3058
EARLM. WQQLLEY AND LQREN6. HEPLER
Molecular Asslociation of Hydrogen Bonding Solutes. Phenol in Cyclohexane and Benzene by Earl M. Woolley*Land Loren G. Hepler Department of Chemistry, The University of Lethbridge, Lethbridge, A h & , Canada
(Received March 20, 1972)
Publication costs assisted by the Brigham Young University Department of Chemistry
Enthalpies of dilution of phenol in cyclohexane and in benzene have been measured, with results reported as rela,tive apparent molar enthalpy ( 4 ~values. ) I t has been shown how these results can be interpreted in terms of a monomer-dimer-trimer model and a monomer-dimer-n-mer model. Equations have been derived that permit calculation of @L values from K and AH” values reported by Whetsel and Lady on the basis of their spectroscopic results and the monomer-dimer-n-mer model. These calculated &, values for phenol in cyclohexane and CCL are in marked disagreement with calorimetric values, which indicates the presence of some errors in the interpretation of the spectroscopic results. Our calculations also show thaL it is possible to fit both the calorimetricand spectroscopic results at 25” with K and A H o values based on the rnonornerdimer+-mer model. Strengths and weaknesses of the various models are discussed in relation to all of these calculations. It is pointed out that phenol is clearly considerably more self-associated in Cyclohexane and CCL than in ben~ene,which is consistent with available thermochemical data and the idea of O R . . n bonding.
Introduction Numerous investigations have provided convincing evidence for self-association of phenol in various more or leys inert solvents, but there is widespread disagreement as to idenLification of predominant associated species and a consequent paucity of reliable data for various association reactions. Although there have been few investigations specifically concerned with solvent effects on self-association of phenol or other hydrogen boiiding solutes, sufficient information is available to suggest that these effects may be quite large. A considerable number of earlier investigations (cited in re€ 2-4) of phenol in CC1, have been interpreted in terms of a monomer--dimer equilibrium. On the other hand, we now have convincing evidence from several that associated species larger than dimers are importanb in all but the most dilute solutions. Results of sonie of these investigation^^^^ indicate that the principal equilibrium reaction is the trimerization represented by 3P = P B j while other Investigatorss suggest that the most realistic representabion is dimeriz?;ntioxzfollowed by stepwise association ‘io P, species with n becoming quite large. Philbrick7 has investigated the distribution of phenol betxeen watw and benzene and has obtained results indica1ing that dimerization is the principal self-association readion of phenol in wet benzene. Vapor pressur e lowering measurements by Lassettre and Dickinsona have permitted calculation of AHo for the dimerization reaction. More recently, Johnson, Christian, and Affsprung9 have carried out infrared spectral measurements and thorough investigations of The Journal of Phgsical Chemiatry, Vol. 75,N o . 21, 1978
the distribution of phenol between water and benzene along with measurements of solubilities of water in phenolic benzene. Their distribution data, which are more extensive than those of Philbrick,7 also indicate that dimerization is the principal self-association reaction of phenol in dilute soIution, -vl-ithsome trimers also present as the total concentration of phenol in benzene increases. Their solubility and spectral data further suggest that the actual species in wet benzene are principally PW, and P2W. This naturally raises the question as to whether trimers might be favored over dimers in anhydrous benzene. We also note that cryoscopic measurements (interpretation complicated by solid solution formation) by Vanderborgh, Armstrong, and Spall’o with phenol and several substituted phenols in benzene have led to the conclusion that both dimers and trimers should be considered. (1) Department of Chemistry, Brigham Young University, Provo, Utah 84601. (2) (a) M. M. Davis, Nat. Bur. Stand. (U.S , ) ,M O ~ Q105 Q T(1968). , (b) G. C. Pinlentel and A. L. McClellan, “The Hydrogen Bond,” W. H. Freeman, San Francisco, Calif., 1960, (3) K. B. Whetsel and J. H. Lady, “Spectrometry of Fuels,” Plenum Press, New Pork, N. Y., 1970, pp 259-279. (4) E. M. Woolley, J. G. Travers, B. P. Erno, and L. G. Hepler, J. Phys. Chem., 75, 3591 (1971). ( 5 ) M. Saunders and J . B. Hyne, J . Chem. Phys., 29, 1319 (1958). (6) J. R. Johnson, S. D. Christian, and H. E. Affsprung, J . Chem. Soc., 43, I. (1965). (7) F. A. Philbrick, J . Amer. Chem. Soc., 56, 2581 (1934). (8) E. N. Lassettre and R. G. Dickinson, J . Amer. C‘hhrm. SOC., 61, 54 (1939). (9) J. R. Johnson, S. D. Christian, and H. E. Affsprung, J Chem. SOC. A , 764 (1967). (10) N. E. Vandesborgh, N. R. Armstrong, and W. D , Spali, J . Phys. Chem., 74, 1734 (1970).
MOLECULAR ASf30CIA.?rYON O F
Of the many other aprotic solvents in which one rnlght im~vestigatethe self-association of phenol, cyclohexane js of particular interest because it can reasonably be regarded as more nearly inert than the weakly dectron-donating benzene and CCL. Deardonll has obtaincd ultraviolet spectra of solutions of phenol ~ncyclohexane a i d has interpreted his results in terms of both dimers and. trimers. The more recent and very thorough infrared investigation by Whetsel and La,dyg has led t o hterpretation in terms of two equilibrium, constants, o m for dimerization and one for stepwise nssociatiorr so form P, species with n becoming quite large. e ]lave undertaken the calorimetric measurements described in this paper t o obtain experimental data relevaaat to identification and thermodynamic description of the principal self-association reactions sf phenol in both benzene and cyclohexane. Although only pztrtly anticipated when these measurements were begun, the results dramatically illustrate how solvent effects can change magnitudes of equilibrium constants and other thermodynamic quantities and also lead t o qualitatively different solute self-association behavior in different solvents.
Calorimetric titration measurements of heats of &Jution of pheTol in anhydrous benzene and cyclohexane were made with the LKB 8700 Precision Titration (Clalorirnetry System with a Metrohm Herisau Dosirxiat automatic buret to deliver the titrant sohtions i o the caiorirneter. All results of our calorimetric rneasurernents, which refer to 25.0 =k 0.1", are reportod in term-, of the calorie that is defined equal t o 4.184 J. All so1utioLi compositions are described in terms of molarities represented by M . Analytical reagent grade phenol and spectral grade solvents from Fisher were used. Solvents were distilled from either calcium hydride or sodium-potassium a'bloy. Considerable care was taken during preparations and handling t o keep all solutions dry.
ts and
SSkD
Our heat of dilution results are reported in Tables I and I11 in the form of 4~ values. The relative apparent molar enthalpy represented by 4~ is equal to the negative of the enthalpy of dilution of 1 mol of phenol from a solution of specified molarity to infinite dilution. The imesuits given for cyclohexane solutions were obtained ~.n several series of measurements in which 0.5522 and 10183 M solutions were titrated into pure solvent or into solutions more dilute than the titrant. Results given for benzene solutions are taken t 4~against M , based on a very from a large scale p i ~ of large number 0 " experimental determinations of heats of dilution using 1.3636, 1.5921, 1.8980, and 2.0393 M titrant solutions I
3059
HYDROGEN BONDING SOLUTES
Table I: Relative Apparent Molar Enthalpies of Phenol in Cyclohexane Conen, M
-+L,
Concn,
-+L,
cral/mol
M
cal/mol
0.0057 0,0106 0.0108 0.0362 0.0523 0,0649 0.0749 0.0965 0 0997 0.1060 0.1207 0.1245 0.1426 0.1552 0.1614 0.1814
36 74 110 268 435 569 65 1 903 928 996 1122 1158 1297 1383 1426 1543
0.1838 0.1925 0 2092 0 2370 0.2677 0 2707 0.2859 0,3160 0.3345 0.3415 0.3553
1552 1598 16378 1796 1887 1914 1960 2032 2090 2106 2137 2185 2225 2450 2758
~
I
O,X78O 0 I3993 0 5522 1,0183
-__--
Table I1 : Relative Apparent Molar Enthalpies of Phenol in Benzene Concn, M
Concn,
-$L,
Qd/mOl
IM
oal/mol
9 18 27 36 54 71 101 132 161 191 218 244 269 295
0.550 0.600 0.650 0,700 0 * 750 0.800 0.900 1,000 1.200 1,400 1.600 1.800 2.000
3 19 342 364 385 410 430 473 512 582 640 690 732 755
-$L*
0,0125 0 * 0250 0.0375 0.0500 0,0750 0.100 0.150 0.200 0.250 0.300 0.380 0.400 0.450 0.500
Following methods developed in connection with our earlier work4 on solutions of phenol in CC14, we shall first consider interpretation of our 41, results in terms of a single equilibrium that we represent generally by
nP P, The equilibrium constant for this reaction is
(1)
in which the parentheses indicate concentrations expressed in terms of molarities. At any finite concentration there will be both monomeric and associated species present, while at infinite dilution all phenol will be in monomeric form. We can therefore express the heat of dilution from stoichiometric concentration M to infinite dilution by (11) J. C. Deardon, Can. J . Chern., 41, 2883 (1963). The Journal ofPhu8ical Chemiatru, VoE. 76, N o . $1, 1972
EARLM. WOOLLEY AND LOREN G. HEPLER
3060
Table IV : Phenol in Cyclohexane.
in which CY. and AH,' represent the fraction of monomers that is associated and the molar enthalpy oE the reaction represented by (1). We also have
IC, := a/nM"-'(l
- CY.),
(4)
Equations 3 and 4 may be tested with 41, results by using a computer to find the value of R, that leads to the most consistent value of AH,". Another method of analyzing #L values in terms of a single self.-association equilibrium is based on the following equation derived previously4 =
#L
(AH,",/n) - (I/n)(AH,o)(n-l)'n X (l/K,)l/n(#L/Mn--l)l'n
(5)
Values of K, and AH," can be obtained from the slope and intercept of a graph of - #L against (- (PL/M+~) Tabulated (PI, values are based on measured heats of dilution from one finite concentration to another finite concentration combined with an extrapolated heat of dilution t o zero concentration. Differences in (PL values are therefore properly regarded as purely experimental quantit es, while absolute #I, values are subject t o adjustment following any different extrapolation t o infinite di.ution. It is therefore desirable to o some calculations with A#L values. To do so we combine two equations of the form of (3) to obtain #x,
-F
&L'
==
A& = (a - c r ' ) A H n o / ~
(6)
in which the primed quantities refer to some reference solution of stoichiometric concentration M' # 0. Equations 6 and 4 and an equation like (4) written in terms of M' dnd a' can be tested by using a computer to obtain t,he values of K , and All,' that best, account for the A#L values. Results of our calculations for phenol in benzene and in cyclohexane are listed in Tables I11 and IV. For solutions of phenol in benzene these calculations could be made consistent with our #L results only for n = 2, while for solutions of phenol in cyclohexane this could be done only wiih n = 3. To the extent that a single equilibrium such as (1) is a realistic representation of the self-association of phenol in benzene solutions up to approximately 2 M Table 111 : Phenol in Benzene. Single Self-Association Reaction (n = 2 in Eq 1) Method of calculation
Eq 3-4 Graphical (eq 5) Eq 6 u.
Using
+L
AHz",
Kn
0.132 0.126 0.135* 0.123
kcai/mol
-5.67 -5.81 -5.410 -5.86b
for most concentrnted solution as reference.
* TJsing @I,for mosl, dilute solution as reference.
The Journal of Physical Chemistry, Val. 76, No. 21, 197.8
Single Self-Association
Reaction (n = 3 in Eq 1) Method of caloulation
Ks
lccsl/mol
Eq 3-4 Graphical (eq 5 )
21.3 21.2
-10.95 -10.98
AH3',
and in cyclohexane solutions up to approximately 1 M , we believe that our results and those of some earlier investigators already cited provide good support for the idea that monomers and dimers are the principal species in benzene while monomers and trimers are the principal species in Cyclohexane. ut it is necessary to recognize that it may be possible t o fit experimental data with equations derived from unrealistic reaction models. We should therefore alao consider OUT results in relation t o stepwise association t o form dimers and trimers. This seems especially necessary for solutions of phenol in cyclohexane because it is very unlikely that we can actually have finite ICawith K z = 0. To carry out analysis of our +L results in terms of stepwise self-association reactions (eq I with n = 2 and also n = 3) we write eq 3 in terms of dimers and trimers
M#L = (P,)AHzo
+ (P:$)AHs"
(7)
Combination of this equation with the material balance equation
M
=
(P)
+ 2(P,) 4-3(PB)
(8)
and appropriate expressions for K , and K 8 permits computer calculations that lead to the values of Kz, K B ,AH,", and AH,' that best account for the tabulated #L values. Our calculations with eq 7 and 8 applied to solutions of phenol in benzene lead to K z = 0.135, Ks = 0.015, AHz' = -5.41 kcal rnol-l, and AHa" = -4.37 kcal mol-I when 61, values are weighted more for concentrated solutions than for dilute solutions. Similar calculations in which all 4~ values are weighted equally lead t o K2 = 0.130, K 3 = 0.010, AH" = --5.60 kcal mol-', and AN3" = -4.27 kcal mol-l, These equilibrium constants show that dimers are Considerably more important than trimers, as implied by results of our earlier calculations summarized in Table 111. T o illustrate the relative importance of dimers and trimers point out that at 1.8 M the above K values show that we have 71% phenol as monomers, 23% as dimers, and only 6% as trimers in benzene. At this concentration about 90% of #L is due t o dimers, with only about 10% due to trimers, For more dilute solutions, trimers become even less important. Our calculations with eq 7 and 8 applied to solutions of phenol in cyclohexane lead t o ITz = 0.10, K B = 21.5, AH,' = -4.5 kcal m01-l~ and A H e " = -11.0 kcal mol-l. These K values are consistent with our ~ 7 e
I\'~OLEGULAR ASSOCIATION OF HYDROGEN BONDING SOLUTES earlier concZusioii (Table XV) that trimers are more important than dimers in the phenol-cyclohexane system. For example, ai 0.L6 M we have 3(P3)/2(Pz) = 31, while ~ t 0,9 t M we Enme 3(P3)/2(P2) = 69. UP' selections of '(best" values for K z , K B , AH2", dH,'~ and othm ther~nodynamic functions for selfassociation of phmal in benzene and in cyclohexane at 298°K are Listed in Tribies V and VI.
-~
3061
Ks
z=
(a > 2 )
(Pn)/(Pn-l)(P)
(11)
Whetsel and Lady3 have taken all K , (s represents stepwise) values to be identical so that there are only two independent equilibrium constants t o consider. For later derivations, it is convenient to work also in terms of (n
> 2)
02)
(n > 2 )
(13)
and
2P = Pz
Kn
AH,"
= -5.6 A#zo = -22.9
0.13 AG20 = 1.21
(10)
and
n P = P,
Table 'tv : "Best" Va!ues of Thermodynamic Functions for Self-Association of Phenol in Benzene (298OK) R?,
(PZ)/(P>~
Kz
=
(Pn)/(P)"
Various equilibrium constants are related by
3P = PI
K,
=
K2K',"-2
(n > 2 )
(14)
The material balance equation for this stepwise association model is m
M
'Fable V I : "Best" Values of Thermodynamic Functions for jSelf-Assoeiation of Phenol in Cyclohexane (298°K) AH,'
0.10
AG,O = I :I.
=
Cn(P,) n=l
-4.5
ASz' = -20
=
(P)
+ 2Kz(P)' + 3 K z K 5 ( P ) 3+ 4K&s2((P)4
3P = P3 AH3O = -11.0 ASEO = - 31
KI = 21.5 AG3" = - 1.8
The 61, values show quite clearly that phenol is much more self-associated in cyclohexane than in benzene. In so far as our monomer-dimer-trimer model is realistic, the equilibrium constants in Tables V and VI show "cat the greater complexity of phenol in cyclohexane as compared to benzene is due to the markedly greater stability of trimers in cyclohexane. If it is assumed that most of the trimers are cyclic, this order of stabilities is consistent with the idea of OH. . . n bonding between phenol monomers and benzene. This idea receives support from results of other investigiitiorafi, cited later in this paper. Now we turn t o detailed consideration of the monomer-dimer-n-mer stepwise association model used most recently and most thoroughly by Whetsel and Ladyb in connec tion with their spectroscopic investigations of phenol in CCB, and cyclohexane. Following earlier work of Goggeshal and Saier,lZWhetsel and Lady3 worked with a dimerization equilibrium and a general series of further association reactions represcnted as follows
P,-1 i- P
=
(9)
= P2
P,
(n 3 2 )
Goiresponding equilibrium constants are
+
(16)
Algebraic rearrangement of (16) gives us
Ks2[n/l.- ( P > ] / K 2=
29
(15)
We express (Pz)as K z ( P ) ~and the various (P,) as K,(P)" and then make use of (14) to obtain
2P = Pz
R, =
=
2[K,(P)I2
+ 3[KS(P)l3i-.. .
(17)
By standard methods we also obtain for a general variable B
5 nB"
=
B2(2 - B)/(1 - B)*
n=2
(
Application of (18) to (17) and rearrangement then gives us
Following the Whetsel-Lady-Coggeshall-Saier choice of all K , identical for n > 2, we take all AH," identical for n 3 2 and obtain the general relationship between AH,", AH2", and AH,"
AH," = AH,"
+ (n - 2)AH,"
(n >* 2)
(20)
Appropriate extension of eq 7 therefore gives
M$JL = (P7,)AHz"
+ (Pa)(AHt" + AH,") $(P4)(AHao 3- 2 A H s o ) + . S
I
(21)
Substitution for the various (P,) in terms of (P), K 2 , and K , gives
(9') (12) N. D. Coggeshall and E. L. Saier, J . Amer. Chem. Soc., 73, 5414 (1951). The Journal of Physical Chemistry, VoE. 76, N o . 21, lS72
3
EARLh/I. WQOLLEV AND LOBENG.
By standard rnetk.8od.swe also obtain m
n=2
= B2/(1
- B)
(B < 1)
(23)
and ,'
633/(1
- B)'
( B < 1)
Now comhiriation of eq 22-24 gives us =
k'Z(P)2 M[1 -. IC@)]
X
10
08
M
(24)
n=3
L
OB
04
02
m
Figure 1. The dashed line represents calorimetrically determined relative apparent molar enthalpies for phenol in cyclohexane, while the solid line represents values that we have calculated (eq 19 and 2 5 ) from rewits of Whetsel and Lady.8
i Equations 19 ~ i n d25 now permit us to make several detailed numerical comparisons of our results with those of 'Whetsel and Lady.3 One such comparison begins with use of eq 19 for calculation of various monomer eo ncentrations represented by (P) and corresponding s toichiometric molarities represented by M . Then insertion of these (P) and M values in eq 25 along with K z , AHz", and AH," (our symbols) from Whetsel and Lady3 permits calculation of dlL values to compare with our calorimetric results. We have carried out these calculations for phenol in both CCI, and in cyclohexane and display the results in Figures 1 and 2, alcng with results of present and past4 calorimetric measurements. Figures 1 and 2 clearly show that there are large? concentrat ion-dependent differences between our calorimetric 4~ values and those calculated from the equilibrium constants and AH" values derived by Whetsel and Ladya on the basis of their experimental results and the monouner--dimer-n-mer stepwise association model It is possible thtit the monomer-dimer-n-mer step\vise model is an adequate representation of association in these sysl,erns and that the equilibrium constants yeported by 'Whetsel and Lady3 are close t o the "true" values, I n This case we might attribute the discrepemies between caloulated and calorimetric C$L values t o wrors in the AhTovalues reported by Whetsel and which i s a r.easonable possibility because relatively srnall temperature dependent errors in equilibrium corastmtu can lead to large errors in derived AH" values. We may test the possibility outlined above by rearranging ey 25 .to Hj
The Journal of Physical Chemistry, Vol. 76,N o . 91, 1972
1.0.
26-
2.0.
f -2" c
1.5-
1.0-
01
04
06
08
10
12
11
M
Figure 2. The dashed line represents calorimetrically determined4 relative apparent molar enthalpies for phenol in CCI,, while the solid line represents values that we have calculated (ey 19 and 2 5 ) from resnlts of Whetsel and Lady.3
Then we use our calorimetric 4~ values with equilibrium constants from Whetsel and Lady3 in combination with eq 19 to cvaluate the left side of eg 26 and the term K,(P)/[l - K,(P)] on the right side of eq 26. Graphs of ~ L M I I- K , ( P ) ] / K @ ) 2 against K,(P)/ [l - K,(P)] do lead to straight linea for phenol in CCll and in cyclohexane. Mathematical establishment of the "best" straight lines is difficult because of the complicated dependence of various uncertainties on concentration. On the basis of our estimates of the slopes and intercepts of these lines we obtain AHz" AH," Z -3.1 kcal mol-' for phenol in CCl, and AH'" & AH," i ES -3.6 to -3.7 kcal mol-1 for phenol in cyclohexane. Following this indication that AHz" Zg AH," in the stepwise model, we set AHz' = AH," in eq 25 and rearrange to obtain
concentration. They did, however, treat the a,bsorptivity of associated species as an adjustable pa,rameler. in wlriah AH" without a subscript represents the enOn balance, it seems reasonable t o conclude Lhat the thalpy change f o r any single step in the association of spectroscopic method offers better pot'entiel for ;.vadphenol. Combination of eq 27 and 19 with our $L iiation OF equilibrium constants, On rhe other band., results and equilibrium tants from Whetsel and the calorimetric method appears t o be consi derabiy Ladys leads t o an ayerage * = -3.10 kcal mol-] for better for evaluation of enthalpies of association bephenol in CC2, and t o A f i " = -3.68 kcal mol-1 for cause these quantities are obtainable from the spectronol in cyclohexane. Further combination of these scopic results only by differentiation of calculai:ed a values with laee energies from Whetsel and Lady3 equilibrium constants, which inevi!,a&ly include COLIleads t r 3 the following: bSz" --- .- 10.5 caX deg-l mol-' tributions from (small) experiment'al erro rs and aparid AkT," = - $AI ea1 deg-I mol--l for phenol in CC14; proximations made in the data t AS2" =.I --11,2 n:~1deg-l mo1-l and AS," -8.3 cal The monomer-dimer-trimer deg mol-' for phenol in cyclohexane. It is entirely on the grounds that it excludes .ket'ramers and larger reasonrLble that AS," should be less negative than AX2*. associated species. The best defence of this mode! is N o w that we have reported results of several calcuto admit, thet species larger than trimers mag; exisi-, latione based on 1, he morzorner-dimer-tri~ner and monobut Lo claim that the magnhdes of 1,ha assoeiatinn ~ e r - - ~ ~gel& ~ msociation e ~ - ~ models, j ~ ~ it~ is ~appro~ cons'cants are such that these species are present a,t ~ ~ some ~ conclusions ~ ~ that ~ can ~ he a ~ ~ ? ~ priate to s negligible concentrations in the solutioiis ( ( 2 .M)urider drawn from these calculations and t o consider careconsideration, This argument is most, convincing lor fully srncb cjuestljun~x~ hiatations on various methods phenol in benzene and least convincing for phemo! in of i ~ v ~ s t i g ~and t i ~the ~ i likely realism of the various cyclohexane. models ~ ~ this discussion ~ w e asbume ~ that~ ~ ~ ~ ~ h ~ The monomer--dimer--n.-mermodel is yues&mable on the s ~ ~ c t r ~rewiti-; s c ( of~ Whetsel ~ ~ ~ ~arid ~ Lady3 and the the groun.ds that in principle it requires "Ili.nmI"; ascalorimetric ressdts reported here and earlier4 are resociation species and excludes cyclic species, RecentJ liable. Thus WP ~ ~almost all ~ difficulties ~ t o un~ i ~ ~ ~ ~ t ~ quantum mechanical cahlationsla suggeqt,that serLah certainties in !-lie self-asssocintioia models and to apnonlinear structures (such as cyclic eriraera) rimy be proximations made BII c8at.a treatment. energeticall:y favored over correspondikg linear n-.mers , Jn our calcdatims we have made two thermodynamic which is inconsistent with the W ass~imptions: ( i all activity coefficients have been ge~halI--Sa,ier~**~ model. It can, h taken lto be unity, ant4 (ii) beats of dilution of indithat the unfavorably IOU entropy of cyclic :species riidrzal species have been taken to be zero so that the (such as cyclic trimw) compared to ci~rrespondingaonentire measured heats of dilution could be attributed cyclic species means that the linear. species art; inost to rlecompositioi? of associated species. Many invesnumerous in sol.utions at e ~ , ~ i l ~ b ~Os i ui ~ t' ~ mag ~ i .be tigations of ~ ~ ~ ~ ~ a s s nonelectrolyte o c ~ x t e ~ solutions that there is approximate c o ~ ~ ~of eentha ~ Ipys ~ ~ ~ : evidence that solute activity cohave ~ r o v ~ d eppod d entropy contribwtions so that I
