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A method of determining molecular weights of vapors by effusion

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A method of determining molecular weights of vapors by effusion

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Content A METHOD OF DETERMINING MOLECULAR WEIGHTS OF VAPORS BY EFFUSION A Thesis Presented to the Faculty of the Department of Chemistry The University of Southern California In Partial Fulfillment of the Requirements for the Degree Master of Science by Gerald White February, 1943 UMI Number: EP41545 All rights reserved INFORMATION TO ALL USERS, The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. UMI EP41545 Published by ProQuest LLC (2014). Copyright in the Dissertation held by the Author. O i s w l s t i o f i i PeHisMng Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code ProQuest LLC. .789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106 - 1346 " CL * t 5 % & 8 + This thesis, written by ....... GM^..A....WHITE............ under the direction of hXs.. Faculty Committee, and approved by a ll its members, has been presented to and accepted by the Council on Graduate Study and Research in partial fu lfill ment of the requirements fo r the degree of m S.TER . OF.. 3G IM C E Dean Secretary D ate F eb ru a r y - -1- 9-45 Faculty Committee Chairman TABLE OF CONTENTS CHAPTER PAGE I. INTRODUCTION................. 1 Purpose of study ........................... 1 II. APPARATUS, FUNDAMENTAL THEORY, AND PROCEDURE . . 2 Theory . ................................. 2 Apparatus and procedure ..................... 2 Horizontal differential manometer .......... 4 Theory ................................... 4 Technique ................................. 4 Difficulties ............................. 7 III. RESULTS....................................... 9 Results ..................................... 9 Discussion of the results .................. 9 Modification of equations ............... 13 Moleeular weight determinations .......... 15 IV. CONCLUSION ................................... 19 Suggested modifications.................. 19 BIBLIOGRAPHY ....................................... 24 LIST OF TABLES TABLE I. II. III. IV. V. VI. PAGE Determination of 6 a Determination of cA ......................... 7 Comparative Times for Different Vapors Under Same Pressure Conditions.................... 10 Viscosities of Vapors . .................... 13 Results of Molecular Weight Determinations ... 17 Per Cent Error Determinations ................ 21 LIST OF FIGURES FIGURE PAGE 1. Original Apparatus ......................... - 3 2. Modified Apparatus— Horizontal Differential Manometer............................ $ 3. Plot of Time Against In f(l) ................. 12 A. Plot of t/ln f(l) against l/po* ............ 14 5. Plot of "a" against 16 6. Plot of Po^^ t/ln f(l) against Po2/^ IS CHAPTER I INTRODUCTION Purpose of study. The purpose of this investigation was twofold: (1) to modify the effusion apparatus described by Eyring-*- with a view toward making it a satisfactory method for molecular weight determinations of vapors at low pressures for student use; (2) to study the effusion of gases through an orifice, and to determine the precision with which mole cular weights could be measured with a view to obtaining the composition of vapor mixtures from molecular weight determinations. 1 Henry Eyring, f l Molecular Weights of Saturated Vapors by the Effusion Method," Journal of American Chemical Society, 50:2398-2401, 1928. CHAPTER II APPARATUS, FUNDAMENTAL THEORY, AND PROCEDURE Theory. It is assumed that the rate of flow of two different vapors from a high pressure to a lower pressure is, according to Graham’s law, inversely proportional to the square roots of the molecular weights of these two vapors. The deri vation of a theoretical equation as shown in a previous paper^ is based upon the assumption that the rate of flow is propor tional to the pressure difference on either side of an orifice. I 2 - k<Pl-P2) (1) where p^ * pressure in (see Figure 1), and p2 = pressure in V2. If we assume the Initial pressure in V2 to be zero and let ck - ^1 + V2 , then Vl t = K In < k Pi - PQ (2) <A Pf - po where p = original pressure in V^; J?± = pressure in Vq when t * o; Pf = pressure in Vq when t = t. Apparatus and procedure. The general technique is to start with zero pressure in V2, and any pressure, po, in Vj 1 G. A. White, ”A Study of Eyring’s Effusion Apparatus” (unpublished Research Paper, 290L, The University of Southern California, Los Angeles, 19£2.) o (Figure 1), and the time required for the pressure in to change from pi to Pf is measured by a stopwatch. At low pressures the use of a vertical mercury manometer was found p to be too insensitive. A far more sensitive Nujol manometer was unsatisfactory because of a pronounced wetting of the glass by the Nujol. Horizontal differential manometer. For the above reasons it was decided to employ a horizontal differential manometer as shown in Figure 2. The manometer consisted of a 2 mm. capillary tube, each end of which was connected to through a stopcock, and a small globule of mercury to serve as an indicator-piston. The mercury globule was always brought to vest at point 1 on the manometer before each run; the system was evacuated with stopcocks D and E open and then the pressure in Vi was allowed to build up to any desired amount. Stopcock D was then closed and the gas allowed to flow through the orifice at B by opening stopcock A. The rate of effusion was measured by timing the rate of increase in the volume between the stopcock D and the mercury globule. The original volume of Vo was so chosen as to allow for a rea sonable length of flow-time, while the pressure in de creased approximately to one half of the original pressure. 2 White, loc. cit. G» 6 Equation 2, converted to terms of lengths and volumes or the differential manometer, takes the form: [( d -1) -£2 - io - i] / (^£ 4 lo 4 1) t « k in ---------- = ---------- (3) [(<A -1} 4 ^ ' lo ] / + lo ) where "a” is the cross sectional area of the capillary; "lo" is the distance along the manometer between point 1 and point 2 at whieh timing beings; ”1” is the distance traveled by the mercury while being timed. is experimentally determined from the relationship, po Vo = pf (Vo 4 a 1) or Vo s Pf 1 a Po - pf where po and pf are the pressures in ' tlie start and finish of any particular run. The determinations of shown in Table I, lead to an average value = 33.5- TABLE I DETERMINATION OF .^2 po (cm. Hg) Pf (cm. Hg.) l(em.) JfSL. 31.03 21.39 1 4' . 98 33.2 31.03 19.11 20.86 33.4 31.03 I6.3O 30.39 33.5 61.1 42.39 14.89 33.6 61.1 37.71 20.96 33.8 61.1 36.67 25.58 33.4 61.1 32.03 30.39 33.5 61.1 26.12 45.09 33.7 7 . Vn + Vo <A » A .4. is determined experimentally from po Vi = pf (Vx + V2) V1 4 v2 - Po — n r " ~Pr~ po is the pressure in V^ and pf fS the final pressure t V 2 . Table II shows the data determining <A . TABLE II DETERMINATION OF^ po (Cm. Hg.) Pf (cm.) ck 26.04 5.43 4.79 51.43 IO.83 4.77 The flow of the mercury globule at pressures above 10 cm. was smooth and consistent with respect to time; at lower pressures the mercury had a tendency to stick to the glass and successive times would not agree for the same pressure reading. The cause was thought to be in the condi tion of the glass so the manometer was detached several times from the apparatus and cleaned thoroughly each time. Since no improvement in the flow of the mercury was obtained it was decided that this behavior was inherent in the mercury-glass system at low pressures. Hickman and Sanford^ have discussed 3 LC. Hickman and C. R. Sanford, "The Purification, Properties, and Uses of Certain High-Boiling Organic Liquids," Journal of Physical Chemistry, 34-:637-653, 1930. or where in Vi this possibility, together with suggesting several organic liquids to be used as lubricating agents for the mercury. The substances suggested were not easily available consequently a substitute, Nujol, was used. Upon introducing a small amount of the Mujol into the manometer with the mercury the flow of the lubricated globule was very smooth and extremely sensi tive to small changes in pressure, so that the manometer was considered to be satisfactory in every way. The technique employed was to start the flow from point 1, but to time between point 2 and any or all of the succeeding points. This method was followed because at pressures below 2 mm. the mercury would not start immediately of its own accord but required tapping. Once in motion, the globule moved normally. CHAPTER III RESULTS Results. Comparative runs (see Table III) were made with hydrogen, nitrogen, carbon dioxide, sulfur dioxide, water vapor, and iso-propyl ether vapor. No purification was attempted on the ether or gases which were introduced into the system from cylinders; the water was boiled for half an hour before use. Discussion of the results. It can be seen by an in spection of Table III that at low pressures the simple theory as developed above is not adequate to explain the small dif ferences in times between nitrogen, carbon dioxide, and sulfur dioxide. At pressures above 25 cm. of mercury the times are in the ratio of the square roots of the molecular weights; this is not true at lower pressures. Since at high pressures the flow was as expected, the time was plotted against [(cA -1) - lo - 1] / ( lo * 1) In f(l) - -------------------------- ---------- [( A -1) - lo ] / (-|2 + io ) for all of the initial pressures as shown in Figure 3. A linear relationship between the time and In f(l) for all pressures is obtained, but it is only at values greater than 25 cm. that the ratio of the slopes of the curves is in the i same ratio as the square roots of the molecular weights of N- £ N ~ i ) : i ! 1 ! 1 : { 1 ____1 < s f ~ \ 1 I ■i i V ■ ! I k. i \\ i i 1 1 ? i I i* N O i , ' . ■ 2 RAY lOS! A N 3 C L C ; lo TABLE III COMPARATIVE TIMES FOR DIFFERENT VAPORS UNDER SAME PRESSURE CONDITIONS Po(cm.) l(cm.) ^t(see) ^t( sec) ^^t(sec ) ^^t(sec , H20(g)t(8( 0.64 4.80 20.1 20.35 20.6 14.5 0.64 9.33 36.9 36.75 37.95 27.0 0.64 15.30 58.3 57.15 58.6 41.3 0.64 20.03 75.9 73.9 75.3 52,8 0.64 24.83 93-9 89.3 90.7 63.9 1.24 4.80 15.4 16.3 16.7 12.5 1.24 9.33 28.7 30.5 31.0 22.8 1.24 15.30 15.7 45.1 47.5 48.0 35.4 1.24 20.03 19.7 57.9 61.3 60.6 44.9 1.24 24.83 70.6 73.5 7 2 .8 54.1 1.84 4.80 13.7 13.8 1 6.1 11.1 1.84 9.33 24.85 25.7 28.8 20.3 1.84 15.30 14.18 38.7 39.6 43.7 30.4 1.84 20.03 16.53 49.75 50.4 56.0 39.1 1.84 24.83 60.1 60.6 66.4 47.2 3-84 4.80 10.6 11.7 3*84 9.33 19.7 21.8 3*84 15.30 9.8 31.1 33.6 3-84 2O.O3 11.7 39.5 42.4 3.84 24.83 47.1 50.9 5.84 4.80 9.1 10.35 12.5 5-84 9.33 18.0 20.1 22.7 5.84 15.30 27.7 31.0 35.1 5.84 20.03 10.05 35.5 39.4 43.7 5.84 24.83 42.0 47.0 51.9 7.84 4.80 9.3 7.84 9.33 17.3 7.84 15.30 26.4 7.84 20.03 33.3 7.84 24.83 39.7 25.84 4.80 9.55 25.84 9.33 17.79 2$.84 15.30 26.7 25.84 20.03 33-65 25.84 24.83 39.65 43.84 4.80 7.5 9.3 10.7 43.84 9.33 14.1 17.5 19.5 43 * 84 15.30 21.5 26.6 29.7 43.84 20.03 27.15 33.5 36.7 43-84 24.83 32.0 39.3 43-3 11 TABLE III (continued) COMPARATIVE TIMES FOR DIFFERENT VAPORS UNDER SAME PRESSURE CONDITIONS Po(cm*) l(cm.) ^2^.^secj ^ 2t(secj C°2t(se<$ S°2t(sec) H2°^t(sec 6 2. 44 4.80 7.4 10.55 62.44 9.33 13.9 19.25 6 2.44 15.30 21.1 29.95 62.44 20.03 26.7 36.3 62.44 24.83 31.4 42.45 1.24 * 12.70 13.2 1.84 * 12.70 12.46 3.84 * 12.70 8.67 * NOTE: (lo = 2.19) ISO-PROPYL ETHER DATA Po(cm.} pi(cm.) Pf (cm.) Po2'? t(sec) 11.34 9.84 6.84 5.05 49.7 11.34 9.84 5.84 5.05 75.0 9 .2 1 8 .8 4 6.84 4.39 34.0 9.21 8.84 5.84 4-39 58.7 5.34 4 .84 3-84 3.06 33.7 5.34 4.84 2.84 3.06 83.2 13 any two vapors. This would indicate that the supposed constant K is a function of the pressure as well as of the specific gas. The term K would thus have to be of such a form as to make the pressure important below 25 cm. and negligible at higher pressures. The simplest modification is to add a term ~p~x to the constant K to give the equation: t = (K 4 & ) In f(l) (4) Po* Figure 4 shows curves for the plot of t/ln f(1) against for different values of x. From Figure 4 it is evident P° 2/3 that t/ln f(1) is very nearly a linear function of l/p0 • Then equation 4 takes the form: t = (K 4 — §/j ) In F(l). (5) Po ' The constant "a" in equation 5 is a function of the specific gas as is shown in Figure 4. It is interesting to note that the times for nitrogen at low pressures are longer than for either carbon dioxide or sulfur dioxide. If the flow is viscous, this result would be anticipated, since inspection of TablelV shows that nitrogen has a larger coefficient of viscosity than either of the other two gases. TABLE IV VISCOSITIES OF VAPORS Vapor Viscosity (25° 0) N 2 176.5 * 10“^ poise 002 147.5 S02 126.5 H20 99. H2 88.5 Ob / or/ oov OS'O 09 V Ob'O or o 2 o 0 ) m w t n n 3 > ■< r 3 1 > z 0 m t o 3ft8 ± t ± £ > £ 7 r OOF A correlation of *aM and y was made by plotting against the slope of the curve for each specific vapor in Figure 4. This curve is shown in Figure 5 and it is evident that the relationship between na" and y is very nearly linear. Accordingly equation 5 becomes: where b and e are presumably independent of the nature of the gas. Equation 6 may be rearranged to give: line should be obtained whose slope is proportional to the square root of the molecular weight. The ratio of the slopes for two different gases should then be in the ratio of the square roots of their molecular weights. The results obtained for a number of different vapors are shown in Table V and Figure 6, and they are in satisfactory agreement with the predictions of equation 7. The data on the water vapor is not in close agreement with the other vapors, at least at the lowest pressure reading. The other two points do not fall far from the theoretical curve for water vapor in Figure 6, but obviously more data are required. Perhaps water vapor behaves abnormally in such a system because times for succeeding trials were not as consistent as for the other vapors. t * (K + -^2/3 ° ) In f(1) Po (6) (7) Hence if p©2/^ t/ln f(l) is plotted against Po2/^» a straight MOO a ■soo X /0 pof s e r NO. 6311. JESSE RAY M IL L E R . LOS A N G E L E S $%&)#%$)%)'*&()#''%+&$)$&$(%&$')()((&#'%()'*$%()#%$(%)*$&()%$'(+#''+%#' *7 TABLE V RESULTS OF MOLECULAR WEIGHT DETERMINATIONS H2 n2 co2 so2 (c3h7)2 0 Slope of curve from Figure 6 25 92 115 140 176 Molecular weight based on: H2 = 2.016 27-3 42.7 63.2 100.0 N2 = 28.0 2.03 - 43-7 64.8 102.2 C02 = 44*0 2.07 28.2 - 65.1 103.0 S02 = 64.0 2.04 27.6 43.2 - 100.9 (C3H7)2 0 = 102 2.02 28.2 43 • 4 64.6 - NO. 6311, J ESSE RAY M IL L E R . LOS A N G E L E S O / '-m 000/ ooor CHAPTER 17 CONCLUSION The results indicate that the method is sufficiently accurate to satisfy the requirements of the student of physical chemistry. There are certain advantages in following this procedure over the apparatus and method described by Eyring. The technique employed by Eyring was to maintain a constant driving pressure, whereas in this method the original pres sure is allowed to diminish during the run. The horizontal differential manometer is very easily read while the mercury globule is in motion, and it is much more sensitive to small changes in pressure than a vertical mercury manometer. There are certain precautions which must be taken, such as allowance for the solubility effects of vapors in the Nujol. Hickman and Sanford-*- have suggested other lubricating agents for a mercury manometer with which they have experimented successfully. The errors in the observed results are believed to be caused by the reading or the initial pressure in 7^, and the assumption that 72 is evacuated to zero pressure at the K. C. Hickman and C. R. Sanford, "The Purification, Properties, and Uses of certain High-Boiling Organic Liquids," Journal of Physical Chemistry, 34:637-653, 1930. 20 beginning of each run. The following calculations are evidence in favor. Assume = k (p^ - p2) Case 1. Initial pressure in V2 *-s ze*°» then as above t = K In Pi - Po ; ^ Pf " Po experimentally K- kVM t b- ^ -2/j0 ■ Po t - (kVS t b 1 4/* *) m - j X 1- - - * (8) Po d Pf - Po Case 2. Suppose the pressure in V2 is not zero initially, but is po2- Then dP2 dt— = k (PI “ CP2 + Po2l) Po Vl - PI Vi * P2 v 2 &P2 £P1 dt " V2 dt ~ IIT * k l<k P1 " (Po + Po2 * Integrating and rearranging, V2 t . ( k V u . » > 9 2 / t 9 .) i n ^ PI ~ (Po •* P02 • ~ T l ~ ) (9 ) Po (A P f “ (P o + P02 Comparative times for hydrogen (g), and sulfur dioxide calculated by equations 8 and 9 are shown in Table VI; the following constants were experimentally determined: - 4. 7 8; k v 17.55; a = 0.916; b = -15.0; - 3.7 8. 21 TABLE VI PER CERT ERROR DETERMINATIONS (Summary of results) Po Po2 t V m 1 M Per cent error in M H2 0.60 0.00 36.1 1.42 2 .01 0.00 0.01 37.3 1.635 2.67 32.8 0.05 43-1 2.71 7.3 8 267 1.20 0.00 25.7 1.42 2.01 0.00 0.01 26.2 1.51 2.28 13.4 0.05 27.9 I.83 3.35 66.8 HoO 0.60 0.00 55.6 4.24 18.0 0.00 0.01 57-2 4.56 20.8 15.6 0.05 66.4 6.25 39.1 101.5 0.10 82.9 9.28 86.1 378 1.2 0.00 43.6 4.24 18.0 0.00 0.01 44* 3 4.37 19.1 6.1 0.05 47.5 4.97 24.7 37.2 0.10 52.1 5.76 33.2 84 1.8 0.00 38.7 0.01 39.1 0.05 40.8 0.10 43*4 SO 2 0.60 0.00 86.9 8.00 64.O 0.00 0.01 89.6 8.48 71.9 12.40 0.05 IO3 .8 11.12 123.4 93 0.10 132.2 16.35 267 161 1.20 0.00 70.9 8.00 64.0 0.00 0.01 72.3 8.28 68.5 7.03 0.05 77.3 9.20 84.5 32 0.10 84.9 10.58 112 91 22 Now assume P©2 = 0 and let po = 0.6. If po is read 0.50 then the molecular weight of hydrogen is 0.722; if p© is read 0.55 the molecular weight of hydrogen is 1. 46. Inspection of Table YI, page 21, indicates very clearly that the pressure readings must be made with considerable accuracy. This is possible only by a magnification of the pressure readings. One possible solution to the problem is the use of two differential vertical manometers, one attached to Vl and the other to V2» using a less dense liquid than mercury in the manometer, such as Nujol. The disadvantages of this oil as found in this experiment would not be confronted here because the method of reading would be entirely static. On a qualitation basis it can be inferred from the size and shape of the orifice used (Figure 7) that the flow at the lower pressures is largely viscous. Yicosity is de pendent upon the radius and length of the capillary in such a manner as to allow for a velocity gradient to be established within the capillary. If the lapse of time between the en trance of the gas into the capillary and its exit is not suf ficient for such a development then no appreciable viscous flow should be observed. One might guess that at high pressures, for an orifice whose length is short that, within the time the gas remains in the capillary, the slow rate of diffusion might prevent the establishment of a velocity gradient from the walls to the center of the tube. At lower pressures, with higher rates of diffusion, one might expect at least a partially established velocity gradient and hence partial viscous flow. It would be interesting to use orifices of known dimensions and lengths to check the suggested behavior. It is possible that the viscosity effect can be eliminated by FIGURE 7. using an orifice made in the wall of a very thin glass bulb. BIBLIOGRAPHY BIBLIOGRAPHY Eyring, Henry, "Molecular Weights of Saturated Vapors by the Effusion Method," Journal of American Chemical Society, 50:2398-2401, 192F: Hickman, K. C. D., and C. R. Sanford, "The Purification, Properties, and Uses of Certain High-Boiling Organic Liquids," Journal of Physical Chemistry, 34:637-653. 1930. White, G. A., "A Study of Eyring*s Effusion Aparatus." Unpublished Research Paper, 290-L, The University of Southern California, Los Angeles, 1942.

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Creator White, G. A (author)

Core Title A method of determining molecular weights of vapors by effusion

Degree Master of Science

Degree Program Chemistry

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag chemistry, analytical,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Copeland, C.S. (committee chair), Burg, Anton (committee member), Cooper, John (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c17-789700

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Rights White, G. A.

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