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5-13-1951
Rate of Reaction and Order of the Esterification of Propylene Glycol With Acetic Acid
Thrygve R. Meeker
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RATE OF REACTION
and ORDER Of TllH E ESTERIFICATION of PROPYLENE GLYCOL with ACETIC ACID
Department of chemistry
Thrygve R. Meeker
5/13/51
This paper is submitted to> the faculty of Orsinus College in partial fulfiiinient of requirements for honors in Chemistry. Submitted:
May 17, 1951 TABLE OF GONTEMTS
Theory 1 Technique of determinations .... 5
Procedure 7 Experimental data 8 Calculations 9
Corrections for c 10 Check on acetic acid loss 12
Curve analysis 13
Results 14
Summary , 14 Graphs 1$ DETERMINATION of ORDER and bPECIEIC REACTION RATE of
ESTERIFICATION OF PROPY.1.ENE GLYCOL with ACETIC ACID at 40° Centigrade
The order of a chemical reaction is a term which designates the number of moles which are involved in a given reaction. Thus the decomposition of calcium carbonate by heating is a first order reaction and the precipitation of silver chloride from silver nitrate with sodium chloride is a second order reaction.
*Let us first investigate the kinetics of a hypothetical first order reaction A B ^^^^ > A -1- B. By the definition of -order given above this reaction is of the first order. From experimental data on reactions known to be of ihis type, the following relationship has made itself evident: the rate of change of the reactant is negatively proportional'-to theloonc- centration at any time. In other v/oras if we plot the rate of change of AB against time, a curve of this general form w;ould result:
Ac_ ALir
*Theory of reaction kinetics taken from Elements of Physical ohemistry, S. Glasstone, XMOstrand Co. New/ York -2-
Expressed mathematically, the above facts give us:
d C AB — k CAB d t
If a is the original concentration of AB, then CAB time t is a - X and our equation becomes:
^ - = - k (a - X ) dt
d (a - x) - - dx
=. k (a - x) at Integration of this equation will yield an expression relating the concentration of AB and the time. The proportionality constant k is called the specific reaction rate.
dx k dt (a - x) J
In a kt a - X
or k , 2.3C3 lo^ a t a - X
In the same way the formuias for second and third order reactions may derived. In a second order reaction, where tvra possibilities exist, there are two different expressions for the specific reaction rate; in the case of third only one of the combinations possible is usually employed in order to simplify calculations. In a second order reaction of the type A T B ^ j
A and B may be of different concentrations in v*rhich case the specific reaction constant is given by:
k = 2-303 log b - X t(b - a) a - X
or A and B may be of the same concentration in which case the
specific reaction constant is given by:
1 - 1 k _ 01 -22- ti - X>2
In the case of a third where two of the reactants are of the same
cpncentration and the third is of a different concentration the
specific reaction rate is given by:
k — 1 1 „ J 2x(2a-b) 2.303 log a(b-2x) L ~ t (b-2a)2 [_ b(b-2x) b(a-x) /
One method of calculation of the order of the reaction
is to substitute the experimental results in all three of the above equations, selecting the one which gives the most consistent values for k, A better approach to the problem would be to obtain a mathematical relationship betv/een dc/dt and n(the order of the reaction). In the reaction A+B+-C-*- +-X Y , where theie are n reactants of the same concentration c, the rate of reaction dc/dt is given by - dc/dt -- k c^. If n is one, then thds form reduces to the forinula previously derived for a first order equation. In an equation of a higher order, Integration results in a different form than that presented before.
C I The kinetic equation tox a second order reaction where the initial concentrations of both reactants are equal is therefore:
\
4
^x - ^,
Since this is of the io»~-m , it is at once evident that 'GT a plot of ^/C'S Mr will yield a straight line.
An actual relationship betv^een dc/dt and n may be derived by assuming at two different concentrations:
— lM(^^ M. X 'K TECHNIQUE OF DETERMINAriONS: A technique to foilow the course of this reaction must take into consideration the following facts: 1. Evaporation of acetic acid in the course of the reaction 2. Hydrolysis (reverse reaction) during analysis of the samples 3. High molarities producing a aiultiplication of small errors in the titrations After several methods were tried, the one finally arrived at reduced the effects of the above errors considerably. However they could not be eliminated completely. The usual technique is to place the desired concentrations of reactants in a flask and to withdraw samples for analysis at the stated time intervals. Since it v/as impossible to open the reaction vessel without loss of acetic acid, this method could not be used. The obvious aolution to this problem is to seal the reactants in the vessel and anatysae at time t without exposing the contents to the air. The only way that this could be done would be to analyze the entire contents of the reaction vessel. Therefore, by allowing the reaction to continue for a longer period in different vessels, the amounts changed at any time may be determined. however, since the original concentrations differ from one vessel to the next, correction factors must be applied so tnat the results will be comparable to each other. This latter is necessary for the plotting of curves. These correction factors will be discussed in the section on analysis of data and calculation of results. -6- In the successive analyses of concentrations at any time, it v;as found that the reaction reversed v^,ry readily in the presence of water to which the mixture was added to reduce its molarity to the same level as that of the base used in the titration. Since the amount of acetic acid regenerated by hydrolysis is dependent upon the temperature and the time, only one portion of the diluted mixture vms titrated and the titration v/as carried out at ©° 0. by means of ice. In order to reduce the last error the entire sample is diluted to five hundred cubic centimeters and twenty-five cubic centimetei'S withdrawn for immediate analysis. This requires only one analysis and only one titration with standard base, thus reducing the time and the errors. -7- PROCEDUKE; 1. Weigh to the nearest milligram a number of I5 cc test tubes equal to the number of time intervals desired. 2. Add the desired amount of propylene glycol from a pipette. This axiount is such that after the addition of acetic acid, the totai volume is always ten cubic centimeters, and such that the molar ratio of propylene glycol to acetic acid is definitely established. 3. Weigh the tubes again 4. At t equals 0 the correct quantity of acetic acid is added and the tubes quickly weighed. and placed in the constant teBiperature bath. 5. At the desired time intervals a tube is withdrawn and opened under water in a beaker; the tube is rinsed inside and out and the resulting solution diluted to $00 cc. 6; 2$ cc. of this solution are at once pipetted out and Bun into ice 7. This is immediately titrated with the proper normality base using phenolphthalein as an indicator. 8. The t equals 0 value is maSe in the same way except that the concentrated reactants are not mixed 'together; they are weighed separately and mixed after dilution; the diluted mixture is then brought up to a volume of $00 cc. and the analysis performed as above. -8- EXPERIMENTAI. DATA: I Data for the determination of order and rate Temperature - 40° centigrade a/b = 1 Tube # Tare Ht. after add. of- time Analysis-*- - propylene glycol -acetic acid cc of .1421 N NaOH Q 12,994 18.786 13.131''-16.693 0 22.21 16 12.927 18.666 23.217 1 day 27.40 17 13.226 18.920 23.449 2 days 26.15 18 13.581 19.307 24.000 4 days 25.38 * Additional tare is necessary according to method of analysis of tube 0. See number 8 under PROCEDURE. 11 Check upon evaporation effects on the resuxts'^'^ Tube # Tare^ Water c W't. after add. of- added -4.280^ -acetic acid time Analysis-^ 6 19.212c. 19.317 23.979 1 hour 29.20 11 19.781 19.879 24.489 2 hours 29.45 26 18.855 18.967 23.569 3 hours 29.55 31 18.468 18.577 23.134 4 hours 29.20 This was taken for a period of only 4 hours instead of for a period of a week as probably Siould nave been taken. However, the vConsItancy is indicated and will be shovm later. H. 2 Actual weight of water not necessary since only changes in acid concentration are measured. 1. imalysis represents oniy 1/20 of entire amount. See procedure 5&6. -9- GALCULATION of values for substitution in kinetic equations'^ Tube fj^ a (grams) b (grams) 0 5.792 3.562 16 5.739 4.551 17 5.694 4.529 18 5.726 4.693 '^ a and b are the original concentrations of propylene glycol ana acetic acid, they are obtained by substraction from Data sheet I. Tube # a (mole's) ^ b (moles) 0 .07612 .05911 16 .07542 .07552 17 .07483 .07515 18 . .07525 .07787 1. These values are obtained from the chart at the top of this page by dividing each value by the proper molecular weight. Ivfolecular weight of propylene glycol 76.09 Molecular v/eight of acetic acid 60.05 Apparent Wi due to the fact that it is only 99.5%is 60.26 Concentrations at times indicated Tube # Analj'-sis according to titration values^ 0 .06312 16 .07787 17 .07432 18 .07213 ^ 2. Moles equal liters x 20 x normality. Only 1/20 of the total was analyzed. -10- CORRECTION of b-x for comparisons and curve plotting Tube #0 16 17 18 a (moles) .07612 .07542 .07483 .07525 b (moles) .05911 .07552 .07515 .07787 (b-x)^ .06312 .07787 .07432 .07213 (b-x)^ .05911 .07292 .06962 .06757 % left in mixture 100.00 96.56 92.64 86.76 (b-x)-(. is the concentration of acetic acid remaining according to the titration. However notice that in tube 0 where no reaction is supposed to have taken place, the molar concentration of acid according to weights does not agree with that according to titration. In order to correct for this discrepancy each value of (b-x)^ is multiplied by the factor .05911/.O6312 to give (b-x)^, the value that the titration should have had. This discrepancy is probably due to impurities in the concentrated acid or to a deviation in the concentration from 99.5 % s-s stated on the acid bottle. Eor purposes of comparison assume b to be the same in all tubes and choose this value of b to be the one nearett to a corresponding value of a . Then b .07552 .07552 .07552 .07552 and assume a = b since the exact amount of a is not measured and will have only a slight effect the reaction itself. The correction factors are therefore necessary for b-rx values. -11- I'rom this standardised b and values for % left a corrected b-s is obtained (b - x)^^ or c in the previously developed formulas for the specific reaction rate. (b - x)^ .07552 .07292 .06995 .06551 In order to plot the curves the follov/ing values were computed: log c 8.8780 - 10 8.8628 - 10 8.8448 - 10 8.8162 - 10 1/c 13.25 13.72 14.30 15.26 l/c2 175.4 188.1 204.4 233.0 Each of these values, c, log c, 1/c, l/c2, was plotted apainst time in days. -12- GHEGK UPON THE LOSS OF AGETIC ACID THROUGH EYAPORATION From experimental data, II, the number of moles of each acid present may be determined by substraction and dividing the weight of each acid by its equivalent weight. TUbe § 6 11 " 26 31 H2SOA (gms) .105 .098 .112 .109 HOAc (gms) 4.562 4.610 4.602 4.557 H2SOA (eq) .0021 .0019 .0022 .0021 KOAc (eq) .075? .O764 .0764 .0758 total acid wt. .0778 .0783 .0786 .0779 anal. ,0830 .O836 .0839 .0830 anal/wt 1.067 1.068 1.066 1.066 From the values of analysed/weighed it is obvious that any error produced by evaporation of acetic acid will probably not have an effevt on the third significant figure of the result. The calculations on this page w?ere made by slide rule. -13- CURVE ANALYSIS From the plots of c, log c, 1/c, and l/c^ , which all seem to give a straight line within the limits of experimental error, it is seen that the plot of c against t curves very slightly as it should for a reaction of order greater thai 0. The apparent linearity of this plot is due to the small changes which occur due to the extreme slowness of the reaction. This apparent linearity shows up in each of the other plots, see Graphs I,11,111,IV. However, in only one of the plots do all four points adhere to the straight line. This is the plot of t against l/c. (Graph 111) This indicates that the reaction is of the second order, as might be expected. Thus the esterification occurs in stages, replacement of the hydrogens of the glycol is a stepv/ise reaction CHOI H CH2O- COCH3 RESULTS: According to the above the formula w^hich we will use to calculate the specific reaction rate constant is, since the order of the reaction is two. E 1/°1 - l/cc) ti - t2 Since the two concentrations are equal. -14- RESULTS: k .47 .58 .48 time interval 0-1 1-2 2-4 These results are expressed in terms of moles and days. Since the constants are usually given in terms of moles and seconds, division of the above results by the number of seconds in a day will result in k 5.44 X 10"^ 6.71 X 10-6 5.55 X 10"^ SUM,IART: The evolved technique seems to be generally satisfactory although some refinements are undoubtedly necessary. The rate of the reaction is in the neighborhood of 10"^ and it is of the second order. IS ,23 22 2.1 ?ATF OF BSTERiNSAlt 16 A PH I £ DAYS. Pi OF C « W CF/V ri?ATIC!7y OF /icfTiC Aqo !7 it , . Y :-?3 , i\p>^yi H.\ ' 1 • i i i 54 "!XT ^ P4% 10 -hp- C, ^ aPAY6 4-i-H \ (5) \ L \ - — - - " 1 ' i ti-i-iflti^titi ] \ 1 , i1 - _.i 1 1i 0 1 2 3 4 5 S 7 8 9 10 II 12 13 !4 It 16 ,<>(,50 .Dfc'iO ,0300 .0130 .o1J"o -O??© .O'bDE) N CEN -TRATICW ( moles) 0 1 2 3 4 5 J.VOP-C 4.^IO!>-io 23 22 PRdPyLSM/e- GuycoL Ac t T I c ACID C, (.MOLesj 18 24 23 22 Zi! rf:-! i i F FsTci? I Fi c/> t/OA/ Pid Pf L £•//g GLycoL. 20 a i§ TlMB 19 PLOT OF 18 35 !7 j i 1 ! J 15 13 12 • / J 'iJ 5 e-li / 4i }M 0 1 2 3 4 5 9 10 11 12 13 14 it !6 '/C- CA. v_i2.