July, 1963
DEHYDRATION OF CYCLOHEXAKOL OVER SULFATE CATALYSTS
and CD4 predominantly and process 2 should give CH4, CHsD, CD3H, and CD, but not CH2D2. It is proposed that the mechanism of methane formation involves reaction 14 CH2
+ c - C ~ H+ ~ c - C ~ H & H ~-+ * CH3
+ CJ&
(14)
This reaction is analogous to the process14
CH2
+ CH4 * C2Ha* --+ 2CH3
(15) The methane is formed either from the methyl radical abstraction of hydrogen or combination of a hydrogen atom with a methyl radical. D. Higher Hydrocarbons.-Because of the complexity of the nature of the higher hydrocarbon prod(14) J, A. Bell and G. B. Kistiakowsky, J . Am. Chem. Sac., 84, 3417
1497
ucts, the mechanism suggested for their formation are somewhat speculative. (1) Ethane is formed probably by recombination of CH3 radicals produced in the consecutive reactions 1 and 6. ( 2 ) Propylene may be formed in a primary process or by association of H with C3H5 radicals formed in reactions 6 and 14. ( 3 ) Propane and n-butane may be formed by association of CHI and CaH5, respectively, with CzH5 being formed by secondary reaction of H with C>H,. (4) ,411ene and propyne are formed by the primary process h ii
c-CaHij + C3H4
+ H,
(16)
( 5 ) The butenes and methylcyclopropanes are formed by isomerization and collisional stabilizations, respectively, of the excited niethylcyclopropane formed in reaction 14.15 (1.5) J. N. Butler and G. B. Kistiakowsky, zbzd., 82, 759 (1960).
(1962).
THE INFLUENCE OF IYCORPORATED RADIOACTIVITY AND EXTERNAL RADIATION ON THE DEHYDRATION OF CYCLOHEXAKOL OVER SULFL4TE CATALYSTSl BY N. A. KROHN AND HILTOS A. SMITH Department of Chemistry, Cniuerszty of Tennessee, Knoxvzlle, Tennessee, and Oak Ridge Xational Laboratory, Oak Rzdge, Tennessce2 Received January 7, 1963 The vapor phase dehydration of cyclohexanol on magnesiuni sulfate and magnesium sulfate-sodium sulfate catalysts was studied. The effects of the incorporation of radioactive sulfur into the sulfate radical, of S-irradiation of the catalyst while in use, and of preirradiation with CoGo?-rays were investigated. When compared on a unit surface area basis, the radioactive catalysts were found to be less active than non-radioactive catalysts of similar composition. This effect persisted even after the radioactivity had substantially decayed. Keither preirradiation with GoGo7-rays nor X-irradiation of the catalyst while in use had any effect. It is concluded that the reported enhancements of catalytic activity upon the incorporation of S35 are erroneous and that the emission of 8-particles from the catalyst during its use is of no consequence. The reports of enhanced catalytic activity may be attributed to the fact that for a given set of preparative conditions the radioactive catalysts had larger surface areas than their non-radioactive counterparts and that apparently this had not been considered.
Introduction The study of the effects of radiation on solid catalys.ts is a relatively new but growing field. Recent reviews have been written by T ~ r k e v i c h ,H~ a i ~ s i n s k y ,and ~ Taylor.S.6 Bombardment of catalysts by y-rays, X-rays, neutrons, protons, electrons, a! particles, and argon ions has shown beyond doubt that ionization and displacement effects caused by radiations can affect the catalytic activity of solids, sometimes favorably and sometimes adversely. I n most studies, the catalysts were irradiated before use. In a few cases, radiation was externarlly supplied while the reaction took place. Balaiidin, Spitsyn, and co-workers in a novel approach have iiivestiga,ted the effects of incorporating radioisotopes directly into solids. One of the systems (1) This paper is based on a thesis presented to the University of Tennessee by N. A. Krohn in partial fulfillment of the requirements for the Ph.D. degree, June, 1962. The work was carried out a t Oak Ridge National Laboratory. (2) Operated b y Union Carbide Nuclear Company for the U. 8. Atomic Energy Commission. (3) J . Turkevich, Proe. U . N. Con!. Peaceful Uses At. Energy, find, Geneva, 1968, 2*, 378 (1959). (4) M. Haissinaky, Actes congr. intern. catalyse, be, Pavie, 1960, 1, 1429 (1961). ( 5 ) E. H. Taylor, J . Chem. Educ., 86, 396 (1959). (13) E . H.Taylor, Nucleonice, 110, No. 1, 53 (1962),
studied was the vapor phase dehydration of cyclohexanol over magnesium sulfate-sodium sulfate catalysts that contained various amounts of sulfur-3.5.' Their results indicated that radiosulfur enhanced the catalytic activity, the percentage increase being proportional to the logarithm of the specific radioactivity of the catalyst, and reaching 171% of the activity of lion-radioactive catalyst when the concentration of S35 was 105.2 me. S35/g. The apparent activation energies were found to be 1-2 kcal./mole lower on the radioacbive catalysts. In later studies on the dehydration of n-dodecyl alcohol of MgSO, catalysts, the presence of sulfur-? 3 was found to decrease the catalytic activity.s In this same paper, data were reported on the dehydration of cyclohexanol over MgSO4 which showed the radioactive catalyst to be more active a t t,emperatures above -330°, but less active a t lower temperatures, with the reaction having a much higher apparent activation energy on t,he radioact,ive catalyst. I n both cases, (7) A . -4. Balandin, V. I. Hpitsyn, N. P. Dobrosel'skaya, I. E. Mikhailenko, 1. V. Vereschinskii, and P. Ira. Glazunov, Actes co?zgr. intern. catalyse, Ze, Paris, 1960, 2, 1415 (1961). (8) V. I. Snitsyn, I. E. Mikhailenko, and Q. N, Pimeova. DOLL Aknd. N a v k S S S R , 140, 1880 (1961).
N. A. KROI~S .4SD HILTOS-1. SXITH
1498
however, the apparent activation energies were lower then previously reported for magnesium sulfate. I n view of these conflicting results, a program was undertaken to study these phenomena more extensively. Experimental Cyclohexano1.-Eastman Kodak cyclohexanol was redistilled through a 1 m. oacuum-jacketed coliimn packed with glass helices. The purified product had the following properties: b.p. 161" (760 mni.); m.p. 25.1'; n 3 0 ~1.46286. Catalysts.-The catalysts were prepared by evaporating to dryness mixtures of stock solutions ok" C.P. MgRO, and Na2S04. The resultant cake was ground and sieved. The 30-40 mesh particles obtained were further dried in air anti ZYC uncvo a t 400 to 500" prior to use. Bulk densitiea varied from 0.48 to 0.85 g./ml., depending primarily on batch size. Radioactivity was added as hIgS3604 obtained by neutralizing HiP504 with 1lgO. The HCl present with tlie H2S3;04(as obtained from the Oak Ridge Sational Laboratory Isotopes Division) was remaved by evaporating to fuming three times with 0.5 ml. of concentrated HiSOa. This procedure was also followed in preparing non-radioactive catalysts in several cases. I n order to make valid comparisons of the catalytic activity of radioactive and non-radioactive catalysts, the surface areas were measured bv the R.E.T. method with nitrogen and krypton as adsorbates. The Russian workers did not report surface areas and a,pparently assumed that similar preparation procedures would produce catalysts of similar specific surfare areas. Our results indicate that this is not the case, and that in general, radioactive catalysts prepared side by side with non-radioactive ones have larger specific surfaces, as shown in Table I. I t was also found that exposure to moist air must be completely avoided in order to get reproducible surface area measurements on anhydrous hlgS04.
TABLE I SURFACE AREASOF RADIOACTIVE AND NON-RADIOACTIVE CATALYSTS AFTER SIMILAR D R Y ~ N TREATMEKTS G
Catalyst composition
NIgSOc RlgRO4
XgSOe MgSO1
-
-
hfgSO4 - 2
Heat treatment Temp., Time, hr. "C.
,500
20
1% Na
400
16
1 . 4 % Na
450
16
1 6% Xia
410
16
5% Na
425
4
Specific radioactivity, mo,/g.
0 48 0 0 45.8 0 7.5 0 40 ?e 0 10 3
Surface area by X-Ray Xi2 ad- orystalsorption, lite m%/g. size, 8.
4.6 7 0 6.0 13.1 1.8 9.0 2.2 3 2 3.3 4.2
656 508
...
... ... ...
... 722 454
Apparatus.-The kinetic measurements were made in an inclined tube flow system heated in a tube furnace. The cyclohexanol was metered in as liquid a t 0.314 ml./min. from a syringe operated through a gear train by a 1-r.p.m. Bodine motor. The reaction tubes were made of 8-10-mm. Pyrex glass tubing about 60 mi. long with 50-150 mg. of 30-40 mesh catalyst supported in the middle between two glass wool plugs. The lower plug WRRSsupported on indentatkms in the tube wall and after insertion was tamped down to give a flat upper surface. The catalyst was then loaded into the tube which was then lightly tapped to settle the catalyst bed. The second glass wool plug B-as then inserted and gently tamped so that the catalyst be? was held firmly in place. The good reproducibility between data taken on several catalyst beds of several sizes indicated that uniform packing of the catalyst beds was achieved by this technique. The upper half o f the tube was filled with glass beads to act as an evaporator for the cyclohexanol. At the outlet the products and unreactcd alrohol were condensed and collected in a graduated receiver. Temperature was controlled to & l oby adjusting the voltage supplied to the tube furnace. Procedure.-The catalysts lose activity with time in use. Therefore, after determining their initial activity as a function of
Vol. 67
temperature, they were aged to steady state conditions by 7 to 12 hr. of reaction time a t the highest temperature at which they were subsequently to be used. After this treatment, the temperature dependence of the catalyzed reaction rate was again determined. The extent of reaction was determined by measuring the bromine number of samples collected while the reaction tube was maintained a t constant temperature. No measurable dehydration took place in the absence of catalyst. No products other than cyclohexene and water were detected by vapor-phase chromatography or by infrared analysis regardless of the catalyst coniposition or the presence of radioactivity. Under the experimental conditions used, the extent of reaction rarely exceeded lo%, PO the per cent, reacted could be plotted against the reciprocal of absolute temperature to obtain apparent activation energies. I n preliminary experiments the effect of changing the space velocity was studied by varying the feed rate from 0.125 to 0.314 ml./min. a t constant bed size and by varying the bed size from 50 to 150 mg. a t constant feed rate. It was found that the fraction of alcohol dehydrated varied inversely with the space velocity indicating that the measurements were not diffusion or eyuilibrium limited. It was also shown that contamination of the hygroscopic cyclohexanol with as much as 10 mole 7G of water had no effect other than as a feed diluent.
Results Initial Rate Studies.-The variations found between the measured surface areas of radioactive and 11011radioactive catalysts, even when prepared in the same manner, made it plain that obtaining radioactive and non-radioactive catalysts of the same surface areas and with the same preparation histories for comparison purposes was not practicable. Therefore, a series of experiments was made on non-radioactive magnesium sulfate and magnesium sulfate-sodium sulfate catalysts to determine the effect of variations in the specific surface area and in the preparation procedure on the catalytic activity in the dehydration of cyclohexanol. One large batch of non-radioactive magnesium sulfate cataIyst prepared from the C.P. salt and one large batch prepared by the reaction of magnesium oxide with sulfuric acid were split into several portions and each portion given a different heat treatment. Two other batches, sm&IIer in size in order to duplicate more closely the 'radioactive preparation procedures, were prepared from C.P. magnesium sulfate. These were not divided and only a single heat treatment was given in each case. Catalyst properties are given in Table 11. The initial catalytic activity for the dehydration of cyclohexanol was determined for each of the catalyst preparations as a function of temperature. The results are shown by the upper line in Fig. 1. All of the erfperimentally observed numbers were normalized to one square meter of catalyst surface as measured by the B.E.T. method d t l i nitrogen gas as the adsorbate. Actual conversions ranged from 0.6 to 28.8%. For simplification a single line was d r a m through all the points from all of the ruQs to show the over-all behavior. The apparent activatioh energy is 24.6 + 0.6 kcal./ mole. When normalized to unit surface area, the catalytic activity of non-radioactive magnesium sulfate was constant to within regardless of variations in the specific surface area or the method of preparation used. For comparison, three radioactive magnesium sulfate catalysts were prepared and their initial catalytic activities determined as a function of temperature. When the per cent of cycIohexano1 reacted was normalized to one square meter of caSalyst surface, as shown in the lower curve of Fig. 1, good agreement was again obtained among the radioactive catalysts, but
July, 1963
1499
DEHYDRATION OF CYCLOHEXANOL OVER SULFATE CATALYSTS TABLE I1
PROPERTIES OF C.4T.4LYST PREP.4RlTIONS
Catalyst
MRA" MRB" MRC" AIRI)" MRF" MOAh h[OBb
MOCh MOP IAB" IAR' AA" AB AC" MSBd MSCd ISL4' ISB"
Surface a.rea.' ml./w. After Initial use (Nd (Kr) (Rr)
12.2 15,2 7.7 3.6 7.0 10.3 8.7 2.6 4.9 4.5
2.7 5.5
2 4
4,;)
Sa6
activity, mc./g.
0 0 0 0 0 0
0 0
Wt. Ka
0 0 0 0 0 0 0 0 0 0
Bulk density,/ g./nil.
0.83 .78 .76 .85
3.0
5
X
i
\ I
MRF MOA MOB
72 ,76 .73 ,
0 0 .48 8.8 0 c .49 7.4 5.2 5.0 45.5 0 .48 .i.x 4 . 4 35.6 0 I57 3.3 2.1 :t"2 0 .4A ,5.7 4.1 2.7 0 1 .A3 .7R 1.5 1.1 0 1.63 .is 6.2 4.4 3.9 0 0.98 .57 3.3 2.2 2.2 0 '2.13 .TI 19-2s 3.0 0 1.60 ASAc j.0 3.9 3.8 10.3 c.93 .55 ASBC 2.2 2.0 11.3 2 54 a C.P. MgSOa solutions dried under various conditions. Me;SO,from reaction of MgO with H2804 dried under various ronditions. C.P. hlgSO, plus indicated ?;azSOa and 31gP3 O4 mixed in solut,ions and dried in sma!l batches. Solution of Psing C.P. MgSOa and Na2S04dried under various conditions. 16.2 A.z and 19.5 for the arew of 1 2 and Kr, respectively. Measured on 30-40 mesh particles. 3.3
2
I
A MRC V MRD
A \
@
0
AA AB
A
AC
t-
, 45.5 , 35.6 I
mc/g
32.2 mc/g
0
24.5 d 1.0 kcal/mole
31 i 46
I 154
1
w,
L
I 162
17c
?&-I)
Fig. 1.-The temperature dependence of the rate of dehydration of cyclohexanol on fresh magnesium sulfate catalysts.
I
\ "
C A l A L Y ST
I
A MSB MSC
\
v
IS-2A
x 1%
o ISA they were less than half as active catalytically as the A ASB, 11.3 mc/g non-radioactive preparations. The specific surface ASA, 10.3 mc/g areas varied from 3.3 to 7.4 m.*/g. as measured by the B.E.T. method using nitrogen as the adsorbate, and the sulfur-33 content varied from 32.2 t o 45.5 mc./g. a t the time of the kinetic measurements. The yalue of the apparent activation energy from a least squares fit of all of the poiiits was 24.5 rt 1.0 kcal./mole, in good agreement with the values observed for the noiiradioactive catalyst. Similar experiments with sodium sulfate containing catalysts again showed the radioactive materials to be poorer catalysts than the non-radioactive, but iii this case an increase in the apparent activation energy was also observed, as shown in Fig. 2. The initial catalytic activity per unit surface ]vas constant within ~ k 3 0 7 ~ despite variations in the amouiit of sodium present, but was somewhat lower than that for pure magnesium sulfate. The large decrease in catalytic activity upon the addition of similar amounts of sodium sulfate reported in the literature apparently mas not corrected for differences in specific surface area.? Since the presence of sodium sulfate enhances the sintering of magFig 2.--The temperature dependence of the rate of dehydration of cyclohexanol on fresh magnesium sulfate-sodium sulfate nesium sulfate considerably, catalytic activity comcatalysts pared on a weight basis shows a large effect, its magnitude depending on the time and temperature of drying The break in the curve of catalytic activity vs. time of the catalysts. is difficult to explain. It is not purely a temperatureAging Studies.-The aging of the catalysts under time phenomena, but occurs only on use. Balandin reaction conditions is a complex phenomenon. Typical reported similar behavior at 270 to 330' on 30-ml. beds aging curves are given in Fig. 3. The dashed portions of magnesium sulfate after periods of time in use of 70 of the curves indicate the time that elapsed during the to 90 hr. and attributed the effect to progressive hyinitial rate measurements as a function of temperature. dration of the s ~ r f a c e . At ~ the temperature of aging The second point on each curve represents the activity (9) A. A. Ralandin, At. B. Turova-Polak, A. E. Agronomev, I. M. Khorof the catalyst upon reheating to 402 to 404'. h a , and L. S. Konkova, Dokl. Akad. Nauk SSSR, 114, 773 (1957).
I
K. A. KROHN AND HILTON A. SMITH
1500
Vol. 67
CATALYST o IAA A MRF 2O
148 MOC A AA. 45.5 mc/g 7 AB, 35.6 m d g A C 32.2 mc/g
v
0
$
\
5
i
I
I 200
I
0
I
I 600
I
I
a00 TIME IN USE I N MINUTES.
Fig. 3.-The aging of magnesium sulfate catalysts; 50 mg. of catalyst, 402-404’ : open symbols, non-radioactive; filled symbols, radioactive catalysts.
Cafalyrf:
0 A
IAB MRD MRF
0
AA AC
A
, 45.5 , 32.2
O i
-
0 6 1
1’50
mc/g
’
1 46
mc/g
I
\ I
I 50
’
1 I 54
1
, 1
I I 5a
1.66
I62
103 Fig. 5.-The temperature dependence of the rate of dehydration of cyclohexanol over aged magnesium sulfate-sodium sulfate catalysts
d
27.8 f 1.5 ksal,’male
1-1 1.46
1.50
1.54
I 5a
I 62
1.66
170
103 (OK”),
Fig. 4.-The temperature dependence of the rate of dehydration of cyrlohcxanol on aged magnesium sulfate catalysts.
used in the present experiments, however, hydration is unlikely. Even in the presence of a 654 mm. pressure of water vapor, magnesium sulfate is in the anhydrous form at temperatures above 37Oo.l0 Further, if only hydration were involved, the catalytic activity should be regenerated upon redrying of the material, whereas it was shown iii our work that such is not the case. Therefore, the phenomenon must be related to a permanent change in the structure of the catalyst surface which requires an induction period in the presence of the reacting vapors. Steady-State Reaction Rate Studies.-After aging to steady-state activity, the temperature dependence of the reaction rate was again determined for several (10) J S Cho, F. A. Olsen, and hl. E. Wadsworth, “Infrared Evidence for Bmulfrtte Formation in the Dehydration of Magnesium Sulfate,” Technical. Report No. 1, University of Utah, Ootober b , 1962,
$ 1
I
LL
I
I I
0
80
160
I
2. 3
TIME AFTER PREPARATION I N DAYS.
Fig. 6.-The effect of storage time on the activity of magnesium sulfate-sodium sulfate catalysts a t 408”: 0 ,radioactive; A, non-radioactive.
catalysts. Because of the small size of the catalyst beds, the final surface areas of the catalysts were measured using the B.E.T. method with krypton as the adsorbate. Comparison of results of krypton adsorption with those using nitrogen for ten different catalyst preparations showed the latter to average 1.37 f 0.07 times as great. Therefore, the results of these experiments, shown in Fig. 4 and 5, were normalized on the basis of a surface area obtained by applying this factor to the measured surface areas, so that direct comparisons can be made between these figures and those presented above when surface areas were measured with nitrogen as adsorbate. It is seen that aging decreases the catalyst activity in all cases and tends to
ORBITAL ELECTROSEGATIVITIES OF SEUTEAL ATOMS
July, 1963
increase the apparent activation energy. The radioactive catalysts remain inferior. Miscellaneous Experiments.-One of the most interesting observations reported in the literature of the effect of S35on these catalysts was a decrease of catalytic activity as the radioactivity d e ~ a y e d . ~This appeared to be powerful evidence that the reported enhancements of catalytic activity depended on the rate of emission of @-particlesby the catalyst during use. However, studies were apparently not made of the behavior of the non-radioactive catalysts after similar storage times. To clarify this point, the catalytic activities of a radioactive and non-radioactive catalyst were redetermined after storage times up to 227 days. It was found that the catalytic activity decreased linearly with time in both cases and that radioactive and non-radioactive catalysts lost the same fraction of their steadystate activity in the same period of time as shown in Fig. 6. Since the effect is linear with time over the period studied, it is obvious from the radioactive decay law that the decrease of the catalytic activity of the radioactive catalyst is also linearly related to the logarithm of the specific radioactivity. However, since the non-radioactive catalyst showed similar behavior, the effect must be a property of the catalyst not dependent on radiation. In another group of experiments, the problems which arise in trying to duplicate catalyst surfaces for comparative purposes were circumvented by directing Xrays generated a t 180 and 300 kv. on the catalyst bed while the dehydration reaction was pr0ceeding.l' The dose rates of 123 and 113 rad/min., respectively, were comparable to those from the SS5in the radioactive catalysts. No effecis were found, in agreement with (11) N. A. Krohn and H. A. Smith, J . P h p . Chem., 65, 1919 (1961).
1501
previous Russian work utilizing an 800-kev. electron beam.' Preirradiation with Gos0 y-rays to 10" ergs/g. was also without effect. Conclusions From the results of these experiments, it is concluded that the reported enhancements of catalytic activity in the dehydration of cyclohexanol by the addition of radioactive sulfur to the sulfate catalysts are erroneous because comparisons were apparently made on the basis of unit weight rather than unit surface area. When compared on the latter basis, the radioactive materials were found to be less active catalytically than non-radioactive catalysts of the same composition. I n general, for a given set of preparative conditions, the radioactive catalysts have larger surface areas than their nonradioactive counterparts, and this was not apparently considered in the previous work. It is also concluded that since both the non-radioactive and radioactive materials lose catalytic activity with storage time this phenomenon is not related to the decay of the radioactivity, but is a property of the catalyst surface. Thus, the emission of @-particlesfrom the catalyst during the time the dehydration reaction is taking place is of no consequence. This conclusion is supported by the fact that irradiation of the catalyst with X-rays or electrons while the reaction was proceeding had no effect. Acknowledgments.-The authors are indebted to many members of the ORNL staff, especially to W. R. Laing, G. S. Brown, J. S. Eldridge, and R.T . Sherman of the Analytical Chemistry Division and to R. G. Wymer and D. M. Helton of the Chemical Techno1o.y Division for their assistance in carrying out this program. Also of assistance were P. G. Dake and E. A. Woy of the Oak Ridge Gaseous Diffusion Plant.
ELECTRONE(GATIV1TY. IV. ORBITAL ELECTROKEGATIVITIES OF THE NEUTRAL ATOMS OF THE PERIODS T H R E E A AND FOUR A AND OF POSITIT'E IONS OF PERIODS ONE AND TWO1 BY JURGEN H I K Z EAXD ~ H. H. J A F F ~ Department of Chemistry, University of Cincinnati, Cincinnati ,91, Ohio Received January 10, 1963 The orbital electronegativities of the neutral atoms of the A elements of rows three and four and of the monopositive ions of periods one and two are reported and briefly discussed.
Introduction In the preceding a,rticles of this series,I electronegativity has been discussed, based on Mulliken's theoretically well justified3,4definition5
x
I,
=
+ E,2
(1)
This discussion leads to the conclusion that electro(1) (a) J. Hinse and H. H. JaffB, J . Am. Chem. Soc., 84, 540 (1962); (b) J. Hinze, M. A. Whitehead, and H . H. Jaff6, ibid., 85, 148 (1963); ( e ) J. Hinae and H. H. JaffB, Can. J . Chem., 41, 1315 (1963). (2) Department of Chemiaitry, Rice Univ., Houston 1, Texas. (3) R . S.Mulliken, J. (?him. Phya., 46, 497 (1949). (4) W.Moffitt, Proe. Roy. SOC.(London), 81102, 548 (1950). L6) R3 S . Mullikenl J , Cham, P h y s , , a, 782 (1934) I
negativity is the property not of an atom, but of an orbital of an atom in a molecule. The electronegativities computed in the light of these considerations for the elements of the first and second rows of the periodic systernla and for the elements of the first transition series1= show that such orbital electronegativities are considerably dependent on the character of the orbitals considered, and differences of more than one Pauling unit in electronegativity of the same atom but different hybrid orbitals are no exception. Consequently, it seems of interest to have available orbital electronegativities for different valence states for the heavier elements also. Furthermore, it has been indicated in the first article'" that, on the basis of Mulliken's definition, one has to
