@@ KINETICS OF PHOTOREDUCTION OF FERRI-OXALAT E- DEACTIVATION AND INNER FILTER CAUSED BYAMMONIUMMOLYBDATE* -

Tadashi SHIROTSUKA and Hideo NISHIUMI

Department of Applied Chemistry, Waseda University,Tokyo, Japan

The kinetics of photoreduction of potassium ferrioxalate in the presence of ammoni-ummolybdate was studied at 365 6m//. Measurementswere madein a batchwise andparallel-beam reactor operated at atmospheric pressure and at room temperature.The concentrations of potassium ferrioxalate and ammoniummolybdate were changedfrom 6.17X10 8 to 3.45xlO"6 and from 2.94xlO"8 to 5.07X10"8 mol/cm3, respective-ly. The decrease in the reaction rate can be explained by the mechanism in which addi-tion of ammoniummolybdate causes both deactivation and inner filter.

The ratio of the rate constant of deactivation, ko, to that of the forward reaction, k±9was 12.5 at 365/6m//.The effect of the inner filter accompanied by addition of a substance on conversion isnegligible when the optical thickness of all absorbing substances, r(c+//*), is verymuch smaller than 1.

Undesirable wavelengths causing useless photo-chemical side reactions or opaque tar from poly-chromatic light of a light source can be isolated byseveral methods: filter solution7), filter glass8), or a

fluorescent substance mixed in cooling water6). Butthese are not the best industrial methods, because theyreduce not only undesirable radiation, but also a sig-nificant amount of effective radiation for a photo-chemical reaction.We are interested in a new method which reduces

undesirable radiation by adding a substance causingdeactivation or inner filter to a photochemical re-actant solution. As the first step to start the research wechose the photoreduction of potassium ferrioxalate tostudy the general characteristics of deactivation andinner filter.

It is well knownthat the rate of the photoreductionof potassium ferrioxalate in 0.1-N sulfuric acid is pro-portional to the absorption rate of radiation by thereactant, and that its quantum efficiencies of ferrousion formation are independent of the concentrations ofthe reactant over a wide range of concentration1'^.On the other hand, our experimental results showed

that the addition of ammoniummolybdate caused adecrease in the quantum efficiencies, which were en-tirely dependent on the concentrations of both am-moniummolybdate and the reactant.The objectives of this paper are to present data onthe photoreduction of potassium ferrioxalate in thepresence ofammoniummolybdateand to obtain a rateequation based on reaction mechanismin order toinvestigate the general characteristics of deactivation

and inner filter.Measurementswere madein a batchwise and

parallel-beam reactor operated at atmospheric pressureand at room temperature at 365/6 rn.fi. The concen-trations of potassium ferrioxalate and ammoniummolybdate were changed from 6.17x lO"8 to 3.45X10~6 and from 2.94xlO~8 to 5.07xl0"6 mol/crn*,

respectively. The analysis showed that the decrease inreaction rate by addition of a substance was attri-buted to both deactivation and inner filter.

Deactivation and Inner Filter

The mechanismfor the ferrioxalate decompositionin the absence of any added substance has not beenclarified4), but it is known that the ferric ion is re-

duced stoichiometrically to ferrous ion according to theoverall equation

Received on March 6, 1972Presented at the 36th Annual Meeting of the Soc. of Chem.

Engrs., Japan, April 2, 1971.

T980 {ii]-&ffjnfiiLiMiSc39-i nut

@@ 178 @@ JOURNALOF CHEMICALENGINEERING OFJAPAN

@@ 2K3[Fe(C,O4)3] ->2Fe(C2O4) + 3KaC2O4 + 2GO2

As stated above, the quantum efficiencies of ferrousion formation by the photoreduction in the absence ofammoniummolybdate are not only independent of theconcentrations of the reactant but are also overunity1'3). On the other hand, its quantum efficienciesin the presence of ammoniummolybdate depend onthe concentrations of both the added substance and thereactant.

Wepropose the following mechanismconsistent withthe experimental data for the decomposition of po-tassium ferrioxalate in the presence of ammoniummolybdate, although not as a complete description ofthe reaction.

@@ A -

A*+A

A*+B-%A*

i%A+B* (1)(2)(3)

where A, A*, B, B*, and C are the ferric reactant, theexcited ferric ion, the added substance, the excited

added substance, and the ferrous product, respectively.Eqs.(l), (2), and (3) represent excitation of the re-

actant A, reaction of one excited ion with one reactantmolecule to give two molecules of the ferrous product,and deactivation of an excited ion by one molecule ofthe added substance, respectively. k± and k2 are rate

constants for the corresponding reactions.The rate equations for components A, A*, and C areas follows :

@@d[A]_dt= - $Q.a - kx[A*].[A] + k,[A*].[B\

d[A*] _~dt

d[C] _dt(4)*Q.A -ki[4*Wl -W-[B\ (5)2k1 lA*].[A\ (6)

where [A], [A*], [B~\9 and [C] are concentrations of

respective components. 0 is the primary quantum ef-ficiency in Eq.(l). QArepresents the absorption rateof radiation energy by the reactant A.Assuminga stationary state concentration for A*andputting Eq.(5) =0, we have

@@ [A*]k,[A] + kt[B](7)

Substitution ofEq.(7) into Eqs.(4) and (6) gives

@@d[C]_dtd[A]kt[A]kx[A\ + k2[B]

å Qa (8)

where 0O=20. By putting [B]=0 in Eq.(8), we

obtain the quantum efficiency in the absence of anadded substance, 0O, whose value is 1.21 mol/ein at

365/6 m/i1'^. The effect of deactivation by the addedspecies on the reaction rate is represented in Eq.(8).A suitable expression for the material balance involvingthe inner filter caused by the added substance as well asdeactivation is developed below.

@@ Io C*Då  Tl

à"

@@/: Path length, S: Incident cross-section areaV: Volumeof the reaction mixture

Iq : Incident intensity of a parallel beam of radiation@@Fig.1 Coordinate system and geometry

Consider a completely mixed and batchwise photo-chemical cell with flat paralle windows transparent tothe wavelength regions concerned. This situation is

depicted in Fig. 1, where /, S, and Vdenote the pathlength, the incident cross section area, and the volumeof the reaction mixture, respectively. A parallel beamof radiation of incident intensity 70 propagates normalto the plane of the windows. It is necessary to empha-size the absorption coefficient as a function of concen-tration because of the change in concentration througha reaction. In the present paper we call it an ab-sorption function ^ of an absorbing species i. AssumingBeer's law for components A and B, we have

@@ ftA = SA-l-A]

(IB = SB-[B](9)(10)

where ^A and pB represent absorption functions of thecomponents Aand B, respectively. eA and sB are theirrespective molar absorption coefficients. The ab-

sorption rate of radiation energy of the reactant Ainthe irradiated part of the cell is given by5)

@@dA=VA

P-A + f*Bà"[1 - exp (- {pA + /tB).l)]

(ll)where it has been assumed that the absorption of radi-ation energy by a mixture is additive.

Substituting Eq.(ll) into Eq.(8), and taking into

account the effect of the shaded part on the reactioncell, we find

@@ dt dt V 9o' k^A] + k2[B]

X ^ [1-exp(-(^+^)/)]

(12)[^]=[A]a, [C]=0, when ^=0

where [A], [B] and [C] are their respective concen-

trations to be measured. The effects of both inner filterand deactivation by the added substance are involvedin this equation.

Experimental

A lamp, a housing, a filter system and a reactor wereplaced in line. The ultraviolet light source was a Ushio

@@VOL6 NO.2 1973 @@ 179

@@fy"in:: ( C® ) )1. Reactantsolution 2. Window 3. Stirrer

4. Incident light 5. Irradiated section@@Fig. 2 Schematic diagram of reaction chamber

USH-500Dhigh-pressure mercury 500w point-sourced-c lamp. The parallel beam housing for the lamp wasof type Ushio UI-501C. The filter system composedof a Corning glass color filter CS7-51 and a 1-inchquartz filter cell containing 0.2M nickel sulfate aque-ous solution was used to isolate a 365/6 m^ beam fromthe spectrum of the lamp.The schematic diagram of the reaction chamber is

shownin Fig. 2. The reactor tube was madeofacrylicplastic, 25 mm.i.d., 94 mm.o.d. with optical path

lengths of 1 and 5 cm. The reactor windowswere madeof quartz. The stirrer was driven at moderate speed byan electric mixer so as to achieve good mixing.

Experiments were made in a dark room. The ferrio-xalate solutions with ammoniummolybdate in 0. 1-Nsulfuric acid were irradiated at 365/6 m^ on an opticalbench with periodic mixing during the photolysis.

The concentrations of the ferrous ion produced bythe ultraviolet light ^?er§ measured with a spectro-

photometer in a complex compoundwith 1,10-phenanthroline, which was added to the solution after

irradiation. But we found that 1,10-phenanthroline

gave not only a complex compoundwith ferrous ion,but also precipitates with ammoniummolybdate,which made quantitative analysis impossible. In orderto eliminate molybdic ion an excess of lead acetate wasadded to the irradiated solution and we obtained theprecipitates of both lead molybdate and lead sulfate.

The further addition of 1,10-phenanthroline gave anorange color with ferric ion only. When the samplestabulated in Table 1 were centrifuged, the precipitateswere collected in the bottom of the centrifuge tube.

The concentrations of the ferrous iron in the clearliquids were measured in a spectrophotometer at

5 10 m^. The concentrations of the total iron in the clearliquids were determined by a similar method after re-duction, noted in Table 2. Conversion was given as theconcentration ratio of the ferrous iron to the total ironin one sample.

Results and Discussion

Evaluation of rate constant ratio

@@Table 1 Comparison of centrifuged sample@@ Components Volume [cm3]

Sample a0.1-N sulfuric acid 5.00-a0.8-N lead acetate 1.500.1 % 1, 10-phenanthroline* 1,00Buffer solution* * others

Total 10.00

* Added after precipitants by lead acetate formed.** Mixed a 100m/ of cone sulfuric acid with a 822g of sodium

acetate and diluted to 10/

@@Table 2 Determination of total iron concentration@@ Components Volume[cm3]

clear liquid ft0. 1 %-phenanthroline 1.001 % -hydroquinone 1.00pure water others

Total 10.00

It is convenient to use the following variables toobtain the rate constant ratio k^\kx from the experi-

mental data :

@@y V.(d[C]ldt) pA+pB L J(13)

Y=y-±- (14)00

Furthermore,@@ (15)

which is proportional to [B~\j[A\ in accordance withBeer's law. And Kis defined as

@@ jy-1 k^A

(16)

where eA and eB represent respective molar ab-

sorption coefficients. With these variables Eq. (12) canbe rearranged to give the equation

@@r=k-x(17)

If the kinetics model explains the experimental data,a plot of Yversus x will give a straight line through theorigin.

Conversions were so low that concentration did notchange significantly. This allowed the reaction rate tobe given by the simple formula

@@d[C]/dt = J[C]/Jt

where z/[C] is the concentration of ferrous iron formedand At is irradiated time. The values of Y and x9 respec-tively, calculated from the experimental results usingEqs.(14) and (15) are given in Table 3. The rate ofincident radiation energy S-Io was measured with anac-tionometer using the reaction in this paper at highconcentration of ferric iron. The ultraviolet spectrawere recorded efte a Shimadzuspectrophotometer, typeUV200, and the absorption functions of potassiumferrioxalate and ammoniummolybdate at 365/6 m^were found to obey Beer's law:

@@ fiA= 1.45 X W.[A]HB= 1.70 x 105.[£]

(18)(19)

@@180 @@ JOURNALOF CHEMICAL ENGINEERING OFJAPAN

@@Table 3 Experimental results for evaluation of rate constant

@@Run / V S-IoXlO* fxB pa ~^~X1012 x yNo* [cm] [cm3] [ein/sec] [cm"!] [cm"!] [cml/sec.cm3] [-] [ein/mol]

1 1.13 5.00 2.81 0.860 0.860 7.20 1.00 32.72 2.81 0.335 0.730 14.8 0.458 17.3

5 2.06 0.0100 0.190 28.0 0.0528 1.986 2.06 0.0100 0.470 100.0 0.0213 0.867 2.06 0.00500 0.190 38.0 0.0263 1.268 2.06 0.00500 0.470 66.0 0.0106 1.749 2.06 0.0100 0.470 64.0 0.02 1 3 1.8010 2.06 0.00670 0.470 62.0 0.0142 1.90

1 1 2.06 0.00500 5.58 40.8 0.000895 0. 1 712 2.06 0.0100 1.86 26.0 0.00538 0.56

13 2.06 0.0100 0.93 12.3 0.0108 0.8114 2.06 0.00500 1.86 32.2 0.00269 0.29

29 5.00 25.0 2.22 0.800 0. 100 0.0283 8.00 34531 2.22 0.800 0.800 0.607 1.00 72.532 2.22 0.800 1.50 1.10 0.532 52.033 2.22 0.800 3.00 2.58 0.267 25.430 2.22 0.800 5.00 4.00 0.160 18.3

@@where sa =.1.45 X 106 cm3/mol, sb = 1.70 X 105 cm^/mol, ^50 = 1.21 mol/einat365m^3)

@@ E

I.0

OQtf O/ O

, -2 .rt-1

10'3 10 10 1 10

x (")

@@ Fig. 3 Effect of deactivation caused byammoniummolybdate

@

@ 8\ Eq.(22)/_ \ ^^T^-^.\\ -l\

\ / \Eqs.(22) \\ W(2«>\ Eq.(23) \ &(23) \ ]\? \/

? 6 \ >v \Eqs.(22>> L^ \ ^V V8,(23) \

2- \Eq.(24).à" Eq.(24) - ^(24\^ V "

(a) X. (b) (c) (d)\o I-<-'-å  >-»"-'-'-'-'-'---J*-'-'-'-'-M-'-I-:J

0 3 0 3 6 0 3 0 3

e (-)

(a) (b) (c) (d)7] 9.53 0.256 0.136 0.000

t 0.97 0.21 1 0.527 1.87

@@Fig. 4 Comparison of experimental with calculatedvalues

@@Fig. 3 shows a plot of Y versus x on logarithmicpaper. The experimental data fit a linear relationship,and the slope of the straight line is unity. Hence a plotof Y versus x on ordinary paper gives a straight linethrough the origin. From the intercept ofy at x=l inFig. 3 the value ofKcan be obtained;

@@K=88.0 ein/molEq.(16) can be rewritten as

@@ (20)

Substituting numerical values for the quantities K>0O, sB, and eA mto Eq.(20), we have

@@ *1=12.5 (21)

Comparison of deactivation with inner filterOn the assumption that absorption functions obey

Beer's law, use of dimensionless parameters@@ C :=

[A] __ t.<po.(S-Io) = jA, 4IS]

rj=Mo

@@p*=M. PA_ eB

£a = e-rj.MoA=

allows Eq.(12), taking into account inner filter as wellas deactivation, to be written as

@@dc_W111 +hrjfc 1 +e-rjfc

X [1 -exp(- t-(c+£.97))](22)

Eq.(22) shows that the relation between ~c and 0 can beclarified with parameters e, k, rj, and r.

Putting £=0 in Eq.(22), we obtainW=-T+W'[1"eXP(~r")] (23)

which represents the effect of deactivation only.Furthermore, setting yj=O in Eq.(22) in the ab-

sence of any added substance, we get@@dc

=- [1 -exp(-T--c)](24)

The relation between c and d calculated from the

experimental data are shown in Table 4. Both thesolutions of Eq.(22) through Eq.(24)* and the corre-sponding experimental values are shown in Fig. 4. It isclearly seen that the inner filter by ammoniummolyb-date has little effect on the rate of photoreduction offerric oxalate under the experimental conditions, be-These equation were solved by the Runge-Kutta method.

@@ VOL6 NO.2 1973 @@ 181

@@Table 4 Experimental results for c vs. 0 curves*@@RunNo.M»x107[nlol/m/][B]X107

[mol/m/]^=[fl/Mo r[-] [-]

105.32

1.15

2.8 50.7

0.294

0.3929.53

0.256

0.1360.97

0.211

0.5272.303.84

0.5870.7820.9781.965.87

0.360

0.4320.5034.320.980

0.951

0.9570.9110.9000.8920.867

0.9280.9080.869

0.646

10.20.000 0.0001.87 0.707

1.460.5020.143

e=(U'17 for Eq.(22) and s=0 for Eq.(23); £=12.5

@@ (a) ' /' (b) ' ' """

2.0" /o © /Eq.(25) /\ Eq.(25) / o

0.5 X ^ X CB""°

V^ CA=0 v^0K . 1 »- JIZ- 1 1 1 l_

0 50 100 0 5 10CB (ppm) Ca^107 (mol/cm3)

@@Fig. 5 Comparison of experimental and calculatedvalues of absorption functions

@@ fl^s^ Eq.( 27)

? 6 1*U ^N. ^=0.05 ^^

0 3 6 9 12

e (-)

Fig. 6 Effect of optical thickness on inner filtercause the close agreement between the solutions of

Eq.(22) and those of Eq.(23) is recognized. Therefore,the differences in the solutions are attributed to de-

activation. The values of 37, which are related to themagnitude of deactivation, decrease from Fig. 4(a) to

Fig. 4(d) in turn. Comparison between these figuresshows that the deactivation has a large effect on con-

versions for the reaction system. On the other hand,the calculated values from Eq.(22) agree well with theobserved values represented by open circles in Fig. 4within a maximumerror of0.05 in conversion.Absorption of radiation by a mixtureFig. 5 shows the absorption functions of potassium

ferrioxalate A, ammoniummolybdate B, and theirmixtures in 0.1N sulfuric acid recorded on a Shimadzuspectrophotometer, type UV200, at 365/6 m^. ptA andfiB, which are represented by solid lines, are found toobey Beer's law as expressed in Eq.(18) and Eq.(19),

respectively.

Assuming that the absorption of radiation is additive,we have

Pa+b = ffA + Pb (25)where [iA+B is an absorption function of a mixturecomposed of A and B whose respective absorptionfunctions are jua and ^tB. Open circles in Fig. 5(a)

indicate observed values for a mixture in which theconcentrations of B are varied when [A]=5.00X

10~7 mol/cm3, and in Fig. 5(b) the concentrations ofA are changed when [2?]=50.0 ppm. In this case, theobserved values of mixtures agreed approximately with

the theoretical values represented by the dotted lines inFig. 5. Generally speaking, it is necessary to testwhether an absorption function ofa mixture is additiveornot.

If the absorption of radiation by a mixture is ad-ditive, the ratio of radiation energy absorbed by a

component A to that by a mixture is given by@@ t*A

Pa -r f*B(26)

Effect of Inner Filter

Setting k=0 in Eq.(22)? and considering ju^=S'7j, wehave

@@ dc__ 1

I.C. 0=0,[l-e .-r(C+^)l(27)c=1

This is the equation in the presence of inner filter only.Eq.(24) in the absence of inner filter can be solvedanalytically as follows :

@@ 182 @@ JOURNALOF CHEMICALENGINEERING OFJAPAN

@@e=-ln[l + (f- !).«-'à"«] (28)

From Eq.(28) c approaches 1 -0 when T becomes infi-nite.

Fig. 6 shows the comparison of the calculated valuesin the absence of inner filter [Eq.(28) or (24)] with

those in Eq.(27) when /*#=1. From Fig. 6 the innerfilter by an added substance can be seen to be neglectedwithin a maximumerror of 0.05 conversion whenr^0.2. In our previous paper5) we have mathemati-cally proved that the solution of Eq.(24) is identicalwith that ofEq.(27) when rf+^X1*

The calculated results indicating that addition of anabsorbing species little affects the rate of the photo-

chemical reaction seem strange. The reason lies in twoopposing effects compensating each other; one is thedecrease in available radiation energy of A by ab-sorption ofB and the other is the increase in the totalradiation energy absorbed by a mixture. The calcu-lated results indicate that the effect of the former is ofthe same degree as that of the latter.Similar results can be obtained not only in the caseofk=0 as stated above, but also in the case of othervalues of A:. Therefore, the reason for the small effectsof inner filter in Fig. 4 lies in the small values of

Recently, newtransparent paints utilizing photo-polymerization have been used for coating wood2).

Consider the photopolymerization paint consisting ofalkyd resin and a,a'-azobisisobutyronitrile for initiator.The molar absorption coefficient of the initiator at365 m^, eA9 is 23.0//moLcm. Supposing the concen-

tration of the initiator and the film thickness in the wetpaint are 0. 1 mol//, 50^, respectively, the optical thick-ness of the initiator T=(23.0)(0.1)(50x 10"4)=0.0115.Then, even if the absorption function of impurities, ad-ditives or alkyd resin is 10 times as big as that of theinitiator, r(c+fi+)^(0.0115)(1+10)=0.127, which

is much less than 1.0. So, according to our discussion,wecan foretell that absorption by substances otherthan the initiator have little effect on the photopoly-merization reaction rate.

Conclusions

The kinetics of photoreduction of potassium ferri-oxalate in the presence of ammoniummolybdate wasstudied in batch reactors. The decrease in the reactionrate can be explained bv the mechanismin which

addition of ammoniummolybdate causes both deacti-vation and inner filter.

The ratio of the rate constant of deactivation k2 tothat of the forward reaction k± was 12.5 at 365/6 m^.

The effect of the inner filter accompanied by ad-dition ofa substance on conversion is negligible whenthe optical thickness of the absorbing reactant,

r(£+/**) is much smaller than 1.

@@Nomenclature= M/Mo [-]

= incident intensity of radiation [ein/cm2 -sec]= rate constant represented in Eq.(2) [cm3/sec-mol]= rate constant represented in Eq.(3) [cm3/sec-mol]

= *2/*l [-]= value defind in Eq.(16) [ein/mol]

= path length [cm]= absorption rate of radiation energy [ein/cm3 -sec]= incident cross-section area [cm2]= irradiated time [sec]

= volume of the reaction mixture [cm3]= value denned in Eq.(15) [-]

y = value denned in Eq.(13) [ein/mol]Y = value denned in Eq.(17) [ein/mol]sa - molar absorption coefficient of a reactant A

[cm2 /mol]sb = molar absorption coefficient of an added

species B [cm2/mol]£ = Sb/sA [-]v = [B]I[A]O [-]o __ t<f>o(Sio) T_1

~~mar L Jfj.A - absorption function of a reactant A [cm"1]p.B = absorption function of an added species B [cm"1]J"* = PBlftAO [-]T = fiAO'h optical thickness [-]<p = primary quantum efficiency [mol/ein](j)Q = 2<f>, overall quantum efficiency in the

absence of an added species [mol/ein]< Subscripts>

= reactant

= excited ion of reactant A= added species= product= initial value= concentration

Literature Cited1) Hatchard, G. G. and C. A. Parker: Proc. Roy. Soc. (London),

A235, 518 (1956)2) Murata, K. : Shyokuzai-Kyokai-shi, 44, 70 (1971)

3) Parker, C. A.: Proc. Roy. Sue.,(i«Qpdon), A220, 104 (1953)4) Parker, G.A. and C. G. Hatchard: /. Phys. Chem., 63, 22 (1959)5) Shirotsuka, T. and H. Nishiumi: Bull. Sci. Eng. Res. Lab.,

Waseda Univ. 54, 43 (1972)6) Tokkyo Koho, Showa 39-103367) Tokkyo Koho, Showa 39-179178) Tokkyo Koho, Showa 39-22959

@@VOL6 NO.2 1973 @@ 183