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 this chapter, the kinetics of four different reactions are studied experimentally. They are chosen because they give results which can be easily described in simple mathematical terms and because they illustrate a first-order reaction a second-order reaction, a catalyzed reaction, and a complex reaction.

In studies of chemical kinetics^1-6 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 essentially constant and so the second-order reaction then appears to be of the first order.

REACTION OF ETHYL ACETATE WITH HYDROXYL ION FOLLOWED BY ELECTRICAL CONDUCTANCE

This experiment illustrates the use of a conductance probe for measuring the progress of a solution reaction and the determination of order and rate constant from such data.

Apparatus

Two 250 ml glass stoppered volumetric flasks (D); two 250-ml glass stoppered Erlenmeyer flasks (S); conductance probe (S); glass stoppered weighing bottle (D); buret (S); 1 ml graduated pipette (S); 25 ml pipette (D); 50 ml pipette (D); 25^oC thermostat (L); 35 ^oC thermostat (L); timer (S).

Chemicals

250-ml 0.02 N ethyl acetate (P); 250 ml 0.02 N NaOH (P).

MEASUREMENT OF ELECTROLYTIC CONDUCTANCE ⁷

CONDUCTANCE PROBE. Alternating current must be used to prevent electrical polarization of the electrodes and the impedance of the device used to measure voltage must be very high. The basic structure of the conductivity probe is given in figure 1.

Figure 1. Schematic diagram of the conductivity probe.

How the Conductivity Probe Works

The Vernier Conductivity Probe measures the ability of a solution to conduct an electric current between two electrodes. In solution, the current flows by ion transport. Therefore, an increasing concentration of ions in the solution will result in higher conductivity values.

The Conductivity Probe is actually measuring conductance, defined as the reciprocal of resistance. When resistance is measured in ohms, conductance is measured using the SI unit, siemens (formerly known as a mho). Since the siemens is a very large unit, aqueous samples are commonly measured in microsiemens, or mS.

Even though the Conductivity Probe is measuring conductance, we are often interested in finding conductivity of a solution. Conductivity, C, is found using the following formula:

C = Gk_c

where G is the conductance, and k_c is the cell constant. The cell constant is determined for a probe using the following formula:

k_c=d/A

where d is the distance between the two electrodes, and A is the area of the electrode surface.

1 cm

1 cm

~

d=1cm

Figure 2. Schematic diagram of conductivity probe.

For example, the cell in Figure 2 has a cell constant: k_c = d /A = 1.0 cm / 1.0 cm² = 1.0 cm^-l. The conductivity value is found by multiplying conductance and the cell constant. Since the Vernier Conductivity Probe also has a cell constant of 1.0 cm^-1, its conductivity and conductance have the same numerical value. For a solution with a conductance value of 1000 mS, the conductivity, C, would be:

C = Gk_c = ( 1000 mS) x ( 1.0 cm^-1) = 1000 mS/cm

A potential difference is applied to the two probe electrodes in the Conductivity Probe. The resulting current is proportional to the conductivity of the solution. This current is converted into a voltage to be read by a Vernier interface.

Alternating current is supplied to prevent the complete ion migration to the two electrodes. As shown in the figure below, with each cycle of the alternating current, the polarity of the electrodes is reversed, which in turn reverses the direction of ion flow. This very important feature of the Conductivity Probe prevents most electrolysis and polarization from occurring at the electrodes. Thus, the solutions that are being measured for conductivity are not fouled. It also greatly reduces redox products from forming on the relatively inert graphite electrodes.

One of the most common uses of the Conductivity Probe is to find the concentration of total dissolved solids, or TDS, in a sample of water. This can be accomplished because there is generally a direct relationship between conductivity and the conductivity concentration of ions in a solution, as shown here. The relationship persists until very large ion concentrations are reached.

Specific

conductivity

(mS/cm)

Ion Concentration TDS (mg/L)

The Vernier Conductivity Probe has three sensitivity range settings:

• 0 to 200 mS (0 to 100 mg/L TDS)

• 0 to 2000 mS (0 to 1000 mg/L TDS)

• 0 to 20,000 mS (0 to 10,000 mg/L TDS)

These ranges are selected using a toggle switch on the end of the amplification box attached to the probe. It is very important to consider this setting when loading or performing a calibration; no single calibration can be used for all three settings.

CONDUCTANCE OF POTASSIUM CHLORIDE SOLUTIONS. In a very careful

and exacting research, Jones and Bradshaw⁸ have redetermined the electrical conductance of standard potassium chloride solutions for use in the calibration of conductance cells. The results of the work are summarized in Table 1. The values given in this table do not include the conductance due to water, which must be added and should be less than K_H2O = 10^-6 ohm^-l cm^-1 in work with dilute solutions. The potassium chloride should be fused in an atmosphere of nitrogen to drive out water, and in the case of salts which are deliquescent, it is necessary to use a Richards bottling apparatus⁹ to avoid exposure to air.

Table 1. Specific Conductance of Standard Potassium Chloride Solutions

Grams of potassium Specific conductance, ohms^-l cm^-l

chloride per 1000 g

of solution in vacuum) 0°C 18°C 25°C

71.1352 0.0651766 0.09783s 0.111342

7.41913 0.0071379 0.0111667 0.0128560

0.745263 0 00077364 0.0012205 0.00140877

CONDUCTANCE WATER. In all conductance measurements made in aqueous solution it is necessary to have very pure water. Distillation in a seasoned glass vessel and condenser with ground glass joints or with a block-tin condenser can give water with a specific conductance of about 1 X 10^-6 ohm^-1 cm^-1 if a little potassium permanganate is added to the flask. If such a distillation is carried out in air, the water is saturated with the carbon dioxide of the air (0.04 percent). Some of the dissolved carbon dioxide can be removed to give a higher resistance by bubbling carbon dioxide-free air through the water.

It is interesting to note that Kohlrauseh and Holborn¹⁰ reported the preparation of purified water with a specific conductance at 18° of only 0.043 X 10^-6 ohm^-l cm^-l

Conductance water for laboratory use may be prepared on a large scale by redistilling distilled water and condensing in a block-tin condenser. By condensing the water at relatively high temperatures, the absorption of carbon dioxide is reduced.

Question: What other method could be used to follow the reaction of ethyl acetate with hydroxyl ion?

THEORY.^1-6 The reaction studied in this experiment is

CH₃COOC₂H₅ + OH^- Þ CH₃COO^- + C₂H₅OH (1)

Since the actual reaction mechanism may involve several steps, the equation for the overall reaction does not necessarily suggest the correct form for the rate law. However, it has been found that reaction (1) does follow the second-order equation,

dx/dt = k₁(a—x)(b—x) (2)

where t = time elapsed from initiation of reaction

x = number of moles per liter reacted at time t

a = initial molar concentration of CH₃COOC₂H₅

b = initial molar concentration of OH^-

k₁ = rate constant for reaction (1)

provided the reaction mixture is not so close to its equilibrium state as to require inclusion in Eq. (2) of a term for the reverse reaction.

Integration of Eq. (2) for the case a ¹ b leads to the result

(3)

For the case a = b one obtains

(4)

The temperature dependence of k₁ can be related to DS^‡ and DH^‡ for the formation of the activated complex from reactants (page 140). From measurement of k₁ at two or more temperatures, DH^‡ can be found with the use of Eq. (14) of the preceding experiment.

The experimental problem is to determine x as a function of t for a solution in which reaction proceeds at a constant temperature. The reaction mixture undergoes a marked decrease in conductance with time as hydroxyl ion is replaced by acetate ion. The progress of the reaction can therefore be followed by measurement of conductance. ¹¹

PROCEDURE. Preparing the Conductivity Probe for Use:

You can be ready to measure conductivity or concentration using the Vernier Conductivity Probe in just a few minutes:

• To help ensure that the electrode surfaces are free of residues, soak the lower portion of the probe in distilled water for about 10 minutes. Blot the electrode surfaces dry (on the inside of the elongated hole near the probe tip).

• Connect the Conductivity Probe to one of the ports (channels) of your Vernier interface box. You are now ready to perform or load a calibration for the probe.

As some of the experiments are to be based on Eq. (4), solutions of NaOH and of ethyl acetate of equal normality, nominally 0.02 N. are prepared; 250 ml of each is require.

The ethyl acetate solution must be prepared the day it is to be used, because a slow reaction occurs even in the absence of OH^-. A technique which reduces error from volatilization of the ethyl acetate is to weigh the latter in a weighing bottle containing some water (the bottle and water having previously been weighed) and then transfer the sample quantitatively to the volumetric flask for preparation of the final solution. The solution of NaOH of the same normality is prepared by quantitative dilution of standardized stock solution using benzoic acid.

Three runs are to be made at 25°C:

[CH₃CO₂C₂H₅] = 2[OH^-] ; (2) 2[CH₃CO₂C₂H₅] = [OH^-] [CH₃CO₂C₂H₅] = [OH^-]

and one at 35°C:

[CH₃CO₂C₂H₅] = [OH^-]

It is essential that the reactants be mixed rapidly and the timer started simultaneously. Place 25 ml of one reactant in one Erlenmeyer, and 25 or 50 ml of the other reactant, as the case may be, in the other Erlenmeyer. Place these Erlenmeyers in thermostat; when thermal equilibrium is attained, initiate reaction by pouring contents of one flask into the other flask and the timer is started. The conductivity probe should be in the reaction mixture at time zero. The conductivity should be measured at intervals of several seconds (~10), until the rate of change has become relatively slow (about 45 min).

For runs 1 and 2 it is necessary to know R_c, the resistance which the cell would have if the reaction were to reach completion, i.e., until one reactant is used up. It is also helpful to have R_c for runs 3 and 4. While R_c can be found by actual measurement with solutions of NaOH and CH₃COONa made up to the appropriate concentrations, it is more easily obtained by calculation as described below. As matter of principle, it should be noted that R_c is not quite the same as R_¥ latter being the value of resistance approached asymptotically as the system reacts toward its final equilibrium state. For reaction (1), the equilibrium condition is so far to the right that R_¥ is very close to R_c but for cases where the distinction is important, R_c rather than R_¥ is the quantity needed for the subsequent analysis of the data.

CALCULATIONS. For the calculation of x from the conductance data, it is assumed that the conductance of the solution G_t at time t obeys the equation

(5)

If

where l_j = equivalent ionic conductance of species j

c_j = concentration of Species j in equivalents per liter

k = cell constant

In Eq. (5), we are assuming that the NaOH and CH₃COONa are completely dissociated and that the ethyl acetate, ethanol, and water do not contribute to the conductance. The solutions employed are sufficiently dilute to justify the further assumption that I_OH- and I_CH5COO- are constant even though the concentrations change during the run.

The value of x ranges from x =0 to x = c, where c is the initial concentration of the limiting reactant, that is, a or b, whichever is smaller. For the case of equal concentrations, c = a = b Eq. (5) leads, in all cases, to

(6)

Thus x is given by

(8)

By substituting Eq (8) into (3) and rearranging, one obtains the working equations for the runs with unequal concentrations,

were

Similarly, introduction of Eq. (8) into (4) yields an equation for the runs with equal

concentrations,

(10)

which upon rearrangement becomes

(11)

Plots of resistance versus time are prepared for all runs. These are useful for judging the quality of the data and for extrapolation to zero time to obtain R_o. As a check, the values available from the preliminary measurements on the NaOH solutions should be placed on the graphs. If R_c was not measured directly, the ratio , R_o/R_c can be calculated for each case from Eq. (5), which reduces to

For computing this ratio, handbook values for ionic conductance at infinite dilution may be used as approximations to I_Na+, I_OH-, and l_CH3COO-. It should not be overlooked that the conductance are dependent on temperature. The measured or calculated values of R_c should be marked on the graphs.

For the cases with a ¹ b, Eq. (9) is used for a graphical analysis of the data. The quantity on the left-hand side is plotted against time. If the data are consistent with Eq. (2) and the other assumptions made in deriving Eq. (9), these graphs should, within experimental error, fit straight lines with intercepts at log (a/b). Values the rate constant k₁ may be calculated from the slopes.

For the case a = b, the quantity (G_o—G_t)/t may be plotted against G_t. If the data are consistent with Eq. (11), k₁ may be found from the slope. If an estimate R_c is available, it can be used to predict the intercept with one axis and thereby improve the accuracy of k₁.

In examining these graphs, it is important to take into account the experimental uncertainty of the points, which is quite different for different regions of the graph The computations of this experiment can conveniently be made by a computer.

The enthalpy of activation DH^‡ is calculated from the values of k₁ at 25 and

35°C.

Suggestions for further work. As an alternative to the conductimetric method, a procedural which may be used to follow the progress of the reaction is to withdraw samples from the reaction mixture at definite intervals, discharge them into excess standard HCI to arrest the reaction and back-titrate with NaOH. For best results, CO₂-free water should be used to prepare the NaOH solutions. In other respects, the procedure followed may be similar to that described above. A suitable equation for graphical analysis of the data for the case a + b is obtained by expressing a - x and b - x as functions of the titration volumes and substituting into Eq. (3); the results of this is

where V_t = volume of NaOH solution required to titrate sample in which reaction was see at time t

V_a= volume of HCI into which samples were discharged

N = normality of NaOH solution used for titrations

N’ = normality of HCI solution

v = volume of each sample taken

It should be noted that, for a given run, the only time-dependent quantity in the first term on the left side of Eq. (13) is V_t

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. Bar. 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. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” 2d ed., p. 87, Academic Press Inc., New York, 1959; T. Shedlovsky in A. Weissberger (ed.), “Technique of Organic Chemistry,” vol. 1, “Physical Methods in Organic Chemistry,” 3d ed., pt. 4, Interscience Publishers, Ine., New York, 1960.

8. G. Jones and B. C. Bradshaw, J. Am. Chem. Soc., 55: 1780 (1933).

9. T. W. Richards and H. G. Parker, Proc. Am. Acad. ATTS. Sci., 32: 59 (1896).

10. F. Kohlrauseh and L. Holborn, “Leitvermogen der Elektrolyte,” 2d ed., Teubner Verlagsgesellschaft, Leipzig, 1916.

11. J. Walker, Proc. Roy. Soc. London, ser. A 78: 157 (1966).