1815
VAPORPRESSURE ISOTOPE EFFECTS IN METHANOL
Vapor Pressure Isotope Effects in Methanol by J. L. Borowitz*l and F. S. Klein The Weizmann Institute of Science, Rehovoth, Israel
(Received September 18, 1970)
Publication costs borne completely by The Journal of Physical Chemistry
The relative volatilities of the systems methanol-180-methanol-160 and methan~l-W-rnethanol-~~C have been measured in CHaOH, CH30D, CDaOH,and CD30D. The measurements were made with the aid of an adiabatic distillation column using a kinetic technique. The deuterated methanols were synthesized: CH3OD by hydrolysis of dimethyl carbonate; CD30Dby heterogenous catalysis from CO and deuterium; and CDSOH by isotopic exchange between CD30D and NH4N03. Isotopic analysis for deuterium was made by nmr. The and contents of methanol samples were determined mass spectrometrical!y after decomposing the samples relative volato CO. The results are summarized in Table 11. The temperature dependence of the 180/160 tility has led to conclusions concerning the effect of deuterium substitution on the intermolecular forces. Within the temperature range measured, the following can be stated: (a) the intermolecular forces are greater in CD30H and CD30D than in CH30H and CH30D,respectively; (b) isotopic substitution by lacor D in the methyl group causes an increase in the vapor pressure of methanol; (e) this increase is mainly due to changes in the intramolecular vibrational frequencies on condensation; (d) isotopic substitution by 1 8 0 or D in the hydroxyl group causes a decrease in the vapor pressure of methanol; (e) while the deuterium substitution appears to affect the hydrogen-bond strength, substitution of and does not. These conclusions are borne out by spectroscopic observations. Introduction Isotope effects in vapor pressure have been shown2& to be of considerable usefulness in the investigation of intermolecular forces in liquids. This paper describes the measurements of the relative volatilities of a number of isotopic methanols. The relative volatility a! of (two components in) a liquid mixture is defined by the equation
N where n and N are the mole fractions of one component in the vapor phase and in the liquid phase of the system, respectively. In the case of an ideal mixture of liquids, the vapors of which are ideal gases, a! may be shown to be equal to the ratio of the vapor pressures of the pure liquids. The corrections for nonideality are very small in the case of isotopic mixtures, and have been discussed by Rozen2bamong others. Applying the Wigner quantum correction to the partition function of the liquid, Herzfeld and Tellera showed that the theory of isotope effects on the vapor pressure of liquids requires in a first approximation that the logarithm of the relative volatility a be inversely proportional to the square of the absolute temperature T. It has been observed, however, that in many cases In a changes sign a t a given temperature. The expression of In a! = f(T) must therefore contain at least one other term. Topley and Eyring4 showed that this term is of the form B I T and that it is associated with a shift in the internal frequency of the component on con-
densation. The relative volatility may then be given in theform In
a!
=
A / T 2- B/T
(2)
It has furthermore been shown2athat theories which relate isotope effects to changes of mass only fail in the interpretation of experimental results and that structural parameters, such as the relative shift of centers of force vs. mass with isotope substitution, have to be considered. Methanol, being the first member of the alcohol series, was chosen as a comparatively simple molecule for the study of intermolecular bonding in alcohols. The dependence of the intermolecular forces on the distribution of mass between the alkyl and hydroxyl groups as well as the contribution of each of these two groups to the intermolecular bonds were investigated by examining the effect of carbon and oxygen isotope substitution, respectively, on the vapor pressure of deuterium-substituted methanols. The results of these investigations also indicate the form and extent of the effect of isotopic substitution of hydrogen on the intermolecular forces. Experimental Section The relative volatilities of methanols were measured by a distillation method taking transient and equilib(1) To whom correspondence should be addressed at Soreq Nuclear Research Centre, Yavne, Israel. (2) (a) Reviewed by J. Bigeleisen, J . Chem. Phys., 34, 1485 (1961); (b) A. M. Rozen, “Theory of Isotopic Separation in Columns,” Office of Technical Services, U. S. Dept of Commerce, Washington 25, D. C. (3) K. F. Herzfeld and E. Teller, Phys. Rev., 54, 912 (1938). (4) B. Topley and H. Eyring, J . Chem. Phys., 2, 217 (1934).
The Journal of Physical Chemistry, Vol. 76, No. 18, 1971
1816
J. L. BOROWITZ AND F. s. KLEIN
TO VACUUM rium data. This limited the number of pure isotopic --r il species required to four, vix. CH30H, CH30D, CD30H, and CDSOD, and obviated the need for the pure lS0 and 13Cforms of each of these materials. The distillations were carried out under total reflux, with zero feed and product rates, in a column with a large boiler and no distillate or feed reservoir. The materials distilled had l80and 13C concentrations of approximately natural abundance, so that each could be considered as if it were part of a binary system. The relative volatility of the lSO/leO pairs, such as CH3180H-CH3160H,was calculated from the initial rate of change in the isotopic composition of the vapor a t the top of the column during a distillation run and from the final composition, i.e., the steady-state enrichment attained in the run. This method has been described by Bigeleisen and Ribnikar.6 It uses two sets of data to determine the number N of theoretical plates in the column and E = a - 1. The first set is the initial Figure 1. Scheme of column. isotope enrichment in the column. The experimental enrichment as a function of time is given by the expression jacket it is surrounded by a third tube C in which methanol vapor is circulated a t the same pressure as that a t (QI - 1)2 = 2nNe2Lt/H (3) the top of the distillation column. The top of the where Q t is the enrichment at time t of the experiment, column is connected to the condenser P, the return line L is the liquid flow rate in the column, and H is the of which is equipped with a buret Q which is used to liquid hold-up of the column. Equatioh 3 is a limiting measure the liquid flow from the condenser. The twoexpression for t 40. way buret valve S is also used for extracting samples of The second set of measurements is the final enrichthe distillate. The region between the top of the colment Qmat steady state given by the equation umn packing and condenser P is surrounded by a heatQm = eeN (4) ing element 2 which serves both to eliminate heat losses and to preheat the liquid leaving the condenser to the E and N can then be evaluated from eq 3 and 4. The temperature of the top of the packing. At the bottom 12C/13C relative volatility was determined by comparing of the column the vapor is separated from the liquid by final enrichments of 180/1a0 and 13C/12Cfor the same means of a cap U, over the vapor line coming from the experimental conditions, on the assumption that the boiler H. The liquid flow from the column into the number of theoretical plates in the column is the same boiler is measured in the vacuum-jacketed buret K, for both species by closing the two-way valve L for short periods. The region between the boiler and the column is also surec = € 0 In Qm carbo& Qmoxygen rounded by a heating element X. There are not sufficient data available to check this The pressure in the column is controlled by a manoassumption for methanol. Using an empirical formula stat VI. The pressure in the vapor jacket is controlled due to Murch6 one can show that the difference between by the manostat Vz, which, in turn, is controlled by VI. the number of theoretical plates of a column distilling The heating elements X and 2 are controlled by a therHzO or D20 under similar conditions is not more than mistor sensing circuit which keeps the temperature on 2.5%. Since isotope effects in methanol are even the outside wall of the region equal to that of the vapor smaller than those in water, it can be assumed that the on the inside. number of theoretical plates of a given column is pracThe materials investigated were the isotopic methtically independent of whether CHIOH, CD30D,or any anols: CH30H,CH30D,CD30D,and CDaOH. other isotopic methanol is being distilled. The CH3OH (Methanol Puriss. p.a., Fluka) was The column (Figure 1)used in these experiments is an dried by reaction with magnesium in the presence of adiabatic, packed column, designed according to a iodine to less than 0.01% moisture content, as detersuggestion by Dostrovsky.’ The column A itself is a mined by Karl Fischer reagent. This was necessary in Pyrex tube of 1-cm i.d., which is packed with “Helipak 3012” stainless-steel packing to a height of 2 m. It is ( 5 ) J. Bigeleisen and S. Ribnikar, J . Chem. Phys., 35, 1297 (1961). surrounded by a glass vacuum jacket B for insulation. (6) D. P. Muroh, Ind. Eng. Chem., 45, 2616 (1953). I n order to minimize heat losses across the vacuum (7) I. Dostrovsky, private communication.
The Journal of Physical Chemistry, Vol. 76,No. 18, 1971
1817
VAPORPRESSURE ISOTOPE EFFECTS IN METHANOL order to minimize any possible effect of water on the relative volatility of the methanol. CHaOD was prepared by the hydrolysis of dimethyl carbonate after Streitwieser, Verbit, and Stang.8 Using D20with a deuterium content of over 99.5% the methanol obtained contained over 98% deuterium in the hydroxyl group, as determined by nmr spectroscopy. This material was dried on "Drierite" and distilled in the column to over 99% deuterium content in the hydroxyl before starting measurements. CDaOD was synthesized from CP carbon monoxide (The Matheson Co.) and 99.8% pure deuterium gas (General Dynamics) on Harshaw zinc chromite Zn 0314 I/d-in. catalyst. The synthesis was carried out at a pressure of 4 atm absolute in a glass system similar to that used by Beersmans and J u n g e r ~ . ~The product methanol contained over 99% deuterium in both the methyl and hydroxyl groups, as determined by nmr spectroscopy, and less than 0.01% moisture. lo CDaOHwas prepared from CD30Dby exchange with ammonium nitrate (ACS purity). The ammonium nitrate was dried before use to constant weight over P205in a vacuum desiccator. CDaOD (76 g) was vacuum distilled onto ammonium nitrate (17 g). The salt was allowed to dissolve, and the CD@D was then vacuum distilled onto a further batch of ammonium nitrate. Solution1' and distillation were repeated until the hydroxyl deuterium content fell to below 1%, as determined by nmr spectroscopy. CD,OH was obtained with a yield of about 95%. The moisture content of the product was less than 0.1%. Methanol samples from the distillation experiments were analyzed by mass spectrometer for the 13C and l8O content. The samples (approximately 0.2 ml for a distillate sample, and 0.5 ml for a boiler sample) were decomposed on a platinum filament at approximately 900" to carbon monoxide and hydrogen in a decomposition vessel. This vessel was equipped with a silverpalladium thimble through which the hydrogen was removed as it was formed.12 The abundance ratios mass 28 mass 30 and mass 29 mass 28 mass 29
+
in the CO formed were measured on an Atlas ?I/I 86 mass spectrometer. The 13C and l80concentrations were calculated from these ratios by comparison with the respective ratios obtained from a standard sample of CO. The measured ratios were reproducible to *0.5% on a single sample. The standard deviation of the average of the ratios obtained from six identical samples of methanol was f0.1%. I n the calculation of enrichments the contribution of 1zC170to the mass 29 peak had to be taken into account. This was done by assuming that the 170enrichment in a distillation experiment is l/z of the l80 enrichment. An error of 10% in this estimate leads to an error of only 0.1% in the calculated 13Cenrichment.
Results An example of the operating conditions and the results of a single experiment,are given in Table I. Table I: Experimental Parameters of a Typical Distillation Experiment CHsOH a t 430 Torr Flow rate of liquid, ml/min Hold-up, ml Boiler content, ml Pressure drop across column, Torr Ne2 Final 1 8 0 enrichment, & m a
NE ( E = 01 - 1) Number of theoretical plates, iV Final enrichment, Qiac
eiao
eiao
0.99 & 0.02 8 . 3 =I=0 . 1 50.0 16.0 i 3 2.49 X 10-8 1.77 0.572 4.22 x 10-3 132.0 0.948 -4.2 x 10-4
a Q = (isotope concentration in boiler)/(isotope concentration in condenser) a t steady-state conditions.
At least three such experiments were done a t each pressure and for each of the isotopic methanols (except for CDaOH). I n some cases, up to seven experiments were carried out on a single material a t one pressure in order to increase the precision of the results. Assuming that the number of theoretical plates N in the column is not dependent on the isotopic composition of the methanol being distilled, the results for N can be averaged over all the experiments at any single pressure. The average fl was thus used to calculate eo and ec from the Qm data for each experiment. The ratio R of the final enrichments Qm of the 13Cand l80isotopes was averaged over all the experiments at one pressure for a given material. This ratio was then used to obtain the relative volatility for 13C from the l80result for the same material and pressure. Table I1 presents the average values of the relative volatilities as a function of the vapor pressure P for all four 180-160 and W-12C methanol pairs. The errors given in the table are standard deviations.
Discussion Summarizing the present results we observe that the vapor pressure of methanol increases with 13Csubstitution in the methyl group and decreases with l80substitution in the hydroxyl group. (8) A. Streitwieser, Jr., L. Verbit, and P. Stang, J . Org. Chem., 29, 3706 (1964).
(9) J. Beersmans and J. C. Jungers, BUZZ. Soc. Chim. Belg., 5 6 , 7 2 (1947).
(10) J. L. Borowitz, J . Catal., 13, 106 (1969). (11) The repeated solution of ammonium nitrate in the methanol was necessary because it was found that hydrogen exchange takes place only with the dissolved salt, albeit quickly, while exchange between dissolved and undissolved salt at room temperature was too slow t o be detectable over a period of 24 hr. (12) J. L. Borowitz, A . Raviv, P. Ronah, D. Sadeh, D. Samuel, and F. Klein, J . Label. Compounds, 1, 259 (1965). T h e Journal of Physical Chemistry, Vol. 76, X o . 12,1071
1818
J. L.BOROWITZ AND F. S. KLEIN
Table 11: Average Relative Volatilities € = a - 1 Pressure, Torr
Temp, OC
760 420 250 200
64 51 39 35
Pressure, Torr
CHsOH
CHaOD
CDsOD
€180 x 108 2.6f.0.3 2.2f.0.2 1.7f.0.5 1 . 0 1 0 . 3 3.750.2 3.450.2 3.250.5 2.650.2 4.63t0.2 4.33t0.3 3 . 8 3t 0 . 3 5.0
CHaOH
CHiOD
x 760 420 250 200
CDaOH
CDaOH
CDtOD
104
- 2 . 8 5 0 . 5 - 2 . 9 5 0 . 6 - 3 . 4 f.1.0 - 2 . 0 i 0 . 6 - 3 . 4 5 0 . 3 - 4 . 1 5 0 . 3 -4.2f.0.8 -4.73t0.4 - 3 . 3 f.0 . 4 - 4 . 7 f.0 . 6 -6.1 5 0.5 -3.6f.0.4
The effect of isotope substitution of l80in the hydroxyl group is about one order of magnitude greater than that of lacsubstitution in the methyl group. (Similar relative effects were observed for D-substitution in the hydroxyl and methyl group^.^) Our results for eo and eo of CHIOH are generally in fair agreement with previous m e a s ~ r e m e n t s ~(see ~-~~ Table 111). Only the ec value of Zelvenski differs significantly from the present value, but Rozen’s recalculation brings this result more into line. Table 111: Comparison of Results a t Atmospheric Pressure with Those of Previous Workers €0
x
10’
3.0 2.9 1.5 2.6
fo
x
2.9
I
I
I
3.0
3.1
3.2
1/T x IO3 deg-‘
.
I.
3.3
Figure 2. Temperature dependence of 1 8 0 relative volatilities: 0, CHaOH; X, CDaOH; 0, CHIOD; A, CDaOD.
where is the mean square forcel9 on an atom (or a molecule, as a first approximation, as in our case). M is the molecular weight.20 The constant B,22given by
(7) corrects for changes in the internal frequencies VT on condensation. Comparing CHaOH and CHBOD(Table IV), we see that the values of A are equal within experimental error. The same is true of the pair CD30H and CD3-
Ref
104
14 15 16
-2.0 -5.0 -2.3 -2.8
Present paper for
CHsOH at 760 Torr
The relative volatility data, eo and e,, were fitted to B , using the least-squares the equation T E = A / T method. The calculated constants A and B are given in Table IV. Figure 2 shows plots of this function for the oxygen data. The above equation was given by Bigeleisen, et aZ.,17 in the following form A -B In = (5) T2 T
+
The term A / T z results from the quantum correction1* to the partition function of a monoatomic liquid-vapor system. A is given by
The Journal of Physical Chemistry, Vol. 76, No. 12, 1971
(13) I. Dostrovsky, E. D. Hughes, and D. Llewellyn, Bull. Res. Counc. Iw., 1, 133 (1954). (14) P. Baertschi, H. Kuhn, and W. Kuhn, Nature, 171, 1018 (1953). (15) Ya. D. Zelvenski, V. E. Sokolov, and V. A. Shalygin, Nauch. DoM. Vyssh. Shlc., Khim. Khim. Technol., 388 (1958). (16) Reference 2b, p 487. (17) J. Bigeleisen, M.J. Stern, and W. A. van Hook, J. Chem. Phys., 38, 489 (1963). (18) L. D. Landau and E. M. Lifshitz, “Statistical Physics,” Pergamon Press, London, 1958,p 293. (19) F z is normally not assumed to change with isotopic substitution as it is a function of electronic interactions only. Deuterium substitution, however, is known to affect interatomic distances,2* so that in this case F z must change on deuterium substitution. 1 8 0 substitution in methanol is therefore a useful tool to study these changes in p2. (20) In the case of polyatomic molecules the moments of inertia should be taken into account. Friedmannz’ incorporated the moments of inertia of a linear molecule into an “effective mass,” which is substituted for the mass M in eq 6. In order to examine the effect of intermolecular librations, methanol was considered as a linear molecule with moment of inertia equal to the average of the moments of inertia about the two principal axes nearly perpendicular to the CO bond. Replacing the masses in eq 6 by effective masses did not however alter the conclusions of the present discussion and for the sake of simplicity the ordinary mass, M , is therefore used in this discussion. (21) H. Friedmann, Advan. Chem. Phys., 4, 225 (1962). (22) M.J. Stern, W. A. van Hook, and M. Wolfsberg, J. Chem. Phys., 39, 3179 (1963).
1819
VAPORPRESSURE ISOTOPE EFFECTS IN METHANOL Tsble IV: Values of Coefficients A and B of Equation 50rb
CHaOD
CHsOH
CDaOH
CDaOD
4 . 1 i:0.4 -11.6i: 1 . 6
3.5 f 0.6 -9.9 f 1.8
- 0 . 2 i:0 . 2 0 . 5 =k 0 . 5
- 0 . 5 f 0.1 1 . 3 i:0.3
‘80 A B
x
10-8
2 . 2 i.0 . 4 -5.6 f 1.3
A B
x
10-8
- 0 . 3 i.0.05 0.7 4 0 . 2
2 . 5 i:0 . 4 - 6 . 7 i : 1.1
-0.3
1%
a
See ref 17.
* 0.05 0.7 * 0 . 1 5
* Relative volatilities for 1 8 0 isotope substitution in deuterated methanols.
OD. However, the values of A for the second pair are greater than those of the first pair. Using expression 6 for A and neglechg the small difference in fi on 1 8 0 substitutionj20i.e., @ = we calculate
w,
(i
-
&)PCHaOD
=
2.20 2.51
i.e. F~CHaOH
- 0.83
f
0.2
F;CHs0~
We find that the intermolecular force in CHaOH is smaller than that in CH30D. The fact that CHaOH is more volatile than CH30D may thus be at least partly due to differences in the intermolecular forces in the two liquids. There should also be an intramolecular contribution to In a because we are dealing with molecules and not with atoms, but it is apparently smaller in this case than the intermolecular contribution. The same, again, holds for the pair CD30H-CD30D where FCD~OH/FCD~OD = 0.88 f 0.2. However, when considering the pair CD30H-CH30D, we obtain similarly to the above F%DaOH/FcHaOH
= 2.2
* 0.2
that is the intermolecular force is greater in CD30H than in CH30H, and similarly, the intermolecular force is greater in CD30Dthan in CH30D. In these two cases, however, the heavier molecules are more v ~ l a t i l e . ~ Clearly, the intramolecular contribution to the relative volatility is greater than the intermolecular contribution in the methyl-deuterated molecules. The fact that the B term for the methyl-deuterated methanols is larger than that for the methylunsubstituted molecules supports this conclusion. An accurate analysis of the intramolecular contribution is not warranted a t present, considering the given accuracy of the data.
The respective values of A and B for isotopic carbon substitution (Table IV) are about one order of magnitude smaller and of opposite sign than the analogous oxygen values. The analysis of these values is, however, less straightforward than that of the oxygen values. The reason for this is that the isotope effects here may include additional factors neglected in the treatment of the l8O results. This is discussed further below. The above conclusions on the intermolecular forces in deuterated methanols are borne out by spectroscopic data. The O-H out-of-plane bending vibration of frequency VT is a good indicator of the strength of the intermolecular force.23 In the liquid this vibration replaces the internal rotation about the C-0 bond in the gas. The frequency increases sharply on condensation (see Table V) and is also strongly isotope dependent. Clearly, the larger this frequency in the liquid, the stronger is the intermolecular force. We see from Table V that VT is always larger in the deuterio-methyl molecule than in the protium-methyl methanol. With regard to the intramolecular effects, we consider the frequencies, v, and V b , of the OH stretching and the inplane bending vibrations, respectively. These frequencies change markedly on condensation. Their values in the liquid phase have been used as measures of hydrogen bonding.2a Table V shows that the sum of these frequencies, again, is larger in the CDa molecules than in the CH3molecules. We see, therefore, that the spectroscopic data confirm the conclusions drawn from the l8O results; the B term is always larger in a heavy molecule (see Table IV), i.e., intramolecular effects are larger in a heavier molecule. I n general, we can conclude that, in methanol, when the heavier molecule is more volatile than the light, this is due to domination of the relative volatility by intramolecular effects. The vapor pressure of the deuterated methanols increases in the order CH30D, CD30D, CHIOH, CD,(23) G. C. Pimentel and A . L. McLellan, “The Hydrogen Bond,” W. H. Freeman, San Francisco, Calif., and London, 1960, p 75.
The Journal of Physical Chemistry, Vol. 76, No. 13, 1971
J. L. BOROWITZ AND F. S. KLEIN
1820 Table V : Vibrational Frequencies of Methanol"3bin Wave Numbers (ern-') --CDsOH-Gas V#
3690 1297
Avb YT
AVT a
3310
r-CHaOHGas
Liquid
7CDsODGas Liquid
,---CHaOD-Gas
3682
3337
2724
2720
380
Av# Yb
Liquid
270
- 94
- 395
345 1391
1346
665
2 70
-74 - 385
2474 250
1420
776
655
213
-42
- 270
Liquid
2485 235
818
863
483
213
942
- 79 - 262
M. Falk and E. Whalley, J . Chem. Phys., 34,1554 (1961); M. Margottin-Maclou, J . Phys. Radium, 21,634 (1960).
b
475
A v = vgas
-
Vliquid.
OH.9 This sequence is the same as that in which the sum vs 4- V b increases, and opposite to the order of increase in YT. It would appear that the changes in the vapor pressures of the deuterated methanols are directly correlated with the changes in hydrogen-bond strength on isotopic substitution. The l80and 13Ceffects, on the other hand, decrease in the order of the molecular weights, i.e., in the order CH30H, CHaOD, CD30H, CD30D. This indicates that these effects are not related to the changes in the hydrogen bond strength on isotopic substitution. The 13Cand CD, relative volatilities are an order of magnitude smaller than those of the "0 and hydroxyldeuterium substituted species. This means that, for the methyl-substituted species, the inter- and intramolecular contributions almost balance one another. Thus small effects which do not affect the l80 result significantly (to the accuracy of the present measurements) may make up a significant part of the 13C rela-
The Journal of Physical Chemistry, Vol. 76,N o . 18,1971
tive volatility. Such effects may be changes in the intermolecular force constants with t e m p e r a t ~ r e . ~ ~ The fact that the 13C effects are so much smaller than the l80effect can be ascribed, in part, to the position of the methyl group with regard to the hydrogen bond in the liquid. Following FriedmanqZ1we note that increasing the mass of the methyl group moves the center of gravity of the molecular away from the center of interaction, thus increasing the zero-point energy of the molecule in the liquid phase, and thereby decreasing the intermolecular contribution to the isotope effect. In the, case of l80substitution the center of gravity moves in the opposite direction and the intermolecular contribution is increased. We see that with 13C substitution inter- and intramolecular contributions tend to balance, whereas with '*O substitution a large isotope effect will be observed. (24) J. N.Finch and E. R. Lippinoott, J . Chem. Phys., 24,908 (1956); J . Phys. Chem., 61, 894 (1957).
