Chemical reactions.

Except in the case of very rapid reactions the rate of a chemical reaction is often as important as the thermodynamics of the reaction. If there is a decrease in free energy when the reaction takes place, at constant T, P. it may go spontaneously but will be useful only if it takes place in a reasonably short time. Moreover, if several different reactions are thermodynamically possible, the one which is fastest will use up the reactants first and result in a larger yield of the product. Application of the principles of thermodynamics and chemical kinetics makes possible the prediction and control of chemical reactions, but the overall reaction becomes complicated when several different reactions are taking place together.

In studies of chemical kinetics (Refs. 1 to 6) it is important to determine the rate expression which will give the concentration of one or more of the reactants or products as a function of time and to obtain the numerical value for the specific rate constant k.

Although chemical reactions which accurately fit these formulas are chosen for illustration, the student must realize that a great many chemical reactions involve so many simultaneous competing successive and reverse reactions that the mathematical analysis in simple terms has not been possible. The development of electronic computers is now making possible the mathematical analysis of many of these complicated reactions.

Unimolecular reactions are those which involve the breakdown or rearrangement of one type of molecule such as

AB ® A + B or ABA ® BAA

Bimolecular reactions involve a collision between two molecules such as

A + B ® AB or AB + CD ® AC + BD

Termolecular reactions involve a collision between three molecules. But the rate determining step in the reaction usually does not involve a mechanism of a simple uni-, bi-, or termolecular reaction. The order of the reaction, n, which must be evaluated experimentally, is important in determining the mechanism by which the reaction takes place. It is defined by the equation

dc/dt = kcⁿ (1)

where n is evaluated from the rate of change of concentration of reactant c with time. If n is 1, the reaction is first order, if it is 2, the reaction is second order, and if it is 3, the reaction is third order. If (as is usually the case) n is found to have other values that are not integers, the reaction is complex and involves more than one uni-, bi-, or tri-molecular reaction. Fortunately the rates of many unimolecular or bimolecular reactions can be estimated from molecular structure or other properties, and often a complex reaction may be broken up into a series of predictable units molecular and bimolecular reactions.

The first-order reaction equation

-dc/dt = kc¹ (2)

is integrated to give

- ln c = kt + constant (3)

or

(4)

where c₁ and c₂ are the concentrations at times t₁ and t₂.

For first-order reactions k is numerically equal to the fraction of the substance which reacts per unit time, usually expressed in reciprocal seconds (or minutes). in such reactions it is not necessary to know the initial concentration of the reactants or the absolute concentrations at various times. The concentrations may be determined directly by experiment using chemical or physical measurements; or any property, e.g., volume, electrical conductance, or light absorption, which is proportional to the concentration may be measured and substituted for c in formulas (3), (4), or (5).

The kinetics of a second-order reaction is described by the equation

-dc/dt = kc_A² (5)

where c_A is the concentration of the reactant A, or

dc_A/dt = kc_Ac_B (6)

where c_A and c_B are the concentrations of two reactants A and B.

The numerical value of the rate constant k for a second-order reaction depends on the units in which the concentrations are expressed, such as moles per liter moles per cubic centimeter, or atmospheres. In a first order reaction these units cancel out, but in a second-order reaction they do not. In a second-order reaction, if one reactant is present in sufficiently large excess, its concentration remains essen tially constant and so the second-order reaction then appears to be of the first order.

HYDROLYSIS OF METHYL ACETATE

Apparatus

25^oC thermostat (L); 35^oC thermostat (L); three 250 ml Erlenmeyers (D); two 125 ml Erlenmeyers (D); 5 ml pipette (D); 50 ml pipette (D); timer (S); Buret (S); Buret Clamp (S).

Chemicals

Two liters 0.2 N NaOH (P); phenolphthalein indicator (S); 500 ml 1 N HCl (L); Distilled H₂O (L); ice (L); 25 ml methyl acetate (S).

NOTE: It is important to initiate the first reaction no later than 30-45 minutes after the laboratory period has begun (the sooner the better). When preparing the two liters of 0.2 N NaOH, weigh out the necessary amount of NaOH pellets into a glass container (NO WEIGHING PAPER IS TO BE USED).

CAUTION: NaOH pellets are CAUSTIC, use a spatula for transferring. NO HANDS.

Procedures

Two runs are made at 25^oC during the first laboratory period (your instructor may ask that you do these runs at room temperature) and two runs are made at 35^oC the second laboratory period

The concentration of methyl acetate at a given time is determined through titration of samples with a standard sodium hydroxide solution; the experimental accuracy depends chiefly on the care used in pipetting and titrating. The sodium hydroxide solution used could be prepared by dilution of a saturated stock solution to minimize the amount of carbonate present and hence to reduce the fading of the phenolphthalein end point. It is not necessary, however, to use CO₂-free distilled water, because the amount of carbonate introduced in air-saturated water is negligible when titrating with 0.2 N sodium hydroxide.

A test tube containing about 12 ml methyl acetate is set into a thermostat at 25° C. Approximately 250 ml of standardized 1 N hydrochloric acid is placed in a flask clamped in the thermostat. After thermal equilibrium has been reached (10 or 15 min should suffice), two or three 5-ml aliquots of the acid are titrated with the standard sodium hydroxide solution to determine the exact normality of the sodium hydroxide in terms of the standardized hydrochloric acid. Then 100 ml of acid is transferred to each of two 250-ml flasks clamped in the thermostat and 5 min allowed for the reestablishment of thermal equilibrium. Precisely 5 ml of methyl acetate is next transferred to one of the flasks with a clean, dry pipette; the timing watch is started when the pipette is half emptied. The reaction mixture is shaken to provide thorough mixing.

A 5-ml aliquot is withdrawn from the flask as soon as possible and run into 50 ml of distilled water. This dilution slows down the reaction considerably, but the solution should be titrated at once; the error can be further reduced by chilling the water in an ice bath. The time at which the pipette has been half emptied into the water in the titration flask is recorded, together with the titrant volume. Additional samples are taken at 10-min intervals for an hour; then at 20-min intervals for the next hour and a half. A second determination is started about a quarters of an hour after the first one to provide a check experiment.

In similar fashion, two runs are made at a temperature of 35°. Because of the higher rate of reaction, three samples are first taken at 5-min intervals, then several at 10-min intervals, and a few at 20-min intervals. It is convenient to start the check determination about a half hour after the first experiment is begun.

The 5 ml aliquots are best quenched by diluting in 50 ml of ice water! Use an ice-H₂O slurry! Titrate them immediately with 0.2 N NaOH using two drops phenolphthalein as indicater.

THEORY.[1-6] The hydrolysis of methyl acetate presents several interesting aspects. The reaction, which is extremely slow in pure water, is catalyzed by hydrogen ion:

k₁’

CH₃COOCH₃ + H₂O + H⁺ Û CH₃COOH + CH₃OH + H⁺ (7)

k₂

The reaction is reversible, so that the net rate of hydrolysis at any time is the difference between the rates of the forward and reverse reactions, each of which follows the simple rate law given by Eq. (7). Thus

(8)

where k₁’ is the rate constant for the forward reaction and k₂ for the reverse reaction. For dilute solutions, water is present in such large excess that its concentration undergoes a negligible proportional change while that of the methyl acetate is changed considerably. For this case Eq. (8) may be written

(9)

In the early stages of the hydrolysis, the concentrations of acetic acid and methanol remain small enough for the term involving them to be negligible, and the reaction appears to be of first order:

(10)

The value of k₁ can then be determined by one of the methods conventional for first order reactions.

Evaluation of k_l at two different temperatures permits the calculation of the Arrhenius heat of activation DH_a for the forward reaction:

(11)

(12)

In obtaining the integrated form, it is assumed that DH_a is a constant. The heat of activation is usually expressed in calories per mole and is interpreted as the amount of energy the molecules must have in order to be able to react.

A more accurate calculation of the influence of temperature may be made on the basis of the Eyring equation,

(13)

where N_o is Avogadro’s number, h is Planck’s constant, and DS^‡ and DH^‡ are the standard entropy and enthalpy changes for formation of the activated complex from the reactants

CH₃COOCH₃ + H₂O + H⁺--------> [activated complex]

and k is a constant, of the order of 1/2, defined as the probability that an activated complex will decompose to form product species (rather than regenerating reactant species). Thus DH^‡ may be determined from measurements of k at two or more temperatures, on the assumption DS^‡, DH^‡, and k are independent of temperature.

(13)

(14)

Although DS^‡ cannot be determined from these data, for lack of knowledge of the value of k, it is sometimes possible to gain some information about the magnitude of DS^‡ by making a guess as to the value of k. In ordinary cases, a value of 1/2 to 1 is considered a reasonable estimate, but under certain circumstances k may be very small. The value of DH^‡ can be used, of course, to calculate the value of k_iT at any temperature (over the range in which DH^‡ and DS^‡ remain constant) from a knowledge of k₁ at one temperature.

An explicit solution to the kinetic equation may also be written for the case where the reverse reaction cannot be ignored. If the concentration of methyl acetate is a moles per liter initially, and a - x moles per liter at time t, then Eq. (8) can be written as

- d(a - x)/dt = dx/dt = k_l(a - x) - k₂x² (15)

since for each mole of methyl acetate hydrolyzed a mole of acetic acid and a mole of methanol are produced. Integration of this relation gives

(16)

Making use of the relation that the equilibrium constant K_h for the hydrolysis reaction is given by the expression

(17)

one obtains

Here c^o_H2O represents the concentration of water present, which is treated as a constant in accordance with the assumption made in obtaining Eq. (8) from Eq. (7).

CALCULATIONS. The titrant volume at time t, V_t, measures the number of equivalents of hydrochloric acid and acetic acid then present in the 5ml reation mixture aliquot. Let V_¥ represent what the titrant volume per 5-ml aliquot would be if the hydrolysis were complete. Then V_¥ -V_t measures the number of equivalents of methyl acetate remaining per 5-ml aliquot at time t, because one molecule of acetic acid is produced for each molecule of methyl acetate hydrolyzed. The corresponding concentration of methyl acetate in moles per liter is N(V_¥ - V_t)/5, where N is the normality of the sodium hydroxide solution.

If the reaction actually proceeded to completion, V_¥ could be measured directly by titration of an aliquot from the equilibrium mixture. An appreciable amount of unhydrolyzed methyl acetate is present at equilibrium, however, so V_¥ must be calculated.

The volume of the solution initially formed on mixing the 100 ml of 1 N hydrochloric acid with 5 ml of methyl acetate is designated by V_s. At 25°C, V_s is 104.6 ml rather than 105 ml because the solution is not ideal. Let the number of milliliters of sodium hydroxide solution required to neutralize a 5-ml aliquot of the original 1 N hydrochloric acid be V_x. The number of milliliters required to neutralize the hydrochloric acid in 5 ml of the reaction mixture at any time is V_x100/V_s, on the assumption that the total volume of the reaction mixture remains constant as the hydrolysis proceeds.

The weight of the 5 ml of methyl acetate is 5r₂, where r₂ is the density of methyl acetate (0.9273 g ml^-1 at 25 °C and 0.9141 at 35 °C), and the number of moles in this 5-ml sample is 5p₂/M₂, where 1162 is the molecular weight, 74.08. The number of moles of methyl acetate initially present in any 5-ml aliquot of the reaction mixture is (5r₂/M₂)(5/V_s).

Since 1000/N ml of sodium hydroxide of normality, N, is required to titrate acetic acid produced by the hydrolysis of 1 mole of methyl acetate, (1000/N)(25r₂/(M₂V_s) ml will be required for the titration of the acetic acid produced by the complete hydrolysis of the methyl acetate originally contained in any 5-ml sample of the reaction mixture. The total number of milliliters of sodium hydroxide solution t required to titrate both the hydrochloric acid and the acetic acid produced by the complete hydrolysis of the methyl acetate in a 5-ml sample of the reaction mixture is

V_¥ = V_x 100/V_s + (1000/N)( 25r₂/M₂V_s) (18)

The value of V_¥, is calculated for each experiment by means of Eq. (18). For each run a tabulation is made of the times of observation and the corresponding values of V_t and V_¥ - V_t.

Two graphs are then prepared. For each temperature a plot is made of log (V_¥ - V_t) versus t; the points obtained in the two runs can be identified by use of circles and squares. The straight line which is considered to best represent the experimental results is drawn for each set of points, and the rate constants for the two temperatures are calculated from the slopes of the two lines, in accordance with Eq. (3). It is not necessary to calculate the actual concentrations of methyl acetate, since a plot of log (V_¥ - V_t) versus t has the same slope as a plot of log [(V_¥ - V_t)(N/5)].

Comparison values of k₁ are calculated at each temperature from several sets of points by use of Eq. (3), to illustrate the dependence of the calculated rate constant on the particular pair of points chosen and hence emphasize the advantages of the averaging achieved in the graphical method. It should be noted that it is not significant to substitute an explicit averaging of the values of k obtained from the successive observations by means of Eq. (4).

From the rate constants found for the two temperatures,-the heat of activation is calculated by use of Eq. (11).

Practical applications. The rate of a chemical reaction is important in determining the efficiency of many industrial reactions. In organic reactions particularly, where there is the possibility of several reactions going on simultaneously, the kinetic considerations will often be no less important than the equilibrium relationships.

Suggestions for further work. The integration of Eq. (15) to give Eqs. (16) and (17) may be checked to illustrate a typical transformation in chemical kinetics. The integral involved is given in mathematical tables.

The method of least squares may be used instead of estimating by eye the “best” straight-line representation of the plot of log (V_¥— V_t) versus time.

Different acid concentrations or other acids may be used[7]; the influence of neutral salts may be studied[8]. Non aqueous solvents may be used,[9] and methyl acetate may be replaced by other esters,[10] higher temperatures being used if necessary.

References

1. S. W. Benson, “Foundations of Chemical Kinetics,” McGraw Hill Book Company, New York, 1960.

2. A. A. Frost and R. G. Pearson, “Kinetics and Mechanisms,” John Wiley & Sons, Inc., New York, 1961.

3. E. S. Amis, “Kinetics of Chemical Change in Solution,” The Macmillan Company, New York, 1949.

4. Tables of Chemical Kinetics: Homogeneous Reactions, Natl. Bur. Std. U.S. Circ. 510, 1951, and Suppl. 1, 1956.

5. K. J. Laidler, “Chemical Kinetics,” 2d ed., McGraw Hill Book Company’, New York, 1965.

6. E. A. Moelwyn-Hughes, “Kinetics of Reactions in Solutions.” Oxford University Press, Fairlawn, NJ., 1947.

7. R. O. Griffith and W. C. M. Lewis, J. Chem. Soc., 109: 67 (1916).

8. M. Duboux and A. deSousa, Helv. Chim. Acta, 23: 1381 (1940).

9. A. A. Friedman and G. V. Almore, J. Am. Chem. Soc., 63: 864 (1941).

10. H. S. Harned and R. Pfansteil, J. Am. Chem. Soc., 44: 2193 (1922).