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On the measurement of gas-phase ion-molecule equilibrium constants in an ion cyclotron resonance spectrometer
Intewnd 0 Ekvkr
Jownol of Mass Spectromcby Scientific Publishing Company,
- --L--L*.=-_.-s
’ i$. -3 -7-_
ON TEE MEASUREMENT OF GAS-PHASE ION-MOLECULE EQUILIBRIUM CONSTANTS IN AN ION CY CLOTRON RESONANCE SPECTROMEI’ER WILLIAM DONALD Deportment (UxA_] (Fust
R_ DAVIDSO H. AU8 of Chemistry,
received
‘Ml?. BOWERS,
N, NICHAEZ
16 September
University 1976;
TOMOTHY
of Chlifomia in revised
SU * and
Santa Bar&mu,
form
26 October
Cdifonxia
93106
1976)
The technique used iu measuring ion--molecule equilibrium constants, in particular proton-txausfer equilibrium constants, with a high presswe drift cell ion cyclotron resonance spectrometer is described. Experimental aud kinetic problems which occur iu such measurements aud their effect on the determination of accurate equilibrium constanta am discussed, Non-attainment of equilibrium may result from either slow proton-transfer rates or fast competitive side reactiona With proper experimental technique. errors in free energies caused by such kiuetic problems-may ususlI~ be kept-below 0.2 kcal mol-‘. A number of examples are given_ While the analysis is applied to high pressuG drift cell ICR. most of the co . - ts are applicable to equilibrium measure meuts with auy type of apparatus-
lNTRODUCXlON
There has heen considerabIe interest in recent years in the measurement of gas-phase ion-molecule equilibrium consknts [l]_ The. most extensively studied class of reactions is protc rl-k-ansfer equilibrium [2-4] exemplised in eqn- (1) AHY++R==BH++A
(1)
Measurement of equilibrium constants for reactions of thistype yield directly aaaxate gas-phase basicities (GB’s) of A and B. PGO- GB(A) 7 GWB) =--RTl&C In the absence
-* Presnt
-
(2)
of entropy effects, these relative gas-phase basicities are equal
&xress: De-t Dartmf%uti&Masuchnrrtb~2747;U.s.A-
-uaetta
of Qdnistrp.-south-~ .
. -
_
-
Universi~;
North
t& the dative
proton affmities (PA’s) of A and B
AGO = A*
= PA(A) - PA(B) (3) Proton-tzm.&r-equFEibris were first measumd using‘ion cycIotron msonance(ICR)techniques f531,buthavermbsequentIybeenstudiedusinghigh pressure mass spectrometry j4] and ffowing aftergIow techniques WI- FormaUysimikequilibriummeasme~ents havekenmadeonnegativeionsystems [S] yieIding relative -phase acidities. Hydride-transfer [7 J , hahde&an&r [Sl, and charge-txansk 191 equilibria have also been measured recent&, whi.Ie various ionic clustering and exchange reactions have been studied by equilibrium techniques for some time [lOI _ In tfiis paper, we discuss in detail some of the experimental and kinetic probbms that may be encountered in the measure ment of equilibrium constants for proton-trausfkr reactions. In particular, the kinetic consequences ofiheoc cunznce of side reactions in competition with proton-transfer and how such side reactions affect the m easurement of proton-transfer equilibrium constants am considered_ Ion cyclotron resonance tichuiques, particuIady those involving high pressure drift ceII measurements, are discussed here; but the kinetic concepts developed am readiIy applicable to other expersmental metbcxkand EzUSon typesMeasurement of a proton-transfer equilibrium (eqn. 1) presents a problem of competition from potentiahy rapid dimerzation reactions at high pressures-The simple reaction given in eqn- 1 is IikeIy to be much more complex as shown in the kinetic scheme I SCHEME1 BH++A
(AHB+)* _
B li 1T (BwB3* w-=+1* M ?a M. B I I 1 AHA+-AHB+& AH++BA
A
A
BHB +
In Scheme I, M is a stabSzing molecule, usuaUy either A or B, which carries away excess energy from the vibmtionahy excited dimer_ Hundreds of systerns have been studied here and for most amines and oxpgenated molecules, proton-bound dimer formation is observed as a dominant process at higb presumes- The question *en arises whether or not these fsst dimerizatZon IXSiCtiOnS sszbstmtialsp afkd t&e simple proton &anskrequS&iabeingmeasuredOur approach to this problem is twofoid. First, we have soIved the cornpIex kinetics of Sheme I andtheaet5caI.&p_+iictedtlxeef&+qn‘tbeequilibriumoonstantat~us presses for various values of rata2conzitu&s. Set-_
-_;*:-:’ ond, we have measured dimerization rate constants and proton-transfer r&z constants for a number of systems. We then chose pairs of molecuks that would most severely test the abii@~ of the drift cell ICR to measure protintransfer equilibria at high pressure and proceeded to measure apparent equilibrium amstants. The results and a discussion of the iimits within which accurate equilibrium constant can be measured ~6th an ICR kpectrometer are presented here. THEORY
For the purposes of this paper only the magnitude of the dimerization rates relative to the rate of proton transfer are of interest. Hence, *Se detailed mechanism of Scheme I can be more conveniently written as Scheme II SCHEME
LI
ABJ3+
&H+
&2H+
where kl and k_, are bimolecular tions for the disappeaxance
-d!!
proton-transfer rate constants. Rate equaof AH? and Bw can then be written as
= (PI + p2 + v3) [AH+]
df
-
v-dBH+I
(4)
and -
d[BH+l dt
= (Y_~ + V, + v,) [BH+ J -
vl [AH.+]
(5)
where vwl=
vx = k,lBl ~2
=
k,tN
~4
=
k4
Frl
[Al CM1
k-l[A]
va = biBI
WI
~5
LMI
=
k,[BJ
and kz,ks,k4 and kSarethethirdarclerrateconstantsthatcharacterfiethe
variousdim~nreactions: 'phe two dif%renW equations (4) and (5, Can be solved simultaneously. The relatke g&&t’ [C.b
am~~ons.of
AXi? and Bm
---~~~--‘_~~ti=le~‘P-Q~~ -;
--
__s:
-.
2Q -. __ _ . .
;‘
_
- _--
-_
at sky time, _ _-
y
‘_-_ - _ _
_
t, are found “-‘
_
to be _
(6)
(7) where P=
.
(v~+v-~+v*+P~+v~+~s)/2
Q= [(v~+Y~+v~ c,=
-u_~
-v,--v,)2
I(% + v, + us) - (P-
QH-
+&4yrV-11~‘=/2 V-,CBH‘+IdCAH+fo
C,=v_,~B~]~/[AIf'l,-~(v1+-2+~~)-(~+
c, = [(v_~ + vd + us) - (Pc, = Y@W~~/CBWI~-
613
-
813
VI I~lo/P=+lo
W-x + vd* a) - (p + QII
Theratio ofthetwoionintensiti~,experimentallym~,
isthengiven
byeqn-(82 [BEI+],
IBEX+ Jo
cJ=+lt = IAWO
C2e-cP+Q)r
+ C4e-cP-Q’t
+ c2e-
U3)
Inthisstudy,tBefo~~~:noftheprotonatedspeciesis GSUlIldtQkVerg rapid and~einitialIcon~trationsof~andBH'aredirectEyproportional tothepresnues of A and B,respectively [ll].The apparent equilibrium constantforreaction(l)obtained experimentz3lIyatthnetistherefore [Bwlr[A] C3e-~'+Q,r+C~e-
Equilibrium
CONSIDERATIONS
consiants
-
muencyofthe ~al~~risv~~untizitmatches~ecg~~~~‘, _.: it- -_ frequekyofanion. Eady ICR~~~studiesemploydtheco~tmarginaZosc~= ~q.uencyte&nique~2l,ThiswasneceSXug becausethesensitivi~ofthe mazgmalosciiktor wassomeunknownfunctionoffrequency_Themajor drawbacktomeasurin grelativeionintensitiesatconstant~quency-and henqevariablemamretic~ldsisthatthedrifttimesofionsin~edriftcell ICRaredirectlyproportionaltotbemagneticfield.Iftwoionsreachequilibtium conditionsrapidly,andthereareno competit3esidereactionsorion loaves depleting either or botbions,a variationin reaction times willnot affect the measurement of an equilibrium constant_ This point is demonstzatedintheionintensitpcurvescalculated in Fig.l(a)_In thishypothetical proton-transferreaction, BH' and_AH+reach eqtibriumwithin1,5ms. Parametersusedarekl = 6 -lO-lo cm'mol-' s-‘,k_a = 5 -lo-" cm3 mol-l s-l, K=12,thep~ureofA=4-104ton,andthepre~ ofB=l-10' torr.ThepressuresaresimilartothoseusedexperimentallyintheICRdrift
(b)
Ka = 2.5
0
-
LO . time x 103,
2.0 S
3.0
-ceII [Z]; the r&e constants are typicai of proton-transfer rates. It is azmuned that ffieinitialbdensii~oftheionare proportionalt0thepresnrres ofthe If we set the mass of BH‘to be twice that of AH: BH’ neutralspecies [ll]_ wili come into resonance at twice the magnetic field that AH* comes into resonance_ The average drift time of BH‘at resonance will then be twice that of AH*_ However, the ion intensities do not change significantly between tl (when AH’ is measured ) and & (when BH’ is measured) and the measured equilibrium constant wilI not be in error_ If, however, there are competitive reactions or ion losses, such will not be the case_ Suppose that both AEI’and BWare depleted by side reactions with rate constants of ilr3 s-l_ The relative ion intensities fast pseudo fir&order will then be described by F’ig_ l(b). In this case the ion intensities change markediy between t, and t2_ The apparent equilibrium constant would be 2.5 rather than the actual equilibrium constant of 12_ The en-or in Ac” for the reaction would then be O-95 kcal mol-‘_ It should be emphasized that this is an extreme case_ A fistorder toss rate constant of 103 s-* is huger than normaily encountered_ In addition, most of the equilibrium data obtained at variable magnetic fieid have been measured between ions of similar (* lO-30%) mass to minimize the effect due to magnetic field change- Thus tl and & are not significantIy different. and the errors in the free energies are usually not serious. Recently, reliable methods have been developed for calibrating the sensitivity of the marginal oscillator detector as a function of frequency [12]. Hence, it is now possible to operate the ICR spectrometer at constant magnetic fieid- TabIe I compares some equilibrium constants obtained at constant and variable magnetic field. As can be seen, the errors in free energy are usuahy less than 0.3 kcai mol-‘_ The errors in AG” in Table I are closely predicted from the kinetic expression, eqn- (9), using measured values of rate factors v,, v-,, vz and vS for these systems. TYpically, for a reaction such as (I), the neutral species A and B are admitted to the drift cell with a total pressure between 4 and 8 - lo4 torr_ The ratio of the neutrais seIdom exceeds 10 : 1. The magnetic field is kept constant, usually at 14-15 kiiogauss. The parent ions (or fragments) formed in the electron beam generally rapidly protonate the neutrals to form AH* and BEi*_ The ions AH’ and BH’ are observed by varying the margiilaI osciiIator frequency until it matches the M ‘ve cyclotron frequencies of the ions- The power absorbed by the ions is then m easured by sweeping the magnetic field over the peak (usually only a few gauss wide). Under high pressure conditions the inStantaneous power absorbed at resonance per ion,A,, Is 1131 A,/ion=S-
cz’ei
4mE where Ed is the ampiitude tram&r collision wuency,
__
(10)
of the o&erving frequency, g $ &e=momentum and S is a ‘te.un rep resenting the sensitivity of
B
-2
*2NJ5
*ma *NH2 z?BUNH2 Me2NH Pyfidine Me3N nPr2NH N-Mepiperidine sBupNH
m3N
QlliIUlClirline
nBuNH2 fiNI. -2 Me2NH 2-Picoline Et2m nBu2NH
DifferenceinAGOd (kcalmot-1)
KG=
A
0.77 1.23 0.81 1.61 0.58 1.57 0.73 1.30 0.78 0.93
6.1 2.3 0.85 16.4 0.72 4.0 19.3 7.2 22.8 1.4
9.2 1.8 1.18 6.6 1.64 2.7 29.1 4.1 22.8 1.6
-0.25 0.15 -0.2 0.55 -0.50 0.25 -0.25 0.35 O.O= -0.1
a Ratioofthe masesoftheprotonatedspecks. bApparentequiliirium constantatconstantfrequency,D.H.Aue,H.M. Bowel73,unpubIishedresulk c Apparentequiliirium constantatconstautmagneticfield,ref. 3(b). dDiscrepancyinAGObetareenco~t~eldandconstantfreqaencydata. l Littleornodimerizationt.akesplace.
WebbandM.T.
the marginal oscillatorat the observingfrequency_Theintegratedpower absorption &then A&&al)
=
Sn*rq2Es
(11)
4m.C
where n' is the ion concentration and T is the time the ion sr,=ds in resonance.The ratio ofthepowerabsorption fortheionsBw and AH+ at constant Ed is then given in eqn. (12) A,(BH+)
[BH+l ~EH+ ~AIP EAH+ &IV c-r------(12) AptA=) C-3 ~AH+ ~BH- EBH* %I+ Thecollisionfkequenciesathighpmzssure areequaltothehti-widthathaifheight of the output ~al(ie_I=Aw1/2)[13].The half-width obtained experimertanyisinLmitSofgauss.Since oaH/m then Ao=AHI&m Al.so,a~constant
A,(BH+).:s-w [BE]. A&=? IA=+&
~~d,r~=T~,811C18qn_(12)reduceSto AI_irn,ux+ SEE+ J&m+-sAB+
. *
-
(13)
(14)
Thus, by measmmg the peak heights of AH’ and BH: the half-width at halfheight of the peaks, the sensitivity of the marginal oscGator at the two resonance frequencies and the partial pressures of A an5 B, the equilibrium constant for reaction (1) may be caIculafed_ Limitatins
in me aswing equilibrium
constants
gas-phase equilibrium constants, AswithalItechniquesusedtomeasure the drift ceil ICR method has its Iimitations. Due to signal to noise restrictions, it is very difficult to measure relative ion intensities greater than 100 I 1. Although ece manometers are accura te in the lo4 torr range, it is very difficult to measure neutral pressure ratios greater than 10 f 1 with any precision. This means, ignoring kinetic restrictions, that the maximum equilibrium constant that can be measured under ideal conditions onadriftcehwithany accuracy would be 1000, corresponding to a Ac” of 4.2 kcai mol-’ at 305 II. Loss of resolution due to coIlision broadening of the peaks can also be a problem at the pmssures used in drift cell equilibrium experiments. This is particularly serious when the protonamd ion being studied has an unreactive parentorP-1 fragmention.Zftheprotonafxdionisofapproximatelythe sameintensityastheinterferingpeak,thetwopeaks maybedeconvoluted
assuming Lorentzian hne shapes. Such a procedure, if carefully done, leads . . to ~errorsinthetruepeakheightandwidth. Kinetic restrictions must also be taken into account. These limitations are twofold: (1) the rate of equiliition may be too slow to achieve equilibrium within the experimental reaction time, or (2) the rate of equilibration may be too slow to complete with competitive reactions or ion losses. Measurement of eauilibrium constants with a drift celI ICR is thus limited bv the rates of the f&ward and reverse reactions. If there are no competitive reactions (such as dimerization reactions), eqn. (8) may he simphfied to yield [BHX L=+l,
=
(l-2 6sx
y_1
R.
)
R.
-
e-<9+P--lh
1
)
e--
+
~p3 + 1) + (R.
(15)
+I)
where R,, is the ratio of the initial intensities_ Using eqn. (15) and ins&ing various experiment3I parameter% it is pqssihIe.to determine how serious erros in the equilibrium coustsn tmightbedu+ooverlysIowrabesofpro-
ton transfer_Table 2 demonstrateshowtheapparentequilibriumcons&tbecomesLessreliableastheratesoftheproton-transferre~ondecrease.Thetotalpressure usedZnthiscalculationwas6-104~rrwithap~ ratio(A-B)of5:1,Theseare @pical experimentalparametersforequilibriumconstantsofthemagnitudegiveninTable 2.The timeofthereaction wasassumedtobe3ms,atypicalreactiontimeunderexperimentalconditions,F?romTable 2itcan beseen that,forIargeequilihriumconstants,the errorsinthefreeenergyaresubstantialunlesstheproton-transferreactions are fast (>6 -1O-1o cm3 mol-' s-I).Forsmellerequihbrium constants these errorsarelessserious_ Innormaldriftcellequilibriume xperiments,thetotalpressureandpressureratioarevaried.Ifthesystemisinequilibrium,theapparentequilibrium constant should not vary with either pressure or presu~ ratio,Figure 2 efora showshowtbeapparentequiZibriumconstantvarieswithtotalpressur hypothetical reaction in which K=lO, (k, +k,)= 3 -lo-" cm3 rnol-‘~‘~, t=3-10-3s,andthepressure ratio(A:B)is5:l.Asthetotalpressure incre~s,~eapparentequilibriumconstantapproachesthetrueeq~brium constant,aswouldbeexpected_Ifsuchanexperimentwereundertaken,the variationof& with pressure would indicate immediately thatthesystem wasnotateqr3ibrium_Foreveryequilibriumexperimentinthislaboratory, suchacheckFsmadeoveraslargeapresmrrt3rangeaspossible_
(kl+ (an3
k-1) lllol?
K=
-10-J
500
K-SO
K==5
s-=) bra in AC0
K.
496
(0.00)
494 464 460 406 309 187 89 35 11
(0.01) (0.02) :i%:
53.0 50-O 499 49-7 49.2 47.8 it-:
Ka
10
9 9 7 6 5 4 3 2 1 ~hkcdmol=at305g_ ~Etracke-~~in~ cThatOMiB; _ .3_ -. _:
(0:29) (o-6o' (1.05) (1.62) (2-34)
Error8
K.
inAGo
22k S-3
::-x:;
5.00 5.00 5.00 5.00 s-00 ELoo4.99 495 4-75 3.34
pz; (&Ol) (0_02) (0.08) (0.20) (0-4m (1.02)
~6-1~-torr;tberatioP~/PB~S:l;Pndthe~ntime
_.
-
-.
-_
Error’
iRLG0
.
_
-
(0.00) (O-00) (O.Oct) (0.00) (0.00) (0.00) (O-00) (0.01) (0.03) (0.16)
.
_
Notmol
.
120
-
Experkental
_
Range
-
f
10.0 -
.
0
.
0
8.0 -
0
6.0-
0 0
4-O 20o-o0
*
1
I
I t I I 2 4 Total Pressure x 104. Tot-r
Fig_ 2. Pbtofthe apparent equilibrium riumreaetioa(1)_IC=10, k,+k-I= b
I 6
-
constant,K,,Kpresnue 3-10-x0anSmo~*s~-‘.
fortbegeneralequilibandt=3 -IO-’
PA/P~=5,
Therateofproton-transferbetweenthetwobasesAandBdetermines the rate at~~thesystem~comeintothermodynamicequilibrium.Hence, theproton-transferrateconstants, itisveryimportanttobea.bktomeasure at least for the f&treaction_Therate constants forproton-transferusedin thisstudyweremeasured bythreetechniques:(l)trapped-ioncellejection, (2)approach to equilibrium,and (3)lowpressure-lowconversion_Allthree methods involved approximations and/or assumptionsofsomesortandtbe rateconstantsderived~mthemcznonlybeconsideredaccuratetoi20C7. Forthepurposeofthispaper,thisaccuracyisco~deredadequate.Exampies ofeach ofthethreemefhod.saregivenhereaIongwithadiscu&onof theIimitationsofeack The~p~-ioncellejection~quefiasbeendesaibedby McIver and Eykr [14J_Forre~nssuchas(l),oneof~eions(BN'orAH3isejecfed continuo~fromthece~byappIyinganRFvoItageatabrequencyequal tothenesonance~~cyoftbeion_Thed~aseinintensltywithtimeof theotherion(AH+ or BH?isthenrecorded andtheforwardorreverserate constantisobtainedThee~dfonRFvoltageis~appliedaftertheions have~~~equilibrium,AtypicaIcaseisshownin~.3forreaction(l6)
(16)
300
200
(00
0
TLME
(ms~
Fig. 3. Plot of ion intensity vs_ time of protonated pyridine, CsHsNH+, in a mixture of 4 10m7 torr pyridine and 9 - X0-’ torr (CHs)zNH_ The r&e constant of reaction (16) was de-srmined from the decrease in pyridinium ion signal when protonated dimethylamine is ejected from the cell.
ejecting the protonated dimethylamine leads to a rate constant for reaction (16) of 3.2 - lo-lo cm3 mol-’ s-l_ The major disadvantage of the tipped-ion cell ejectionmethod is uncertainty in the pressure measurement. The pressures of the neutral species are measured with an ionization gauge, the ionization gauge being calibrated at high presmres(104 torr)against a capacitance manometer_ It assumed
is
totheextentthat ~at~eionizationgaugecaZibrationisLinearwithpressure itisaccmrateinthe10~-106t.orrpre5surerynge. Measuringthe approach to equilibrium is awellestabkhed technique [X5]_ Wheu there are no side reactions,eqn. (8) may be rearranged-and rewritten,in a form similarto that givenby Benson[l6] togield(17).The neutralspeciesAand
-
[BH+]) =ln([AH+]oK -
WdBl
z,-
CBI+I+jo)
+ &-IIAI If
(17)
s are kept cosistant throughB&admittedtothedriftcellandthepressure o-St the experiment. ‘I&e drift times (and thus he reaction times)- of the ions are varied by chauging the magnetic field. At each magnetic field setting, the i&&.si~~of AH’ and BH’ are measured. A plot of In([AH+lK[B]/[A] [~~7)~fyieldsaslogeequalto_I~l[B] +k,[A]).Ekomalmowiedgeof tile m constant, K, (determined at long drift tlme~), kl and k-s m
i
1
t
I
,
I
.
IS time x 103. s Fig_ 4_ Plot of ln(AHII(B/A - BH> vh time nPT3N;PAIPB=4;PA+PB=6-104torr-
I
2.0 for reaction
(18),
where
A = nPrEtzN;
B =
ob~ed_Suchaplotisgivenforre~on(lS)inFig.4 *cl nPr~NH++nPrE~N nPrEQJH'+nPr~N(13) Ll Thisreaction waschosensincsetherateofproton-bounddimerformationFs very slow for all specks. The derived rate constants are: k1=2.35-10-'0 cm3 mol" 0, k, = 22 - lo-*' cm3 mol" s-l_ lowconversiontech.niquehasbeeuusedexter&velyfn ThelowpressuteofAare drift cel.IICRstudks [17].Forreactionssuch as(l)highpresures admittedto thedriftceII(-1-2-104 torr)_TheAWpeakismonitored_ LowpressuresofB(l-lO-lO"~rr)arethenaddedtothedriftcellandthe decreasintheintensityofAH+ismeasured.Therateequationforthereactionisgivenby(19)
- N-1 dt
(19)
=k,CBlC~l
whichintegratesto
In(s)=
-k,[a]
t
(20)
0.6
-In
A!Y!T (
&H,+ 1
0.4
0.2
o-0
4
2
Fig_ 5. Plot of In(AI-I+/AH~) P*=1-10--4t~;f=2-10-~s.
6
8
10
P(acetane) x t06_ Tarr vs. acetone pressure for reaction
(21)
where
A = isobutene;
The rate constant measked for this reaction was 1.05 - lo* cm3 mol-’ s-l_ This technique has certain disadvantages. The equilibrium constant must he large (Le. k, >> k-,) in order that the reverse reaction does not repLeG& AH*- In addition, adding the neutral B may also increase the-inter&* of AH’, if B’ or fragments formed in the electron beam react with A for form In general, this method will usually give a lower limit to the rate AH‘. constank Some proton-transfer rate constants measured by the various techniques decribed here are given in Table 3_ For those rate constants mm by more than one technique, good agreement was obtained (*20%)_ Dimerization
rate constants
The mechanism of dimer formation in ion--molecule reactions is an active field of study [18,19]_ The mechanism most commonly used to explain the phenomenological dimerization reaction (22) AE++A~AAZH+ isgivenin(23j
(22) -
‘k
(AaH+)* ?!AtH+ (23) ks‘ __ ..% - . - ._ &ereMis_a&‘--‘-gthird_M~~If(A,EE~*is assu&dto‘beina&eady state, *en the jph~omenological rate constant += can be w+kn i& tims of the microsco co+=ti-_. --. _. ._ *_=t= - -AH++A-
cm*
0 CCCH&
+
II
CH,CCbI,-C”&H,
+
-(CH&:dH’
CH,=CtO+,
+
2.6
+
‘CH,@H-
=H3’2N’%
-7O-lo
-
+
A-
ed b Determined c Determined d Determined
= Determin
from
trap cell ejection-
from Iow p4-essure-Iow conversion erpeximents. from from
approach to equilibrium. equilibrium constant
Therateconstantasso~~withthedimerizationisthusthird~onlerinthe LimitM~OandsecondorderinthelimitM~Owitbacontinuoustransitionbetween third-and zcond-otieratintermediate prssures. Themechanism(23)hasbeenshowntx~ bevalidforanumberofsystemsinchxling NH3 and the methy~es[lS
CY-
/
C-
'N
Kxg2c=o a Ref.
19ib
Ref.
20_
are measured are given elsewhere [19]_ A sampling of thirdorder rati constants measured here for various systems is given in Table 4. These rates were chosen to exempw the range of rate constants experimentahy encountered and cover most of the molecules considered in this paper.
rate constants
THE
EFFECT
OF DIBAFXUZ
ATION
ON
PROTON-TRANSFER
EQUILIBRLA
Most nitrogen and oxygen compounds readily form proton-hound dimers. The effect these competitive reactions have on the measurement of equiiibrium constants is dependent upon: (1) the rate constants of the dimerixation reactions, (2) the rate constants of the proton-transfer reactions, (3) the total pressure of neutrals, and (4) the pressure ratio of the neutrals. Many dimeriaation rates have heen measured in this laboratory [19,20], a sampling of which is given in Table 4. The fastest third-order rate constants measumd at room temperature have not exceeded l-2 - lOa cm6 molm2s-l; the slowest rate constants (which are conveniently measurable under drift ceil ICR conditions) are in the 1O36 cm6 mo13 s” range. We can arbitrarily cail a warder dimer rate constaut of 1O33 cm6 mol* s-i, a fast rate con&an*; one of 10”’ cm6 mo13 s-‘, a moderate rate constant; and one of lo*’ cm6 mol* s-l or Iess, a slow rate constant. The effect of such dimerization constants on a proton-tmnsfer equilibrium consmnt is shown in Table 5. It can be seen tipm Table 5 that, if the dime&&ion rate constants, kl and k,,are equ~& the effect on the equilibrium constantisniL-However, when there is a.dS%nce between -k<_pd kS,theapparentequilibziumis &.iftai'~* the-more-alowly N specie& The worst case is 8 fast BHT v-&d .-_ aslow AHYd‘ _ . ‘on. Tile n+d dimer_rate con-
l-lo-= l-lo-= l-lo-= 1-m-= 1-1o-a 1-10-a l-10-2" ;:$I;;
1’
lo-=
10.0 12.4
I- 10-s 1' 10-s 1-m-= ;: 11I-
Yi 10.0 102 7-6 9s 10-o
;gi 10-s 10-a m-25
0.00
-a13 -0.14 0.16 0.00 -O_Ol 0.18 o-01 0.00
= SIpeiimantlil pcsmmnEters:E~lO;tofaIprereure=4-10~ torzP~/P~=l.0;reaction time * 3 ms; k3 and k4 ascuned ~beebeaverageofk2andks;kl+k-l=5-10-10 cm3 morx IJ kcd marl
a-=. at 305K
stanfs(k3 and k4) wouldshow thesameeffect. However,inthistreabnent R,andkqhavlzbeenassuzned tobeequali;oeaclxothezandbethemeanof k, and k+ Ifthedim~onrateco~tis purethird-ordfzroverthepressure range oft&e expehWnt&3Jlincreaseinthetotalpresmue willincreasethe dimeri2xGonrateinahear manner_ With respect to the second-order proton_transferrate,adifferentialdimer~edwouldincreasingl3innuence themeasuedeqGWhxmcon&antwit&in~gpresmue. Inge~eraLthe orderofadimerizathn~constantvaries withtotalpressure -M-order atP-,Ostndsecond~atP+~.Howeves, forthesakeofsimplicity,we wiiIassumethatitmmainspurethird~~overtbepressune rangeweane considering-Figure 6isa~pIotoftheerrorinAG" vs_totalpressureforvariouspro~n~eceqalIibnumconstants,whenethe~~on~AH'is SIOW (pp,=lo*s cmb moI* s*)and-the d.imexiz&ion of_BH'is f&t (k,= X0-= cm? moP s-'I-It must-&z_empl - ' that-Fig_-6ov~ errors,sin~tfrefast~on-rate.c~~_appioachsecon ds: athigher ~lntberthzuiiinezuiyiqczre&ng-as‘~~-~d&~ one wouldexI)Bct;-boy; thehig@r$he_tqcal-+ssure; the-m&serioir;r lheenorsinfbe-measux4equ%.&ium constsmt..T%e~ezzorat-lowpressuresisdueto.n~~t~~~.~~~:~~;if‘ _
-
-,
='.F'-"~I
I
i
I
. ~ - . . ~, -
i
1.2
KilO0 - . ~
o.s
N c
l ~ -
0.4
Normot
K-
Hxperimento!
Range
I
! 2
0
I 4 Totol
1 6
Prate
I 8
x tO 4
l tO
Torr
F~g_ 6 . P l o t o f t h e e r r o z in AG ° vs. total pressure for a system reacting according to Scheme I_I: k l ÷ k - I ~ 5 - 1 0 - z ° c l n 3 t o o l - ~ s - l ; k 2 == 1 - 1 0 - 2 s c m 6 t o o l - 2 s - 1 ; k s = I 1 0 - 2 3 c z n 6 t o o l -:~ s - l ; k 3 = k 4 =ffi(IT¢2 + k S / 2 ) ; P A = P B ; a n d t = 3 - 1 0 - 3 s.
there were no competitive dimexization reactions. The neutrd~ pressure ratio also infl.p~ces the total rate of dimerization, w h i c h i n t u r n a f f e c t s t h e m e a s t t r e m e n t o f t h e e q u i l i b r i i l m c o n s t a n t . T h i ~ is best illustrated by Fig. 7, a plot of error in free energies for various equilibr i - m c o n s t a n t s v s . t h e m o l e f r a c t i o n o f A . Aff~in w e a s ~ m e t h e w o r s t ciro c=]m~nces - - f a s t d i r n e r i z a t i o n o f B H * , s l o w d i r n e x i z a t i o n o f A H ÷. T h e o r e t | 0o0
t
i
i
--
K:I
0.4..I:
\
<3
i= t=.
Normol
0.8-
Kxperi~entol
Range
N K=
I00
ti.l
1.2! 0.2
(;
I 0.4 Mole
F/~ 7. Plot c~ the ~ 8chemm:ll:
kt
lo-~ o cm~ mo~
4- k - I [
~:;
Fraction
m ~ s .
m_ 5 - 1 0 -
I0 . ~
I 0.8
I 0.6
1.0
of A
m o l e ~ a c J ~ o n Of A t c ~ a . ~ . L e m ~
3 ~ F z o l - I.
s- I ;k2.
k~ = k4 - (k2 + ksig);P~.;
-~
=t 1 " 1 o -
1 2 _ ¢ m 3 . t ~o1o- l--1
~
to
s - • ; k s _ ~=1 -
- x o-4 to~. and t = a" 10-3 ~
equilibrium conically, as shown in Fig- 7, the &sf ~situation for accuras stant me asutementsisaneutratmixwithsmallamountsofA(lessthan s of B were used, the mono50%)_ Experim&taE&, however, ifhigh‘plX?SWe mer ion intensities wouId he too low to measure due to the rapid formation of cismerS. Thus, one must be careN not to be fooled by large ion intensities at a high NB ratio which conId Jead to highly erroneous results. When measuring equilibriuxu cronstants ~5th an ICR drift cell, the ratio of neutral species is varied. If the apparent equilibrium constant varies with the mole fraction of neutzaI species, the e xperiment is not u&d to obtain thermochemical data_ If the rate of protin-transfer is close to the rate of dim&i&ion, measurement of proton-transfer equilii+ is in jeopardy_ In Fig_ 8, the error in AGo is plotted vs_ the total proton-transfer rate for a slow/f&& dimerization case for various equilibrium constants_ The total pressure is taken as 4 - IO+ torr, theratioAtBasl~l,andthe~ti
-
1
K= 100 -
I
I
I
I
In$eneral,tbefo~~on~iproton-bounddimerscanhweapronol?n‘dea;_~ eff+t on the_me_asurement of proton-transfere~~~_constan~_Ho~~ ever,withproperexperim entaItechniquetheerrorsinfi~2en~escanbe keptbelow O.Z@almol-I. _SAMPLEEixPExlME
NTALSYE?l?EnuS
Inthis section,the&ectofdimerizationon actualdriftcellequiiibrium experiments will be discussed_The rati constantsforproton-transferxeactionswere measuredby one or more ofthethree techniquesdescribedearlier_Tbedimeri.zationrate constantswere measuredasafunctionofneutral pressure,andtherateconstantscorrespon~tothepressureoftheneutrals intheequiIibxiumexperimentwereused_ Acetone
The
and isobutene
for reaction_(25)
apparent proton-transfer equilibrium co-t OH+ + C&COC&
C(CH,):
n
= CH3 CC&
+ CH,=C(CX-I,)~
. (25)
hasbeenstudiedcarefullysinceisobuteneisakeycom~~din
obtaining
TABLE6 CalcuIatedanderperimental ioninkenzities~ and apparentequilibriumcoxutantsforthe reaction
hAellsity of rntensity of c4s Mole
cH
Og 3
3
xa
flaction
0faaztoIle
Expt-
0.11 0.21 0.29
55 24 13
0.36 0.46 0.60 0.17
6.5 -
-3 -
calc_b
Expt
calcb
11-3 11.5 -
-81 71. 14 6.9 3.6 1.1 0.23
63 48 36 20 IO.2
E&pt.
69 49 36 19 8.9
Et-0 12.3 -14
calcb 12.8 -12.0 12.1 11-8 11.7 11-6 IL4
(abo~_2 -~10~~~)~[20~ZOn'theo~~hand;~~t~u~~-catlondimeriies:verysIowi+andis m_m-third~rcjertiptotf;eisobti~ep~ cif 5.IO_ torr [2O],_TG alird~~tierdiinerizationrate calg%Inh__~ givenin TabIe 4_“Il1e_ forward and reverse proton-tra&ferrate&nstaritsfor%actKoti (27) are given_ti'.lhble3_Tfie variationofthe apparentequil&iumconstant forreaction @7)%kEHi'~oIe friiction of acetime is pres&ted*mTable‘6.-The tdaIpresuretixi%n~ed -at4-~0~tonandthe'reaEtion~ewas2.3 ms.Th&epeiimental-p;aiame~ersrere~~bubsti~~into~.(S) and by itam&on;fheTzue"eq&iibriumc;onstant_iRas determined.'Fortheprotin-tzan&er reactS& (251, the equiEh&mx am&ant which best fits the ~&entalda~isK= 14.Thecalcutated norma&edionfn?znsitiesusing ted along with the experimentalnorthisequilibriumconstaIltarepresen . mahzedintensitiesinTabIe 6.The agreementis extremeIygood.Theerror in tfie&eeenergyisthe&~O.lO kcal mol-'. example bf bt The acetc&+sobutine proton-transferxeactionisagood caseofsIow/fastdim~on,~~ which proton transferisrapid.Theerrors causedbydim~tionares~tandwithinthequotedexperimentalerror lin+(*O.2 kcalmol-I). _ _ Quinuclidine and tr&thylamine This system, given byreaction (261, representsanothercase ofslow/f&st
(26) ~~tionrates.Theproton-transferIs~rapid,aswasthecaseinthe acetone-isobuten&~system.Theprotoxi-trans&rratesZ.WepreSentedinTabIe3. Quinuclidinedime3izes rapidtyandappearstoapproacfiase~nd-orderlimit moP s-' at-h&b quinuclidine presumes methylof R, = 7.9 -10~"cm3 aminedimerizes e&reme&siowly.Thethird-arderrateamstaIltsaregivenin equilibrium constant is 1.65. Usingeqn. (9) and Table4.Themeztsur& ~g~~~p~~leadstoap~~constantofl-_90. TheerrorinAGOis~O.l~mol-i.~,tbe~rdueto~~oqis sIightandwellwit.bineqxMmentalwts. -. -- .- _
&P&dine
(pltl
trime*yh&
:I-
.. .-
r -_ _-
:_._ A. _- -._; -1 -_-
+ CCi+,?,NB
(27) _
_ H-,, 1: -. The Pr&*-@a&e= rate constants a+*&esented.in Table 4. The Lnued drift .celI.q@ibrigm constant ig 3-O; the *cuIated equjli~_~:co~t is 25._Tlxe enxx jn free energy for rgaction (27) is then -0.1 kcal mol:‘_ Re&&on_(27)-qeas-also studied with a high-p&sure mass spectzometer [21] and theT.X&ivtiim of California.,,“› Santa;Barbara trapPed ion cell ICR q+ctrom&er~ The results are p resentedinTable7~-Thetrapc&loper&esat
Iowpresusswilerethird~rderd.im~tionp~cesses arenegligiblea~dthe gasss~ectrometerat extremefy.&#ghpywhelx?totzll equilibriumbetweenallspeciesis~~.The~meptforallthree metbodskquitegood,demonstratingtfiat~edimerizationprocesses arenot greatlyperturbingthem easurementoftheequilibriumconstantinthedrift cellICR for this system_
UP======
eridine
arui dimethylamine
The above reactions -ilha&ate the Worst casfzs for dimerization affecthg equiliiriumconstantmeasurem ent. A mor& typical c& is given by-reaction <28), the proton-tmnsfer betweenpyridiueanddimethylamiue.Pyridine
dnnerizes moderately
fast anddimethyhmineslowiy(see
Table4), Using
eip_ (&the
eqdSium
constant L ii65. The &ror in the &e is O-03 kcal mol-* _
reactiondue $.a dimerizatbti
hsummarg,
prot~n-t&sferreacti~n
energy of the
fkeeenergies measwedinan
-
.
ICR
driftcell-a&t-sli&tiyin error-d~tb~~formationofprotonbo~d-dimes. above;these_errorsa~e_well‘withintheexperimenHowev&~_asdemo&rated taI error_It‘shtiuldbe poi+t&d outtbstallion--moIecuteequilibriumconmassspectrometry,fIowing stan*measmedbyanytecbnique(highpresure ~ow.~~-ioneeIIICR,etc-)aresubjecttoenrorscausedbycompetitiveside r&&ionf& *w‘eq "7 '-on reactions,or dif&rentialion Iosses, by‘thereactionS&emeIIcanbeexpandedto Thekinetic"schem&expres& inchxde all~oEion-moIeculereactionsandionlossme&anismsfo~owingatreaianent&miMtothatappliedhere. Finnllv,ftfiasbeenour-experience~anoccasionalre~onwillnot cometoequilibriumdue~eitherfastcondensationreadionsor~mely slow~brsrtion~reactions.In~esecases,thebestthatcanbedoneisto "~~~t~~econnpoundsof~~usingdoubleresonan~techniques,or othertechniquesthatdemonstratethe occurenceornon~ccuren ceofareaction_Suchbracketingresultspieldproton~ti~~atarecrudebyequilibriumstandard-(2 ~~kcaI),buttheyareoftensufficientformanychemicalapplic&ionsofthedata. ACENOWIXDGEMBNT We
gratefulIy
acknowledge
tionundergrants MPS73-04657
Ihesupportof~eNationalScienceFoundaandinpartMPS7418397.
8462; (b) R. Yamdagni, T-B. McMahon and P- K&arie, J-A&- C&em. Sot-, 96(&d) :_-I 4035. (a) J-J- Solomon and F-Et Field. J_ &n_ Chem, Sec. 95 (1973) 4483; (b) JJ. Solo-xnon, M_ Meot-Ncr and F-H. Field, J- Am- Chem- Sot. 96 (1974) 3727RJ- Biint, T-B_ McMahon and J.L. Beauchamp. J- Am, Chem- h. 96 (1974) 1269_ (a) V-G. Anicich, M-T. Bowers, R-M. Oadailey and K-R. Jennings. Int J- Mess Spectram. Ion Pbys-, 11 (1373) 99; (b) V.G. Anicich and M-T- Bowem, Innt J-Mass Spec trorn Ion Phys_, 13 (1974) 39110 See. for es2unple. ref. l(c). 11 This assumption is valid if the rates of protunation of the two neutrals are similar. For amines this appears to be the case_ This assumption hss most simpb non-hindered aiso been used in other ion-molecule reactions to simplify kinetic formulae (ref. 7(b). 12 P- Kernper and M-T. Bowers, Bev_ Sci Instrum.. in press_ 13 M-T- Bowers. D-D_ BIleman and J.L. Beauchamp, J. Phys Chem.. 72 (1968) 3599; V-G- Anicicb and M-T- Bowers, Int_ J. Mass SpectromIon Phys-, 11(1973) 329; J-L_ Beauchamp, Ph_D. Thesis, Harvard University. 1967. 14 R-T. McIver, Jr. and J-R. ,i&ier, J. Am. Chem- Sot_. 93 (1971) 6334. 15 See, for example. ref_ 7. 16 S-W- Benson, The Foundation of Chemical Kinetics, McGraw-HiLi, New York. N-Y.. 1960, V-G. Anicich, Ph_D_ Thesis, University of California. Santa Barbara, 17 See, for exampie, 1973; V-G_ Anichicb and M.T. Bowers, Int. J- Mass SpectromIon Phys-, 13 (1974) 359. 18 (a) D.K_ Bohme. D.B. Dunkin, F.C. Fehsenfeld and EE_ Ferguso n. J- Chem_ Phys, 49 (1968) 5201; 51 (1969) 863; (b) V.G. Anicich and M-T- Bowers, J- Am- ChemSot_. 96 (1974) 1279; (c) M- Moet-Ner and F-H- Field, J- Am. Chem- Sot-, 97 (1975) 5339. M. Chau, W.R. Davidson end D-H- Aue. J- Am_ Chem_ Sot. 19 M_T_ Bowers, P. Neiison, submitted; M_T_ Bowers, W.R. Davidson, T-Su. L. Bass, P- Neilson and D-H. Aue. 24th AnnConf_ Mass Spectromand Aiiied Topies. San Diego. California. May. 1976. P- Neilson, W-R- Davidson, M.T. Bowers and D.H. Aue, unpublished data. f! W-R- Davidson, unpublished results_
_ . _. .
_ _-:,
I. __
_
r* .:
__._I
-_
-.
._
__
_-
‘--
_
___
_
_ .
-.
. -.
- y__ _
Y
-
=
.‘
-
_
._
._
_
-
_-
-
-I
Jownol of Mass Spectromcby Scientific Publishing Company,
- --L--L*.=-_.-s
’ i$. -3 -7-_
ON TEE MEASUREMENT OF GAS-PHASE ION-MOLECULE EQUILIBRIUM CONSTANTS IN AN ION CY CLOTRON RESONANCE SPECTROMEI’ER WILLIAM DONALD Deportment (UxA_] (Fust
R_ DAVIDSO H. AU8 of Chemistry,
received
‘Ml?. BOWERS,
N, NICHAEZ
16 September
University 1976;
TOMOTHY
of Chlifomia in revised
SU * and
Santa Bar&mu,
form
26 October
Cdifonxia
93106
1976)
The technique used iu measuring ion--molecule equilibrium constants, in particular proton-txausfer equilibrium constants, with a high presswe drift cell ion cyclotron resonance spectrometer is described. Experimental aud kinetic problems which occur iu such measurements aud their effect on the determination of accurate equilibrium constanta am discussed, Non-attainment of equilibrium may result from either slow proton-transfer rates or fast competitive side reactiona With proper experimental technique. errors in free energies caused by such kiuetic problems-may ususlI~ be kept-below 0.2 kcal mol-‘. A number of examples are given_ While the analysis is applied to high pressuG drift cell ICR. most of the co . - ts are applicable to equilibrium measure meuts with auy type of apparatus-
lNTRODUCXlON
There has heen considerabIe interest in recent years in the measurement of gas-phase ion-molecule equilibrium consknts [l]_ The. most extensively studied class of reactions is protc rl-k-ansfer equilibrium [2-4] exemplised in eqn- (1) AHY++R==BH++A
(1)
Measurement of equilibrium constants for reactions of thistype yield directly aaaxate gas-phase basicities (GB’s) of A and B. PGO- GB(A) 7 GWB) =--RTl&C In the absence
-* Presnt
-
(2)
of entropy effects, these relative gas-phase basicities are equal
&xress: De-t Dartmf%uti&Masuchnrrtb~2747;U.s.A-
-uaetta
of Qdnistrp.-south-~ .
. -
_
-
Universi~;
North
t& the dative
proton affmities (PA’s) of A and B
AGO = A*
= PA(A) - PA(B) (3) Proton-tzm.&r-equFEibris were first measumd using‘ion cycIotron msonance(ICR)techniques f531,buthavermbsequentIybeenstudiedusinghigh pressure mass spectrometry j4] and ffowing aftergIow techniques WI- FormaUysimikequilibriummeasme~ents havekenmadeonnegativeionsystems [S] yieIding relative -phase acidities. Hydride-transfer [7 J , hahde&an&r [Sl, and charge-txansk 191 equilibria have also been measured recent&, whi.Ie various ionic clustering and exchange reactions have been studied by equilibrium techniques for some time [lOI _ In tfiis paper, we discuss in detail some of the experimental and kinetic probbms that may be encountered in the measure ment of equilibrium constants for proton-trausfkr reactions. In particular, the kinetic consequences ofiheoc cunznce of side reactions in competition with proton-transfer and how such side reactions affect the m easurement of proton-transfer equilibrium constants am considered_ Ion cyclotron resonance tichuiques, particuIady those involving high pressure drift ceII measurements, are discussed here; but the kinetic concepts developed am readiIy applicable to other expersmental metbcxkand EzUSon typesMeasurement of a proton-transfer equilibrium (eqn. 1) presents a problem of competition from potentiahy rapid dimerzation reactions at high pressures-The simple reaction given in eqn- 1 is IikeIy to be much more complex as shown in the kinetic scheme I SCHEME1 BH++A
(AHB+)* _
B li 1T (BwB3* w-=+1* M ?a M. B I I 1 AHA+-AHB+& AH++BA
A
A
BHB +
In Scheme I, M is a stabSzing molecule, usuaUy either A or B, which carries away excess energy from the vibmtionahy excited dimer_ Hundreds of systerns have been studied here and for most amines and oxpgenated molecules, proton-bound dimer formation is observed as a dominant process at higb presumes- The question *en arises whether or not these fsst dimerizatZon IXSiCtiOnS sszbstmtialsp afkd t&e simple proton &anskrequS&iabeingmeasuredOur approach to this problem is twofoid. First, we have soIved the cornpIex kinetics of Sheme I andtheaet5caI.&p_+iictedtlxeef&+qn‘tbeequilibriumoonstantat~us presses for various values of rata2conzitu&s. Set-_
-_;*:-:’ ond, we have measured dimerization rate constants and proton-transfer r&z constants for a number of systems. We then chose pairs of molecuks that would most severely test the abii@~ of the drift cell ICR to measure protintransfer equilibria at high pressure and proceeded to measure apparent equilibrium amstants. The results and a discussion of the iimits within which accurate equilibrium constant can be measured ~6th an ICR kpectrometer are presented here. THEORY
For the purposes of this paper only the magnitude of the dimerization rates relative to the rate of proton transfer are of interest. Hence, *Se detailed mechanism of Scheme I can be more conveniently written as Scheme II SCHEME
LI
ABJ3+
&H+
&2H+
where kl and k_, are bimolecular tions for the disappeaxance
-d!!
proton-transfer rate constants. Rate equaof AH? and Bw can then be written as
= (PI + p2 + v3) [AH+]
df
-
v-dBH+I
(4)
and -
d[BH+l dt
= (Y_~ + V, + v,) [BH+ J -
vl [AH.+]
(5)
where vwl=
vx = k,lBl ~2
=
k,tN
~4
=
k4
Frl
[Al CM1
k-l[A]
va = biBI
WI
~5
LMI
=
k,[BJ
and kz,ks,k4 and kSarethethirdarclerrateconstantsthatcharacterfiethe
variousdim~nreactions: 'phe two dif%renW equations (4) and (5, Can be solved simultaneously. The relatke g&&t’ [C.b
am~~ons.of
AXi? and Bm
---~~~--‘_~~ti=le~‘P-Q~~ -;
--
__s:
-.
2Q -. __ _ . .
;‘
_
- _--
-_
at sky time, _ _-
y
‘_-_ - _ _
_
t, are found “-‘
_
to be _
(6)
(7) where P=
.
(v~+v-~+v*+P~+v~+~s)/2
Q= [(v~+Y~+v~ c,=
-u_~
-v,--v,)2
I(% + v, + us) - (P-
QH-
+&4yrV-11~‘=/2 V-,CBH‘+IdCAH+fo
C,=v_,~B~]~/[AIf'l,-~(v1+-2+~~)-(~+
c, = [(v_~ + vd + us) - (Pc, = Y@W~~/CBWI~-
613
-
813
VI I~lo/P=+lo
W-x + vd* a) - (p + QII
Theratio ofthetwoionintensiti~,experimentallym~,
isthengiven
byeqn-(82 [BEI+],
IBEX+ Jo
cJ=+lt = IAWO
C2e-cP+Q)r
+ C4e-cP-Q’t
+ c2e-
U3)
Inthisstudy,tBefo~~~:noftheprotonatedspeciesis GSUlIldtQkVerg rapid and~einitialIcon~trationsof~andBH'aredirectEyproportional tothepresnues of A and B,respectively [ll].The apparent equilibrium constantforreaction(l)obtained experimentz3lIyatthnetistherefore [Bwlr[A] C3e-~'+Q,r+C~e-
Equilibrium
CONSIDERATIONS
consiants
-
muencyofthe ~al~~risv~~untizitmatches~ecg~~~~‘, _.: it- -_ frequekyofanion. Eady ICR~~~studiesemploydtheco~tmarginaZosc~= ~q.uencyte&nique~2l,ThiswasneceSXug becausethesensitivi~ofthe mazgmalosciiktor wassomeunknownfunctionoffrequency_Themajor drawbacktomeasurin grelativeionintensitiesatconstant~quency-and henqevariablemamretic~ldsisthatthedrifttimesofionsin~edriftcell ICRaredirectlyproportionaltotbemagneticfield.Iftwoionsreachequilibtium conditionsrapidly,andthereareno competit3esidereactionsorion loaves depleting either or botbions,a variationin reaction times willnot affect the measurement of an equilibrium constant_ This point is demonstzatedintheionintensitpcurvescalculated in Fig.l(a)_In thishypothetical proton-transferreaction, BH' and_AH+reach eqtibriumwithin1,5ms. Parametersusedarekl = 6 -lO-lo cm'mol-' s-‘,k_a = 5 -lo-" cm3 mol-l s-l, K=12,thep~ureofA=4-104ton,andthepre~ ofB=l-10' torr.ThepressuresaresimilartothoseusedexperimentallyintheICRdrift
(b)
Ka = 2.5
0
-
LO . time x 103,
2.0 S
3.0
-ceII [Z]; the r&e constants are typicai of proton-transfer rates. It is azmuned that ffieinitialbdensii~oftheionare proportionalt0thepresnrres ofthe If we set the mass of BH‘to be twice that of AH: BH’ neutralspecies [ll]_ wili come into resonance at twice the magnetic field that AH* comes into resonance_ The average drift time of BH‘at resonance will then be twice that of AH*_ However, the ion intensities do not change significantly between tl (when AH’ is measured ) and & (when BH’ is measured) and the measured equilibrium constant wilI not be in error_ If, however, there are competitive reactions or ion losses, such will not be the case_ Suppose that both AEI’and BWare depleted by side reactions with rate constants of ilr3 s-l_ The relative ion intensities fast pseudo fir&order will then be described by F’ig_ l(b). In this case the ion intensities change markediy between t, and t2_ The apparent equilibrium constant would be 2.5 rather than the actual equilibrium constant of 12_ The en-or in Ac” for the reaction would then be O-95 kcal mol-‘_ It should be emphasized that this is an extreme case_ A fistorder toss rate constant of 103 s-* is huger than normaily encountered_ In addition, most of the equilibrium data obtained at variable magnetic fieid have been measured between ions of similar (* lO-30%) mass to minimize the effect due to magnetic field change- Thus tl and & are not significantIy different. and the errors in the free energies are usually not serious. Recently, reliable methods have been developed for calibrating the sensitivity of the marginal oscillator detector as a function of frequency [12]. Hence, it is now possible to operate the ICR spectrometer at constant magnetic fieid- TabIe I compares some equilibrium constants obtained at constant and variable magnetic field. As can be seen, the errors in free energy are usuahy less than 0.3 kcai mol-‘_ The errors in AG” in Table I are closely predicted from the kinetic expression, eqn- (9), using measured values of rate factors v,, v-,, vz and vS for these systems. TYpically, for a reaction such as (I), the neutral species A and B are admitted to the drift cell with a total pressure between 4 and 8 - lo4 torr_ The ratio of the neutrais seIdom exceeds 10 : 1. The magnetic field is kept constant, usually at 14-15 kiiogauss. The parent ions (or fragments) formed in the electron beam generally rapidly protonate the neutrals to form AH* and BEi*_ The ions AH’ and BH’ are observed by varying the margiilaI osciiIator frequency until it matches the M ‘ve cyclotron frequencies of the ions- The power absorbed by the ions is then m easured by sweeping the magnetic field over the peak (usually only a few gauss wide). Under high pressure conditions the inStantaneous power absorbed at resonance per ion,A,, Is 1131 A,/ion=S-
cz’ei
4mE where Ed is the ampiitude tram&r collision wuency,
__
(10)
of the o&erving frequency, g $ &e=momentum and S is a ‘te.un rep resenting the sensitivity of
B
-2
*2NJ5
*ma *NH2 z?BUNH2 Me2NH Pyfidine Me3N nPr2NH N-Mepiperidine sBupNH
m3N
QlliIUlClirline
nBuNH2 fiNI. -2 Me2NH 2-Picoline Et2m nBu2NH
DifferenceinAGOd (kcalmot-1)
KG=
A
0.77 1.23 0.81 1.61 0.58 1.57 0.73 1.30 0.78 0.93
6.1 2.3 0.85 16.4 0.72 4.0 19.3 7.2 22.8 1.4
9.2 1.8 1.18 6.6 1.64 2.7 29.1 4.1 22.8 1.6
-0.25 0.15 -0.2 0.55 -0.50 0.25 -0.25 0.35 O.O= -0.1
a Ratioofthe masesoftheprotonatedspecks. bApparentequiliirium constantatconstantfrequency,D.H.Aue,H.M. Bowel73,unpubIishedresulk c Apparentequiliirium constantatconstautmagneticfield,ref. 3(b). dDiscrepancyinAGObetareenco~t~eldandconstantfreqaencydata. l Littleornodimerizationt.akesplace.
WebbandM.T.
the marginal oscillatorat the observingfrequency_Theintegratedpower absorption &then A&&al)
=
Sn*rq2Es
(11)
4m.C
where n' is the ion concentration and T is the time the ion sr,=ds in resonance.The ratio ofthepowerabsorption fortheionsBw and AH+ at constant Ed is then given in eqn. (12) A,(BH+)
[BH+l ~EH+ ~AIP EAH+ &IV c-r------(12) AptA=) C-3 ~AH+ ~BH- EBH* %I+ Thecollisionfkequenciesathighpmzssure areequaltothehti-widthathaifheight of the output ~al(ie_I=Aw1/2)[13].The half-width obtained experimertanyisinLmitSofgauss.Since oaH/m then Ao=AHI&m Al.so,a~constant
A,(BH+).:s-w [BE]. A&=? IA=+&
~~d,r~=T~,811C18qn_(12)reduceSto AI_irn,ux+ SEE+ J&m+-sAB+
. *
-
(13)
(14)
Thus, by measmmg the peak heights of AH’ and BH: the half-width at halfheight of the peaks, the sensitivity of the marginal oscGator at the two resonance frequencies and the partial pressures of A an5 B, the equilibrium constant for reaction (1) may be caIculafed_ Limitatins
in me aswing equilibrium
constants
gas-phase equilibrium constants, AswithalItechniquesusedtomeasure the drift ceil ICR method has its Iimitations. Due to signal to noise restrictions, it is very difficult to measure relative ion intensities greater than 100 I 1. Although ece manometers are accura te in the lo4 torr range, it is very difficult to measure neutral pressure ratios greater than 10 f 1 with any precision. This means, ignoring kinetic restrictions, that the maximum equilibrium constant that can be measured under ideal conditions onadriftcehwithany accuracy would be 1000, corresponding to a Ac” of 4.2 kcai mol-’ at 305 II. Loss of resolution due to coIlision broadening of the peaks can also be a problem at the pmssures used in drift cell equilibrium experiments. This is particularly serious when the protonamd ion being studied has an unreactive parentorP-1 fragmention.Zftheprotonafxdionisofapproximatelythe sameintensityastheinterferingpeak,thetwopeaks maybedeconvoluted
assuming Lorentzian hne shapes. Such a procedure, if carefully done, leads . . to ~errorsinthetruepeakheightandwidth. Kinetic restrictions must also be taken into account. These limitations are twofold: (1) the rate of equiliition may be too slow to achieve equilibrium within the experimental reaction time, or (2) the rate of equilibration may be too slow to complete with competitive reactions or ion losses. Measurement of eauilibrium constants with a drift celI ICR is thus limited bv the rates of the f&ward and reverse reactions. If there are no competitive reactions (such as dimerization reactions), eqn. (8) may he simphfied to yield [BHX L=+l,
=
(l-2 6sx
y_1
R.
)
R.
-
e-<9+P--lh
1
)
e--
+
~p3 + 1) + (R.
(15)
+I)
where R,, is the ratio of the initial intensities_ Using eqn. (15) and ins&ing various experiment3I parameter% it is pqssihIe.to determine how serious erros in the equilibrium coustsn tmightbedu+ooverlysIowrabesofpro-
ton transfer_Table 2 demonstrateshowtheapparentequilibriumcons&tbecomesLessreliableastheratesoftheproton-transferre~ondecrease.Thetotalpressure usedZnthiscalculationwas6-104~rrwithap~ ratio(A-B)of5:1,Theseare @pical experimentalparametersforequilibriumconstantsofthemagnitudegiveninTable 2.The timeofthereaction wasassumedtobe3ms,atypicalreactiontimeunderexperimentalconditions,F?romTable 2itcan beseen that,forIargeequilihriumconstants,the errorsinthefreeenergyaresubstantialunlesstheproton-transferreactions are fast (>6 -1O-1o cm3 mol-' s-I).Forsmellerequihbrium constants these errorsarelessserious_ Innormaldriftcellequilibriume xperiments,thetotalpressureandpressureratioarevaried.Ifthesystemisinequilibrium,theapparentequilibrium constant should not vary with either pressure or presu~ ratio,Figure 2 efora showshowtbeapparentequiZibriumconstantvarieswithtotalpressur hypothetical reaction in which K=lO, (k, +k,)= 3 -lo-" cm3 rnol-‘~‘~, t=3-10-3s,andthepressure ratio(A:B)is5:l.Asthetotalpressure incre~s,~eapparentequilibriumconstantapproachesthetrueeq~brium constant,aswouldbeexpected_Ifsuchanexperimentwereundertaken,the variationof& with pressure would indicate immediately thatthesystem wasnotateqr3ibrium_Foreveryequilibriumexperimentinthislaboratory, suchacheckFsmadeoveraslargeapresmrrt3rangeaspossible_
(kl+ (an3
k-1) lllol?
K=
-10-J
500
K-SO
K==5
s-=) bra in AC0
K.
496
(0.00)
494 464 460 406 309 187 89 35 11
(0.01) (0.02) :i%:
53.0 50-O 499 49-7 49.2 47.8 it-:
Ka
10
9 9 7 6 5 4 3 2 1 ~hkcdmol=at305g_ ~Etracke-~~in~ cThatOMiB; _ .3_ -. _:
(0:29) (o-6o' (1.05) (1.62) (2-34)
Error8
K.
inAGo
22k S-3
::-x:;
5.00 5.00 5.00 5.00 s-00 ELoo4.99 495 4-75 3.34
pz; (&Ol) (0_02) (0.08) (0.20) (0-4m (1.02)
~6-1~-torr;tberatioP~/PB~S:l;Pndthe~ntime
_.
-
-.
-_
Error’
iRLG0
.
_
-
(0.00) (O-00) (O.Oct) (0.00) (0.00) (0.00) (O-00) (0.01) (0.03) (0.16)
.
_
Notmol
.
120
-
Experkental
_
Range
-
f
10.0 -
.
0
.
0
8.0 -
0
6.0-
0 0
4-O 20o-o0
*
1
I
I t I I 2 4 Total Pressure x 104. Tot-r
Fig_ 2. Pbtofthe apparent equilibrium riumreaetioa(1)_IC=10, k,+k-I= b
I 6
-
constant,K,,Kpresnue 3-10-x0anSmo~*s~-‘.
fortbegeneralequilibandt=3 -IO-’
PA/P~=5,
Therateofproton-transferbetweenthetwobasesAandBdetermines the rate at~~thesystem~comeintothermodynamicequilibrium.Hence, theproton-transferrateconstants, itisveryimportanttobea.bktomeasure at least for the f&treaction_Therate constants forproton-transferusedin thisstudyweremeasured bythreetechniques:(l)trapped-ioncellejection, (2)approach to equilibrium,and (3)lowpressure-lowconversion_Allthree methods involved approximations and/or assumptionsofsomesortandtbe rateconstantsderived~mthemcznonlybeconsideredaccuratetoi20C7. Forthepurposeofthispaper,thisaccuracyisco~deredadequate.Exampies ofeach ofthethreemefhod.saregivenhereaIongwithadiscu&onof theIimitationsofeack The~p~-ioncellejection~quefiasbeendesaibedby McIver and Eykr [14J_Forre~nssuchas(l),oneof~eions(BN'orAH3isejecfed continuo~fromthece~byappIyinganRFvoItageatabrequencyequal tothenesonance~~cyoftbeion_Thed~aseinintensltywithtimeof theotherion(AH+ or BH?isthenrecorded andtheforwardorreverserate constantisobtainedThee~dfonRFvoltageis~appliedaftertheions have~~~equilibrium,AtypicaIcaseisshownin~.3forreaction(l6)
(16)
300
200
(00
0
TLME
(ms~
Fig. 3. Plot of ion intensity vs_ time of protonated pyridine, CsHsNH+, in a mixture of 4 10m7 torr pyridine and 9 - X0-’ torr (CHs)zNH_ The r&e constant of reaction (16) was de-srmined from the decrease in pyridinium ion signal when protonated dimethylamine is ejected from the cell.
ejecting the protonated dimethylamine leads to a rate constant for reaction (16) of 3.2 - lo-lo cm3 mol-’ s-l_ The major disadvantage of the tipped-ion cell ejectionmethod is uncertainty in the pressure measurement. The pressures of the neutral species are measured with an ionization gauge, the ionization gauge being calibrated at high presmres(104 torr)against a capacitance manometer_ It assumed
is
totheextentthat ~at~eionizationgaugecaZibrationisLinearwithpressure itisaccmrateinthe10~-106t.orrpre5surerynge. Measuringthe approach to equilibrium is awellestabkhed technique [X5]_ Wheu there are no side reactions,eqn. (8) may be rearranged-and rewritten,in a form similarto that givenby Benson[l6] togield(17).The neutralspeciesAand
-
[BH+]) =ln([AH+]oK -
WdBl
z,-
CBI+I+jo)
+ &-IIAI If
(17)
s are kept cosistant throughB&admittedtothedriftcellandthepressure o-St the experiment. ‘I&e drift times (and thus he reaction times)- of the ions are varied by chauging the magnetic field. At each magnetic field setting, the i&&.si~~of AH’ and BH’ are measured. A plot of In([AH+lK[B]/[A] [~~7)~fyieldsaslogeequalto_I~l[B] +k,[A]).Ekomalmowiedgeof tile m constant, K, (determined at long drift tlme~), kl and k-s m
i
1
t
I
,
I
.
IS time x 103. s Fig_ 4_ Plot of ln(AHII(B/A - BH> vh time nPT3N;PAIPB=4;PA+PB=6-104torr-
I
2.0 for reaction
(18),
where
A = nPrEtzN;
B =
ob~ed_Suchaplotisgivenforre~on(lS)inFig.4 *cl nPr~NH++nPrE~N nPrEQJH'+nPr~N(13) Ll Thisreaction waschosensincsetherateofproton-bounddimerformationFs very slow for all specks. The derived rate constants are: k1=2.35-10-'0 cm3 mol" 0, k, = 22 - lo-*' cm3 mol" s-l_ lowconversiontech.niquehasbeeuusedexter&velyfn ThelowpressuteofAare drift cel.IICRstudks [17].Forreactionssuch as(l)highpresures admittedto thedriftceII(-1-2-104 torr)_TheAWpeakismonitored_ LowpressuresofB(l-lO-lO"~rr)arethenaddedtothedriftcellandthe decreasintheintensityofAH+ismeasured.Therateequationforthereactionisgivenby(19)
- N-1 dt
(19)
=k,CBlC~l
whichintegratesto
In(s)=
-k,[a]
t
(20)
0.6
-In
A!Y!T (
&H,+ 1
0.4
0.2
o-0
4
2
Fig_ 5. Plot of In(AI-I+/AH~) P*=1-10--4t~;f=2-10-~s.
6
8
10
P(acetane) x t06_ Tarr vs. acetone pressure for reaction
(21)
where
A = isobutene;
The rate constant measked for this reaction was 1.05 - lo* cm3 mol-’ s-l_ This technique has certain disadvantages. The equilibrium constant must he large (Le. k, >> k-,) in order that the reverse reaction does not repLeG& AH*- In addition, adding the neutral B may also increase the-inter&* of AH’, if B’ or fragments formed in the electron beam react with A for form In general, this method will usually give a lower limit to the rate AH‘. constank Some proton-transfer rate constants measured by the various techniques decribed here are given in Table 3_ For those rate constants mm by more than one technique, good agreement was obtained (*20%)_ Dimerization
rate constants
The mechanism of dimer formation in ion--molecule reactions is an active field of study [18,19]_ The mechanism most commonly used to explain the phenomenological dimerization reaction (22) AE++A~AAZH+ isgivenin(23j
(22) -
‘k
(AaH+)* ?!AtH+ (23) ks‘ __ ..% - . - ._ &ereMis_a&‘--‘-gthird_M~~If(A,EE~*is assu&dto‘beina&eady state, *en the jph~omenological rate constant += can be w+kn i& tims of the microsco co+=ti-_. --. _. ._ *_=t= - -AH++A-
cm*
0 CCCH&
+
II
CH,CCbI,-C”&H,
+
-(CH&:dH’
CH,=CtO+,
+
2.6
+
‘CH,@H-
=H3’2N’%
-7O-lo
-
+
A-
ed b Determined c Determined d Determined
= Determin
from
trap cell ejection-
from Iow p4-essure-Iow conversion erpeximents. from from
approach to equilibrium. equilibrium constant
Therateconstantasso~~withthedimerizationisthusthird~onlerinthe LimitM~OandsecondorderinthelimitM~Owitbacontinuoustransitionbetween third-and zcond-otieratintermediate prssures. Themechanism(23)hasbeenshowntx~ bevalidforanumberofsystemsinchxling NH3 and the methy~es[lS
CY-
/
C-
'N
Kxg2c=o a Ref.
19ib
Ref.
20_
are measured are given elsewhere [19]_ A sampling of thirdorder rati constants measured here for various systems is given in Table 4. These rates were chosen to exempw the range of rate constants experimentahy encountered and cover most of the molecules considered in this paper.
rate constants
THE
EFFECT
OF DIBAFXUZ
ATION
ON
PROTON-TRANSFER
EQUILIBRLA
Most nitrogen and oxygen compounds readily form proton-hound dimers. The effect these competitive reactions have on the measurement of equiiibrium constants is dependent upon: (1) the rate constants of the dimerixation reactions, (2) the rate constants of the proton-transfer reactions, (3) the total pressure of neutrals, and (4) the pressure ratio of the neutrals. Many dimeriaation rates have heen measured in this laboratory [19,20], a sampling of which is given in Table 4. The fastest third-order rate constants measumd at room temperature have not exceeded l-2 - lOa cm6 molm2s-l; the slowest rate constants (which are conveniently measurable under drift ceil ICR conditions) are in the 1O36 cm6 mo13 s” range. We can arbitrarily cail a warder dimer rate constaut of 1O33 cm6 mol* s-i, a fast rate con&an*; one of 10”’ cm6 mo13 s-‘, a moderate rate constant; and one of lo*’ cm6 mol* s-l or Iess, a slow rate constant. The effect of such dimerization constants on a proton-tmnsfer equilibrium consmnt is shown in Table 5. It can be seen tipm Table 5 that, if the dime&&ion rate constants, kl and k,,are equ~& the effect on the equilibrium constantisniL-However, when there is a.dS%nce between -k<_pd kS,theapparentequilibziumis &.iftai'~* the-more-alowly N specie& The worst case is 8 fast BHT v-&d .-_ aslow AHYd‘ _ . ‘on. Tile n+d dimer_rate con-
l-lo-= l-lo-= l-lo-= 1-m-= 1-1o-a 1-10-a l-10-2" ;:$I;;
1’
lo-=
10.0 12.4
I- 10-s 1' 10-s 1-m-= ;: 11I-
Yi 10.0 102 7-6 9s 10-o
;gi 10-s 10-a m-25
0.00
-a13 -0.14 0.16 0.00 -O_Ol 0.18 o-01 0.00
= SIpeiimantlil pcsmmnEters:E~lO;tofaIprereure=4-10~ torzP~/P~=l.0;reaction time * 3 ms; k3 and k4 ascuned ~beebeaverageofk2andks;kl+k-l=5-10-10 cm3 morx IJ kcd marl
a-=. at 305K
stanfs(k3 and k4) wouldshow thesameeffect. However,inthistreabnent R,andkqhavlzbeenassuzned tobeequali;oeaclxothezandbethemeanof k, and k+ Ifthedim~onrateco~tis purethird-ordfzroverthepressure range oft&e expehWnt&3Jlincreaseinthetotalpresmue willincreasethe dimeri2xGonrateinahear manner_ With respect to the second-order proton_transferrate,adifferentialdimer~edwouldincreasingl3innuence themeasuedeqGWhxmcon&antwit&in~gpresmue. Inge~eraLthe orderofadimerizathn~constantvaries withtotalpressure -M-order atP-,Ostndsecond~atP+~.Howeves, forthesakeofsimplicity,we wiiIassumethatitmmainspurethird~~overtbepressune rangeweane considering-Figure 6isa~pIotoftheerrorinAG" vs_totalpressureforvariouspro~n~eceqalIibnumconstants,whenethe~~on~AH'is SIOW (pp,=lo*s cmb moI* s*)and-the d.imexiz&ion of_BH'is f&t (k,= X0-= cm? moP s-'I-It must-&z_empl - ' that-Fig_-6ov~ errors,sin~tfrefast~on-rate.c~~_appioachsecon ds: athigher ~lntberthzuiiinezuiyiqczre&ng-as‘~~-~d&~ one wouldexI)Bct;-boy; thehig@r$he_tqcal-+ssure; the-m&serioir;r lheenorsinfbe-measux4equ%.&ium constsmt..T%e~ezzorat-lowpressuresisdueto.n~~t~~~.~~~:~~;if‘ _
-
-,
='.F'-"~I
I
i
I
. ~ - . . ~, -
i
1.2
KilO0 - . ~
o.s
N c
l ~ -
0.4
Normot
K-
Hxperimento!
Range
I
! 2
0
I 4 Totol
1 6
Prate
I 8
x tO 4
l tO
Torr
F~g_ 6 . P l o t o f t h e e r r o z in AG ° vs. total pressure for a system reacting according to Scheme I_I: k l ÷ k - I ~ 5 - 1 0 - z ° c l n 3 t o o l - ~ s - l ; k 2 == 1 - 1 0 - 2 s c m 6 t o o l - 2 s - 1 ; k s = I 1 0 - 2 3 c z n 6 t o o l -:~ s - l ; k 3 = k 4 =ffi(IT¢2 + k S / 2 ) ; P A = P B ; a n d t = 3 - 1 0 - 3 s.
there were no competitive dimexization reactions. The neutrd~ pressure ratio also infl.p~ces the total rate of dimerization, w h i c h i n t u r n a f f e c t s t h e m e a s t t r e m e n t o f t h e e q u i l i b r i i l m c o n s t a n t . T h i ~ is best illustrated by Fig. 7, a plot of error in free energies for various equilibr i - m c o n s t a n t s v s . t h e m o l e f r a c t i o n o f A . Aff~in w e a s ~ m e t h e w o r s t ciro c=]m~nces - - f a s t d i r n e r i z a t i o n o f B H * , s l o w d i r n e x i z a t i o n o f A H ÷. T h e o r e t | 0o0
t
i
i
--
K:I
0.4..I:
\
<3
i= t=.
Normol
0.8-
Kxperi~entol
Range
N K=
I00
ti.l
1.2! 0.2
(;
I 0.4 Mole
F/~ 7. Plot c~ the ~ 8chemm:ll:
kt
lo-~ o cm~ mo~
4- k - I [
~:;
Fraction
m ~ s .
m_ 5 - 1 0 -
I0 . ~
I 0.8
I 0.6
1.0
of A
m o l e ~ a c J ~ o n Of A t c ~ a . ~ . L e m ~
3 ~ F z o l - I.
s- I ;k2.
k~ = k4 - (k2 + ksig);P~.;
-~
=t 1 " 1 o -
1 2 _ ¢ m 3 . t ~o1o- l--1
~
to
s - • ; k s _ ~=1 -
- x o-4 to~. and t = a" 10-3 ~
equilibrium conically, as shown in Fig- 7, the &sf ~situation for accuras stant me asutementsisaneutratmixwithsmallamountsofA(lessthan s of B were used, the mono50%)_ Experim&taE&, however, ifhigh‘plX?SWe mer ion intensities wouId he too low to measure due to the rapid formation of cismerS. Thus, one must be careN not to be fooled by large ion intensities at a high NB ratio which conId Jead to highly erroneous results. When measuring equilibriuxu cronstants ~5th an ICR drift cell, the ratio of neutral species is varied. If the apparent equilibrium constant varies with the mole fraction of neutzaI species, the e xperiment is not u&d to obtain thermochemical data_ If the rate of protin-transfer is close to the rate of dim&i&ion, measurement of proton-transfer equilii+ is in jeopardy_ In Fig_ 8, the error in AGo is plotted vs_ the total proton-transfer rate for a slow/f&& dimerization case for various equilibrium constants_ The total pressure is taken as 4 - IO+ torr, theratioAtBasl~l,andthe~ti
-
1
K= 100 -
I
I
I
I
In$eneral,tbefo~~on~iproton-bounddimerscanhweapronol?n‘dea;_~ eff+t on the_me_asurement of proton-transfere~~~_constan~_Ho~~ ever,withproperexperim entaItechniquetheerrorsinfi~2en~escanbe keptbelow O.Z@almol-I. _SAMPLEEixPExlME
NTALSYE?l?EnuS
Inthis section,the&ectofdimerizationon actualdriftcellequiiibrium experiments will be discussed_The rati constantsforproton-transferxeactionswere measuredby one or more ofthethree techniquesdescribedearlier_Tbedimeri.zationrate constantswere measuredasafunctionofneutral pressure,andtherateconstantscorrespon~tothepressureoftheneutrals intheequiIibxiumexperimentwereused_ Acetone
The
and isobutene
for reaction_(25)
apparent proton-transfer equilibrium co-t OH+ + C&COC&
C(CH,):
n
= CH3 CC&
+ CH,=C(CX-I,)~
. (25)
hasbeenstudiedcarefullysinceisobuteneisakeycom~~din
obtaining
TABLE6 CalcuIatedanderperimental ioninkenzities~ and apparentequilibriumcoxutantsforthe reaction
hAellsity of rntensity of c4s Mole
cH
Og 3
3
xa
flaction
0faaztoIle
Expt-
0.11 0.21 0.29
55 24 13
0.36 0.46 0.60 0.17
6.5 -
-3 -
calc_b
Expt
calcb
11-3 11.5 -
-81 71. 14 6.9 3.6 1.1 0.23
63 48 36 20 IO.2
E&pt.
69 49 36 19 8.9
Et-0 12.3 -14
calcb 12.8 -12.0 12.1 11-8 11.7 11-6 IL4
(abo~_2 -~10~~~)~[20~ZOn'theo~~hand;~~t~u~~-catlondimeriies:verysIowi+andis m_m-third~rcjertiptotf;eisobti~ep~ cif 5.IO_ torr [2O],_TG alird~~tierdiinerizationrate calg%Inh__~ givenin TabIe 4_“Il1e_ forward and reverse proton-tra&ferrate&nstaritsfor%actKoti (27) are given_ti'.lhble3_Tfie variationofthe apparentequil&iumconstant forreaction @7)%kEHi'~oIe friiction of acetime is pres&ted*mTable‘6.-The tdaIpresuretixi%n~ed -at4-~0~tonandthe'reaEtion~ewas2.3 ms.Th&epeiimental-p;aiame~ersrere~~bubsti~~into~.(S) and by itam&on;fheTzue"eq&iibriumc;onstant_iRas determined.'Fortheprotin-tzan&er reactS& (251, the equiEh&mx am&ant which best fits the ~&entalda~isK= 14.Thecalcutated norma&edionfn?znsitiesusing ted along with the experimentalnorthisequilibriumconstaIltarepresen . mahzedintensitiesinTabIe 6.The agreementis extremeIygood.Theerror in tfie&eeenergyisthe&~O.lO kcal mol-'. example bf bt The acetc&+sobutine proton-transferxeactionisagood caseofsIow/fastdim~on,~~ which proton transferisrapid.Theerrors causedbydim~tionares~tandwithinthequotedexperimentalerror lin+(*O.2 kcalmol-I). _ _ Quinuclidine and tr&thylamine This system, given byreaction (261, representsanothercase ofslow/f&st
(26) ~~tionrates.Theproton-transferIs~rapid,aswasthecaseinthe acetone-isobuten&~system.Theprotoxi-trans&rratesZ.WepreSentedinTabIe3. Quinuclidinedime3izes rapidtyandappearstoapproacfiase~nd-orderlimit moP s-' at-h&b quinuclidine presumes methylof R, = 7.9 -10~"cm3 aminedimerizes e&reme&siowly.Thethird-arderrateamstaIltsaregivenin equilibrium constant is 1.65. Usingeqn. (9) and Table4.Themeztsur& ~g~~~p~~leadstoap~~constantofl-_90. TheerrorinAGOis~O.l~mol-i.~,tbe~rdueto~~oqis sIightandwellwit.bineqxMmentalwts. -. -- .- _
&P&dine
(pltl
trime*yh&
:I-
.. .-
r -_ _-
:_._ A. _- -._; -1 -_-
+ CCi+,?,NB
(27) _
_ H-,, 1: -. The Pr&*-@a&e= rate constants a+*&esented.in Table 4. The Lnued drift .celI.q@ibrigm constant ig 3-O; the *cuIated equjli~_~:co~t is 25._Tlxe enxx jn free energy for rgaction (27) is then -0.1 kcal mol:‘_ Re&&on_(27)-qeas-also studied with a high-p&sure mass spectzometer [21] and theT.X&ivtiim of California.,,“› Santa;Barbara trapPed ion cell ICR q+ctrom&er~ The results are p resentedinTable7~-Thetrapc&loper&esat
Iowpresusswilerethird~rderd.im~tionp~cesses arenegligiblea~dthe gasss~ectrometerat extremefy.&#ghpywhelx?totzll equilibriumbetweenallspeciesis~~.The~meptforallthree metbodskquitegood,demonstratingtfiat~edimerizationprocesses arenot greatlyperturbingthem easurementoftheequilibriumconstantinthedrift cellICR for this system_
UP======
eridine
arui dimethylamine
The above reactions -ilha&ate the Worst casfzs for dimerization affecthg equiliiriumconstantmeasurem ent. A mor& typical c& is given by-reaction <28), the proton-tmnsfer betweenpyridiueanddimethylamiue.Pyridine
dnnerizes moderately
fast anddimethyhmineslowiy(see
Table4), Using
eip_ (&the
eqdSium
constant L ii65. The &ror in the &e is O-03 kcal mol-* _
reactiondue $.a dimerizatbti
hsummarg,
prot~n-t&sferreacti~n
energy of the
fkeeenergies measwedinan
-
.
ICR
driftcell-a&t-sli&tiyin error-d~tb~~formationofprotonbo~d-dimes. above;these_errorsa~e_well‘withintheexperimenHowev&~_asdemo&rated taI error_It‘shtiuldbe poi+t&d outtbstallion--moIecuteequilibriumconmassspectrometry,fIowing stan*measmedbyanytecbnique(highpresure ~ow.~~-ioneeIIICR,etc-)aresubjecttoenrorscausedbycompetitiveside r&&ionf& *w‘eq "7 '-on reactions,or dif&rentialion Iosses, by‘thereactionS&emeIIcanbeexpandedto Thekinetic"schem&expres& inchxde all~oEion-moIeculereactionsandionlossme&anismsfo~owingatreaianent&miMtothatappliedhere. Finnllv,ftfiasbeenour-experience~anoccasionalre~onwillnot cometoequilibriumdue~eitherfastcondensationreadionsor~mely slow~brsrtion~reactions.In~esecases,thebestthatcanbedoneisto "~~~t~~econnpoundsof~~usingdoubleresonan~techniques,or othertechniquesthatdemonstratethe occurenceornon~ccuren ceofareaction_Suchbracketingresultspieldproton~ti~~atarecrudebyequilibriumstandard-(2 ~~kcaI),buttheyareoftensufficientformanychemicalapplic&ionsofthedata. ACENOWIXDGEMBNT We
gratefulIy
acknowledge
tionundergrants MPS73-04657
Ihesupportof~eNationalScienceFoundaandinpartMPS7418397.
8462; (b) R. Yamdagni, T-B. McMahon and P- K&arie, J-A&- C&em. Sot-, 96(&d) :_-I 4035. (a) J-J- Solomon and F-Et Field. J_ &n_ Chem, Sec. 95 (1973) 4483; (b) JJ. Solo-xnon, M_ Meot-Ncr and F-H. Field, J- Am- Chem- Sot. 96 (1974) 3727RJ- Biint, T-B_ McMahon and J.L. Beauchamp. J- Am, Chem- h. 96 (1974) 1269_ (a) V-G. Anicich, M-T. Bowers, R-M. Oadailey and K-R. Jennings. Int J- Mess Spectram. Ion Pbys-, 11 (1373) 99; (b) V.G. Anicich and M-T- Bowem, Innt J-Mass Spec trorn Ion Phys_, 13 (1974) 39110 See. for es2unple. ref. l(c). 11 This assumption is valid if the rates of protunation of the two neutrals are similar. For amines this appears to be the case_ This assumption hss most simpb non-hindered aiso been used in other ion-molecule reactions to simplify kinetic formulae (ref. 7(b). 12 P- Kernper and M-T. Bowers, Bev_ Sci Instrum.. in press_ 13 M-T- Bowers. D-D_ BIleman and J.L. Beauchamp, J. Phys Chem.. 72 (1968) 3599; V-G- Anicicb and M-T- Bowers, Int_ J. Mass SpectromIon Phys-, 11(1973) 329; J-L_ Beauchamp, Ph_D. Thesis, Harvard University. 1967. 14 R-T. McIver, Jr. and J-R. ,i&ier, J. Am. Chem- Sot_. 93 (1971) 6334. 15 See, for example. ref_ 7. 16 S-W- Benson, The Foundation of Chemical Kinetics, McGraw-HiLi, New York. N-Y.. 1960, V-G. Anicich, Ph_D_ Thesis, University of California. Santa Barbara, 17 See, for exampie, 1973; V-G_ Anichicb and M.T. Bowers, Int. J- Mass SpectromIon Phys-, 13 (1974) 359. 18 (a) D.K_ Bohme. D.B. Dunkin, F.C. Fehsenfeld and EE_ Ferguso n. J- Chem_ Phys, 49 (1968) 5201; 51 (1969) 863; (b) V.G. Anicich and M-T- Bowers, J- Am- ChemSot_. 96 (1974) 1279; (c) M- Moet-Ner and F-H- Field, J- Am. Chem- Sot-, 97 (1975) 5339. M. Chau, W.R. Davidson end D-H- Aue. J- Am_ Chem_ Sot. 19 M_T_ Bowers, P. Neiison, submitted; M_T_ Bowers, W.R. Davidson, T-Su. L. Bass, P- Neilson and D-H. Aue. 24th AnnConf_ Mass Spectromand Aiiied Topies. San Diego. California. May. 1976. P- Neilson, W-R- Davidson, M.T. Bowers and D.H. Aue, unpublished data. f! W-R- Davidson, unpublished results_
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