Introduction

It has been shown in Chapter 5 how thermodynamic and kinetic constants are

dependent on temperature. Any fimction relating to Gibbs free energy is\ffected by

temperature but to what extent has to be determined experimentally. A less defined

relationship is the dependence of thermodynamic and kinetic parameters on agitation

or stirring rate of the system. Waterbeemd et a f and Leahy and co-workers^ have both

investigated the relationship between solvent-solvent partitioning rates and

coefficients for a given system. Both studies found that there is a bilinear relationship

between the rate of partitioning and the partition coefficient for a set of chemically

diverse compounds. They found that the rate of partitioning increases with the

partition coefficient until diffusion control becomes a limiting factor and the rate is no

longer dependent on the partition coefficient. Leahy et al also show how the rate of

partitioning at a constant partition coefficient increases with the speed of rotation

when using a rotating diffusion cell to study the solvent-solvent partitioning process.^

In this work the effect of temperature and stirring rate on the equilibrium

position, Keq, and rate of uptake, kup, for the partitioning of a pollutant between water

s and the Cig SPE disk is investigated. This is done by the application of the principles

discussed in Chapter 5 to experimental data obtained for the solid-phase extraction

(SPE) of pollutants from water. Diuron was chosen as the test pollutant for this

intensive investigation for a number of reasons:

• Diuron is a recognised herbicide that is readily available at a high purity

and low cost

• It contains an active chromophore and is sufficiently soluble in water at a

desirable concentration and ^max

• It partitions between water and the Cig disk to a reasonable extent which

aids in monitoring the partitioning and observing the end point

The structure of diuron is given in Figure 8.1. The same on-line UV spectroscopy

procedure detailed in Chapter 7 was utilised in this investigation but this time

partition experiments are carried out at four different temperatures and three different

stirring rates in order to determine Keq and kup and to observe how these physical

conditions'bffect the two parameters. The temperatures studied are 7, 11, 18, and

23°C, the stirring rates being 100, 200 and 400 revolutions per minute (rpm). The

initial concentration of diuron in the water, [A]w°, varied from 0.25-0.95 mmol.f*.

Cl

N H

O

CH3

CH3

Figure 8.1 Chemical structure of the herbicide Diuron

Values of Keq are obtained from the experimental data by the use of equation 7.2:

X

where [ A ] o e q is the concentration of diuron in the disk at equilibrium, [ A ] w ° is the

initial concentration of diuron in the water and [ A ] w e q is the concentration of diuron in

the water at equilibrium, all in mol.f*./is the phase ratio {f= VwA^d, where Vw and

Vd are the volumes of the water and disk in litres). More information on equation 7.2

is given in Chapter 7 along with details of calculating the volume of the disk.

Values of kup are obtained by fitting the partition data for the uptake of diuron

from water to equation 7.16:

O t ‘

Abs = 8M_ + (Abs° - sM ) exp'‘‘“P^ * (7.16)

Z K e q V o Z K e q V o

Abs° is the initial absorbance of diuron in water, Abs* is the absorbance after time t, e

is the molar extinction coefficient at the Xmax of diuron in water, M is the total number

of moles of diuron in the system, kup is the uptake rate constant (s'*), t is time of

exposure (s) and Z is equal to 1 + Vw/KeqVo, where Vd and Vw are the volumes of

the disk and water (litres); K^q is the equilibrium constant determined from equation

7.2 using the initial and final concentrations of the pollutant in the disk and water.

Equation 7.16 takes the form y = b + (a - b) exp^'^"^\ where coefficients a, b and c are

calculated. The rate of uptake, with units of s'*, is calculated from coefficient c since:

c = -kupZ (7.17)

Again, further details of these equations and processes are given in Chapter 7. The

phase ratio (f= 13542) was constant for all the experiments carried out with diuron.

8.1 Results and Discussion

8.1.1 Temperature effects on Keq

Given in Table 8.1 are the logarithmic values for the water-Cig disk

equilibrium constants (log Keq) for diuron at 7, 11, 18 and 23 °C. The standard

deviation, is given for each log Keq value which is the mean of at least three

repetitions. In order to determine if partitioning, or sorption of diuron from water to

the disk is exothermic or endothermie, a van’t Hoff plot of In Keq versus the reciprocal

temperature is necessary.

Table 8.1 Water-Cig disk equilibrium and uptake rate constants, corresponding

standard deviations and some physical constants for diuron.

Temperature (°C) log Keq ' log k„p(100)‘’ log k„p (20t

(s') (s') 7 4.14 ±0.01 (-5.49) -5.08 1 0.05 11 4.1310.02 -5.35 -4.94 1 0.05 5 ^ /') 15 (4.10) (-5.16) (-4.87) .J _{18 4.08 ± 0.02 -5.03 10.01 “ -4.82 10.03} 23 4.03 ± 0.02 -4.89 -4.68 10.04 25 (4.03) (-4.78) (-4.64) AH°(AH^> -11.211.9" 60.5 1 5.7 36.1 12.7» AG°(AG^) -22.510.1*’ 82.110.1 * 81.110.1 * AS°(AS^) 39.716.8 j -76.2119.9 *‘ -15819.5 *‘

( ) Parentheses indicate values from van’t Hoff or Arrhenius equations. ^ Mean value of at least three repetitions, stirring rate 100, 200, or 400 rpm ^ Single value when stirring rate is 100 rpm

® Mean value of at least two repetitions, stirring rate 200 rpm ^ Mean value of two repetitions, stirring rate 100 rpm.

® Standard enthalpy o f sorption at 11®C (kJ mol'^)

^ Standard enthalpy o f activation at 11®C (kJ mol'*) 100 rpm. ® Standard enthalpy of activation at 11°C (kJ mol"*), 200 + rpm. ** Standard free energy o f sorption at 11®C (kJ mol'^)

‘ Standard free energy of activation at 11°C (kJ mol'*) ^ Standard entropy of sorption at 11®C (JK‘* mol"*)

^ Standard entropy of activation at 11°C (JK* mol'*)

Shown in Figure 8.2 is a van’t Hoff plot for diuron that exhibits linearity over

the temperature range 7 - 23°C with a correlation coefficient of 0.95. The standard

enthalpy of sorption, AH®, is calculated as -11.2 ± 1.9 kJ mol * with 95 % confidence

for the SPE of diuron from water using equation 5.20 (b) in Chapter 5 and the slope

given in equation 8.1. 9.6 9.55 - 9.45 - 9.4 - 9.35 - 9.25 4---

3.35E-03 3.40E-03 3.45E-03 3.50E-03 3.55E-03 3.60E-03

m ( K )

Figure 8.2 A van’t Hoff plot for the SPE of diuron from water

The standard error in the slope is used to calculate the error in AH®.^ The negative

value of the sorption enthalpy indicates that the uptake of diuron from water onto the

Cl8 disk is an exothermic process. According to Le Chatelier’s principles an

exothermic reaction favours the reactants with increasing temperature which explains

why the equilibrium constants given in Table 8.1 decrease with increasing

temperature. This relationship can be interpreted as a decrease in the disk’s capacity

for diuron as the experimental temperature increases. The value of log Keq at 15 and

25°C have been calculated from the linear expression (equation 8.1) given by the

van’t Hoff plot shown in Figure 8.2 and are given in Table 8.1 as those in parenthesis.

In Keq = (1346 ±233) + (4.75 ± 0.81) (8.1)

T

The calculated standard Gibbs free energy of sorption (equation 5.8), AG®, and the

standard entropy of sorption (equation 5.6), AS®, corresponding to Keq at 11®C are

also given in Table 8.1. The error in AG® is assumed to be zero therefore the error in

AS® is given as the error in AH® over temperature (T = 11®C).^

The thermodynamic parameters for the SPE of diuron from water using a Cig

disk have never been published before which makes a direct comparison with existing

data impossible. It has been found that the SPME of 60 volatile organic compounds

(VOCs) from drinking water with a polydimethylsiloxane (PDMS) fibre is an

exothermic process with values for -AH® ranging from 2 to 27 kJ mol ^'* This is also

true for the partitioning of chlorobenzenes between water and octanol.^ Values for -

AH® for a set of seven chlorobenzenes range from 17 to 24 kJ mol"\ The numerical

reported in this work are consistent with other reported values even though they are

for different systems.

The standard enthalpy of sorption, standard free energy of sorption and the

standard entropy of sorption for fourteen other pollutants that were studied with the

UV spectroscopy method are given in Table 8.2. The van’t Hoff plot method could

not be used in the determination of AH° for the fourteen other pollutants because Keq

is only available at two different temperatures. However, Equation 5.20 (b) can be

integrated between two temperatures Ti(23°C) and T2(l 1°C), at which the equilibrium

constant has the values Keq(23) and Keq(n) respectively, to give equation 8.2:^’^

dlnKv, = -AH^ (b) (5.20)

d(l/T) R

In Keann = iM P (I/T2 - 1/T,) (8.2)

K eq(23) R

Equation 8.2 was used to calculate AH° for the pollutants listed in Table 8.2 apart

from diuron. The value quoted for diuron is obtained from the van’t Hoff plot in

Figure 8.2. AG° and AS° are calculated at 11°C for all fifteen pollutants. 11®C is taken

as the temperature for the calculation of values given in Table 8.2 since a measured

value of Keq exists at this temperature. The errors in AH° and AS° for the 14

compounds hsted in Table 8.2 are given as twice the error in AH° and AS° for diuron;

ÔAH® = 1.9 kJ m ol'\ 5AS° = 6.8 JK"^mof\ The error in AG° is assumed to be zero.

The value for the standard free energy o f sorption is negative for all the pollutants

investigated in this way which means the thermodynamic partitioning in the water-Cig

disk system is spontaneous for the fifteen pollutants in Table 8.2.

Table 8.2 Some thermodynamic constants for the partitioning of pollutants between

water and the Cig disk

Pollutant K eq(23) Keq(ll) AH°* AG®** AS°"

Benzonitrile 473.0 509.9 -4 ± 4 -15 36 ±14 2,6-Dimethylpyridine 1174.9 1191.6 -1 ± 4 -17 56 ±14 Benzyl alcohol 234.8 250.4 -4 ± 4 -13 33 ±14 4-Chloroaniline 960.9 1255.1 -1 6 ± 4 -17 5 ±14 Naphthalene 5590.1 6760.8 -11 ± 4 -21 34 ±14 4-Chlorophenol 834.1 1172.4 -20 ± 4 -17 -11 ±14 3-Nitrotoulene 3374.2 3717.8 - 6 ± 4 -19 48 ±14 4-Chloro-3-methylphenol 2523.6 3703.5 -22 ± 4 -19 -10±14 8-Hydroxyquinoline 3623.1 4991.7 -1 9 ± 4 -20 5 ±14 Ethyl paraben 4590.7 6707.1 -22 ± 4 -21 -5 ±14 Dimethyl phthalate 3177.7 3813.4 -11 ± 4 -19 31 ±14 Mecoprop 4733.2 5330.2 -7 ± 4 -20 47 ±14 Atrazine 15660.2 23738.5 -24 ± 4 -24 -2 ± 14 Diethyl phthalate 26457.2 38192.8 -21 ± 4 -25 12 ± 14 Diuron 1__ _ r »____ 10728.3 13598.9 - 1 1 ± 2 ‘* T . t - k -23 4 0 ± 7

^ Standard free energy of sorption at 11°C (kJ mol'*) ® Standard entropy of sorption at 11°C (JK'^ mol'*)

Standard enthalpy o f sorption determined from van’t Hoff equation 8.1 (kJ mol'^)

Several conclusions can be drawn from inspection of the data presented in Table 8.1

and 8.2. Firstly, the errors in the quoted values for the standard enthalpy o f sorption

temperatures. However, an assumption is usually made that AH° is constant over a

temperature range, but this is not always the case. If the heat capacity (Cp°) of a

system changes throughout a reaction, then AH° will change too which could account

for a small fraction of the error in AH° obtained by this work, if Cp° # 0.^'^ Although

the temperature range in this work is relatively small and this itself could explain why

the errors are slightly on the high side. Evidently, the method of collecting Keq values

at only two different temperatures, as is the case for the compounds in Table 8.1,

should not be used when a highly accurate value of AH° is required. The fact that the

error in AH® for diuron is much lower indicates that collecting Keq for at least four

different temperatures brings about a more accurate calculation o f AH®.

8.1.2 Stirring rate effects on Keq

Given in Table 8.3 are five values of log Keq all measured at 23®C but with

varying stirring rates. It is evident that log Keq does not vary significantly with stirring

rate. The mean value of all five log Keq values at 23®C is 4.03 with a standard

deviation of 0.02 log units. It is therefore acceptable to say that with such a low

standard deviation, the effects of stirring rate on the equilibrium constant are

negligible over the range 100 - 400 rpm. At other temperatures similar standard

deviations for the mean log Keq values are observed so the same negligible stirring

rate effect can be assumed for the temperature range studied in this work.

Table 8.3 Log Keq for diuron at varying stirring rates

Stirring rate (rpm) log Keq (23°C)

100 4.00

200 4.05

200 4.03

200 4.05

400 4.03

8.1.3 Temperature effects on kup

It should be noted here that values of kup determined in this work are only

r-

^ relevant for the water-Cig disk system and it’s dimensions defined in this work. Never

the less, the principles involved in the investigation of temperature and stirring rate

dependence of kinetic constants still apply. Given in Table 8.1 are the logarithms of

the uptake rate constant (log kup) when the temperature is 7, 11, 18 and 23 °C and

when the stirring rate is 100 and 200 rpm, along with the corresponding standard

-10.0 - 1 0 .5 - §■ .zz c -12.0 -1 3 .0 3 .3 5 E -0 3 3 .4 0 E -0 3 3 .4 5 E - 0 3 3 .5 0 E - 0 3 3 .5 5 E - 0 3 3 .6 0 E -0 3 1 /T ( K )

Figure 8.3 Arrhenius plots of In kup versus reciprocal temperature at 100 (•),

200 (♦) and 400 (A) rpm

The individual log kup values used to determine the mean values in Table 8.1 are

presented in Table 8.4 along with those when the stirring rate is 400 rpm at varying

temperatures. The effects of temperature on log kup can be investigated by the use of

an Arrhenius plot. When In kup is plotted against the reciprocal temperature at 100,

200 and 400 rpm, a linear relationship between In kup and T’* exists when the stirring

rate is 100, 200 and 400 rpm with correlation coefficients of 0.98, 0.95 and 0.91

respectively, this is depicted in Figure 8.3. The linear expressions for In kup versus T ’

given as:

In kup = t-7556 ± 694) + (14.31 ± 2.39) (8.3)

100 rpm, r^ = 0.98

In kup = r-4557±406) + (4.60 ± 1.41) (8.4) T 200 rpm, = 0.95 lnkup= r-5231 ± 16931 + (6.91 ± 5.78) (8.5) T 400 rpm, r^ = 0.91

have been used to calculate kup at 15 and 25°C for 100 and 200 rpm, these values are

given in parenthesis in Table 8.1. From equations 8.3, 8.4 and 8.5, it is possible to

calculate the activation energy, Ea, for the rate of uptake since the gradient o f the

slope = -Ea/R, where R is the gas constant (JK'* mof*).^’^ The Arrhenius plots for In

kup at 200 and 400 rpm are almost indistinguishable from each other, the reason for

this is discussed later but for now we can combine the values of In kup at 200 and 400

rpm over the temperature range to give a new equation:

In kup = (-4631 ± 325J + (4.85 ± 1.13) (8.6)

T

200+400 rpm, r^ = 0.96

Table 8.4 Log kup for diuron at varying stirring rates and temperatures

Stirring rate (rpm) log kup (s'*) Temperature (°C)

100 -4.89 23.0

-5.03 18.0

-5.04 18.0

Stirring rate (rpm) log kup (s‘‘) Temperature (°C) 200 -4.71 23.0 -4.66 23.0 -4.84 18.0 -4.80 18.0 -4.92 11.0 -4.96 11.0 -5.05 7.0 -5.12 7.0 400 -4.67 23.0 -4.82 18.0 -4.77 18.0

The activation energies, when the stirring rate is 100 rpm (equation 8.3) and 200 or

greater rpm (equation 8.6) are 62.8 ± 5.7 and 38.5 ± 2.7 kJ respectively. These

activation energies were then used to calculate the standard enthalpy of activation

(equation 5.23), AH^ standard Gibbs free energy of activation (equation 5.22), AG^

and the standard entropy of activation (equation 5.24), AS^; all are given in Table 8.1.

The standard error in the slope used to calculated Eg is used to obtain errors for AH^

and AS^ the error in AG^ is assumed to be zero.

The two positive values for the standard enthalpy of activation, 60.5 ± 5.7 and

36.1 ± 2.7 kJ m ol'\ for kup at 100 rpm and 200 or greater rpm respectively, indicate

that the kinetic process involved in the SPE of diuron from water is endothermie.

Consequently[^%hq^ the temperature of system increases so does the rate of uptake,

which is reflected in the values given in Table 8.1, A similar relationship was found

by Nilsson et al with the same 60 VOCs partitioning from water onto a SPME fibre

mentioned previously.Heating the sample solution from 20 to 80°C brought about

shorter equilibration times. Again, this data is for a different system but comparisons

can be made to the system in this work to confirm that findings in this investigation

are reasonable.

8.1.4 Stirring rate effects on kup

The rate of uptake is effected by the stirring rate as can be seen in by the

Arrhenius plot given in Figure 8.3. When the stirring rate is 100 rpm compared to 200

rpm at the same temperature, log kup is lower, i.e. the rate of uptake is slower when

the rate of stirring is slower. Leahy shows this to be the case in four different water-

solvent partition systems. He reports that for a given compound at constant

temperature, the rate of permeability from water into chloroform, isoctane, propylene

glycol dipelargonate (PGDP) or octanol, increases with increasing stirring speed.

Interestingly for the water-Cig disk system, when the stirring rate is increased to 400

rpm, log kup is the same as that for 200 rpm at the same temperature. This would

indicate that at 100 rpm the diffusion of diuron through the boundary layer is acting as

a limiting factor. As the stirring rate is increased to 200 rpm or greater the aqueous

diffusion layer around the disk is sufficiently reduced to prevent diffusion from being

a limiting factor in the extraction process. Vaes et al found this to be case for the

SPME of organic compounds from water.* He concluded that as the stirring rate is

increased, the diffusion layer around the fibre is sufficiently reduced so diffusion

uptake rate constant, determined at 200 rpm for a set of 21 pollutants, is almost

independent of the equilibrium constant and that diffusion across the static boundary

layer between the water and Cig disk is the governing factor. Putting it another way, at

200 rpm there is still a significant static layer of water molecules at the water-disk

/ interface to ^ e c t the rate of uptake despite the equilibrium constant increasing.

Diffusion controlled rates are reported by Waterbeemd et aÛ and Leahy et al^ in the

case of water-solvent partitioning rates and coefficients for a set of diverse

compounds and collaborate the findings in Chapter 7. So when the stirring rate is

increased from 200 rpm to 400 rpm and the rate constant does not change (this can be

seen in Figure 8.3), it appears that a diffusion layer still exists when the stirring speed

is 400 rpm. To completely eliminate the diffusion layer so that the rate of uptake into

the disk is independent of diffusion, as was first thought from the results obtained in

this chapter, one would require a stirring rate much faster than those employed in this

work.

In document An experimental and modelling investigation into the solid-phase extraction of pollutants from water (Page 158-172)