemical shift of the H20/HaO+absorption is linearly related to [H30+]the progress of the reaction may be followed by measuring the change of this shift with time. Equation (1) indicates that water participates in the solvolysis reaction, which is assumed first-order with respect to BHB, but since water is present in large excess, the rate expression reduces to eqn. (7)
where k, is the pseudo-first-order rate constant.
' This point has been illustrated experimentally by Gutowsky and Srtika (6) in their theory of chemical shifts in dilute solutions. If desired, the Guggenheim method (7) may be used to calculate the rate constant from a plot of 8 , versus time.
[BHB]1
= a(At - A,)
(9)
Integration of eqn. (7) gives the expression
which after substituting for [BHB], and [BHB], from eqns. (8) and (9) and rearranging, gives 2.303 log (A, - A,) = -kd
+ 2.303 log (Ao - A,)
(11)
However, since A, and A. are constant for a particular system, this becomes 2.303 log (A, - A,) = - k d +
constant
(12)
The value of kl may be calculated from the slope of a straight line obtained by plotting values of log (At A,) versus time.s The Capillary Standard
The standard used in most nmr work is tetramethylsilane (TMS), on which both the 8 and 7 scales for measuring chemical shift are based. I n this experiment, however, the total shift of the HzO/H30+peak is at most 60-70 cps, and therefore a sweep width of 250 or 100 Volume 46, Number 2, February 1969
/ 1 15
cps is desirable. This means t,hat a standard with nn absorption close to the H?O/H,O+ absorption is required. A suitable standard may be simply prepared by filling a capillary melting point tube with distilled water and sealing the open end. This is t,hen inserted into the nmr tube containing the reaction mixture and liediapproximately coaxially with the tube. A further advantage of this type of standard is that it is isolated from the reacbion sample and is unaffccted by changes in the medium as reaction proceeds. Wat,er capillary standards of. this sort have an absorption a t approximately 6 4.7. The Experiment
Dioxane was purified by the method of Beste and Hammett (8). The 80 volume % aqueous dioxane used as the reaction medium was prepared by pipetting 100 ml of dioxane and 25 ml of distilled water into a flask and mixing well. A sample of benzhydryl bromide was weighed into a 5 ml volumetric flask. The flask was then preheated to 395°C and filled to the mark with 80 volume % aqueous dioxane also a t 39.5'C. (If the sample weighs more than 0.6 g, difficuky in obtaining a homogeneous system may be encountered). After thorough mixihg, a sample of the solution was placed in a standard thin-wall nmr tube and the water capillary standard was inserted. The tube was then placed in the probe of a Varian A60 nmr spectrometer which was thermostated a t 39.5"C, and the clock was started. Spectra of the absorptions due to the water capillary standard ana the H 2 0 / H z 0 + of the medium were recorded a t a sweep width of 250 cps, filter bandwidth of 4 cps, RIP field of 0.03 mG, and a spectrum amplitude of 0.1. During the early part of the reaction, the spectrum was recorded a t m i / % mi11intervals, time intervals becoming longer as the reaction proceeded. The t,ime was recorded when the pen indicated the maximum of the H20/H30+ absorption. Figure 2 shows a typical series of traces taken during a reaction. The diagram also includes a value for t = a ,which in practice may be taken as the value after ten half-lives. Since the half-life of the reaction a t 395°C is approximately 6 min, the infinity reading was taken a t t = 60 min. A tabular presentation of the data of Figure 2 i s given in Table 1. Table 2 shows the systematic variation in kl as the initial concentration of benzhydryl bromide isvaried. The dependence of pseudo-first-order rate constants on initial organic halide concentration has been observed previously by Beste and Hammett (a), and could be due to the effect on the solvent conTable 1. Calculation of the Pseudo-First-Order Rate Constant for the Solvolysis of Benzhydryl Bromide (0.360 M ) in 8 0 Volume % Aqueous Dioxane a t 3 9 S ° C . A, (cps shift from l
-
(rnin)
log10
(Ws)
(A, - A,)
40.1 27.0 19.3 14.8 12.3 10.9 10.1 9.0
31.1 18.0 10.3 5.8 3.3 I,
