Robert I. Morse
A MQSS Spectroscopy
Clark University Worcester, Massachusetts 01610
The availability of inexpensive quadrupole mass spectrometers make them attractive as analytical instruments suitable for undergraduate laboratory use. Mass spectrometry can also serve as an experimental basis for instruction in reaction mechanism and rate theory. The following experiment, performed with some variation by students in a physical chemistry course at Clark University, demonstrates the use of mass spectrometry in determining the reaction path for CHaCH2OH+ CH3CH,+ and its homologs. A simple kinetic theory is applied to the prediction of relative mass fragment intensities for methanol, ethanol, 1-propanol, and 1-butanol. A number of statistical or quasi-equilibrium models of the breakup of excited molecules have been proposed a t many levels of sophistication (1-6); the following is based on the Rice-Ramsperger-Kassel theory (6). A molecular species is considered to be made up of n identical oscillators in which a quanta of excitation energy may be accomodated. When a molecule is excited these quanta are assumed to distribute themselves in an equilibrium-lie fashion among the oscillators. Statistical fluctuations in the distribution may give rise to a critical number, a,of quanta in one oscillator. When this occurs, translational energy along an idealized reaction coordinate associated with that oscillator is sufficient to cause the associated bond to break. The probability that a bond will break in a given time or the rate a t which the bond breaks is proportional to the probability of finding a quantain that oscillator. If a molecule is excited by s quanta, this probability is the ratio of the number of ways s - a and s quanta can be arranged among n - 1oscillators
-
-
(8-a+n-l)!. (s - a)!
+ n - I)! 8!
(8
(1)
If s >> n (semi-classical approximation), eqn. (1) can be simplified by the relationship
where N is the number of atoms in the molecule (nonlinear). The rate constant for unimolecular decomposition can be expressed as a frequency factor, on the order of vibrational frequencies, multiplied by the expression in eqn. (4).
The model associated with eqn. (5) has the dissociation rate equal to the frequency at which a molecule moves along a reaction coordinate multiplied by the probability that this motion has high enough velocity to surmount the dissociation barrier. If this barrier is higher in energy than the product state, some of the excess potential energy may be returned to the system as transational energy of the fragments (7). I n most mass spectrometers ions are produced by electron bombardment The asterisk indicates an excited species. Since the excitation energy distribution of the parent ion is the product of the distribution function of the ionizing collision and the energy distribution of the electrons, E, must be estimated or determined by internal consistency as is done below. For electron energies in the range up to 70 V, energy transfer of several eV is reasonable. Mass spectra for methanol, ethanol, 1-propanol, and 1-butanol were taken on a Q-inc quadrupole mass spectrometer. Samples were outgassed by cooling and Resolusample pressures were maintained a t 10-"tor. tion was adjusted for unit mass and electron energy nominally for 45 V. The spectra are shown in Figures 1A-D with a large mass 28 peak from Nz superimposed on the alcohol peaks. The mass 29 peak in ethanol is associated predominantly with the species CH,CH,+. This species may be produced either by a one or two step process
Equation (1) becomes
If the energy of each quanta is r , the total excitation energy of the system is E = se and the critical energy for bond rupture is Eo = me, then1
'
Expressions of this form can be written to account for nonidentical oscillators, noneffective oscillators, rotational degrees of freedom, etc.: see refs. (1-6).
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Both are energetically possible and a mass peak associated with CHaCH20+is observed. Other mechanisms are not considered since, a t these low pressures, collisions rarely occur. However, either of these processes may lead to an excited CH3CH2+where subsequent dissociation is possible. The probabilities of producing CH3CH,+ by either process are
Figure 1.
Mars spectra of (A) methanol, (8) ethanol, (CI 1-pmponol, (Dll-butanol.
Eo Values of Reactions
where the EOvalues are taken from the table. Even a t energies as unrealistically high as 25 eV, Pz/PI2 14. The probability that the CH8CHz+ does not decay, 1 P,,assuming a C-C bond rupture (-2eV) as the most probable event, is essentially unity for the mechanism in eqn. (6) and
-
Transition
EdeV)
Estimated from thermodynamic meagurements and v&lues.
for the mechanism in equ. (7). P3 is less than 0.28 over the possible energy range. Therefore, the mechanism in eqn. (7) is more likely to produce CH&Hz+ than is the mechanism in eqn. (6) by a factor greater than 10 and possibly as great as lo8 (E -8 eV). These arguments can be extended to 1-propanol and 1-butauol. Equation (4) can be used to predict the mass peak heights for a series of homologous alcohols. Ignoring subsequent reactions, the peak height ratio for R + relative to CH3CHz+is
Equation (8) is plotted in Figure 2 as H versus E for R + = CH&HZCHZ+and CH&HZCHZCHZ+.The experimental ratios are shown. Good agreement is found for CHaCHzCHz+ and CH&HzCHzCHz+ at about 9 1 eV. The calculated value for CH3+is far too high, probably due in part to several easily attainable dissociation paths and the small number of degrees of freedom. The experimental data suggest a value for E about 9 eV (Fig. 2). This value, when used in eqn. (4) indicates that reaction mechanism in equ. (7) is more than lo5times as likely as the mechanism in eqn. (6).
*
Figure 2. Calculated m a s spectra peak height for CHaCHzCHn+and CHsCHLHsCHz+relative to CHsCHa+or o function of excitation energy. Experimental valuer ore shown as circles.
Literature Cited (1) R x n . 0. 8 . . A N D R * r s ~ ~ a o = n H.. C.. J . A m r . Chcm. Soc.. 49, 1617 (1927). N. B.,"Theory of Unimole~ulslReaotions." Cornell University (2) SGATER,
Press. Ithiaa, N. Y., 1959. (3) Roselimoc~,H . M.,J . Chcm. Phys., 34, 2182 (lQL31). (4) Yam*=. M.. W*a~nAmla.A,. AND JOINBTON, W . . J . Chcm. Phys.. 37, 1276 (1962). s . "Advances in Mass S p e a t m m ~ (5) R o s e ~ m o c s .A. M..Awn K ~ ~ o sM.. try," Pergllmon Preaa Ino.. N. Y., 1963. (6) K ~ a s e L. ~ . S.. "Kinetics of Homogeneous Ga. Reactions." Chemioal Catalog Co., New York, 1932. (7) HOLDY.K. E.. KLOTE, L. C.. AND WILBON.K. R.. J . Chrm. Phya., 52, 4588 (1970).
Volume 48, Number 6, June 1971
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