Ursinus College Digital Commons @ Ursinus College Chemistry Honors Papers Student Research 5-13-1951 Rate of Reaction and Order of the Esterification of Propylene Glycol With Acetic Acid Thrygve R. Meeker Follow this and additional works at: https://digitalcommons.ursinus.edu/chem_hon Part of the Chemistry Commons Click here to let us know how access to this document benefits ou.y Ursinus College Library, URSINUSIANA COLLECTION Class_^ Box C%An-y 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. <Cx =. Ac 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.