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Exact determination of chemical reaction rate constants by mass spectrometric probing the diffusion cloud in flow
123
International Journal of Mass Spectromeby and Ion Physics, 46 (1983) 123-126 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
EXACT
DFTERMINATION OF CHEMICAL REACTION RATE CONSTANTS SPECTROFc0?TRICPROBING THE DIFFUSION CLOUD Ihi FLOW
I3Y MASS
V.L,TALHOSE, A.F,DODONOV, Y,V.ZELENOV and V,P,STRUNIN Institute of Chemical Physics, Academy of Sciences of the USSR, 777334 l’/Ioscow (USSR)
ABSTRACT The improvements in measurisg and calculating technique of m&s8 spectrometric probing the diffusion cloud in flow are described, They make it possible to exclude systematic error8 arising due to the influence of the carrier gas flow from capillary and its retardation on the capillary outer surface upon the rate fields. The theoretical grounds and experimental application of the improved technique are given. The rate constants of the reactions of atoys and radicals are reported with the qccuracy of higher than -10 % instead of the earlier accepted -30 %, The mass spectrometric probing of the diffusion cloud (MPDCFF), devised earlier (ref.71 (see Fig.11, finds ever greater application nowadays. Before when treating the experimental data, the flow velocity and the concentration of the active particlea were supposed to be constant ower.the all cloud, The present paper describes the improvements in the measuring and calculating technique. It enables ua to exclude systematic errors arising due to the effect of capillary 2 and sampler 3 on the gas flow velocity as well as due to the inconstancy of the active particles concentration in the reaotion Bone, The relative change in the velocity by the capillary is (ref.2): (1)
where Q. P g& flow through the capillary; $ 0: kiqematic viscosity; ri and r, P inner and outer radii of the capillary; 1 = the capillary tip length; V = the flow velocity in the absence of the capillary; x,r = point references in the reactor (Fig.1). The distortion of the velosities profile by the capillary will be minimal wpen the flow through the capillary equals to l Kr oi r V (2) QE = 1.04 -VI&
l l
0020-736l/63/000~000/$03.00
0
0
1983 Elsevier Scientific Publishing Company
124
A+Ee
to
ion
source
B+He -
Fig. mary
1. Reactor with free radicals),
Fig.2 reaction
shows zone
the diffusion
B = molecules,
the distribution near
the inlet
cloud in flow. A q atoms Fe - carrier gas
of the gas flow
velocity
(prf-
in the
cone,
obtained by experimental Curves O-6 represent the distribution of the modelling technique. relative velocity of gas flow along the reactor redius, 0,7,2,3,4, 5,6
mm from the inlet cone tip measured at Reynolds number of 6.5, The distribution of the relative flow velocity along the reactor
Ax(x)
2. The distribution of the gas flow velocfty Fig, cone ‘* Fig. 3. On the contact time determination,
near
the inlet
125
axis near the inlet hole can be perfectly approximated by the relation: V(x>/f = 2[1 - exp(-ax)] (3) where 7 P a mean flow velocity in the reactor; x = a distance from the inlet cone tip; the factor "an equals to 4.7-+0,25, 4.920,25, 520.25 for Reynolds numbers of 6.5, 11, 22 respectively, That ie the factor 1,aIrdepends but slightly on the flow velocity, From the shape of the curve8 of Mg,2 and equation (3) we can draw two conclusions: 1. near the reactor axis the inlet cone has a zone where the velocJity alightly changes by the radius; 2, by the tip of the inlet cone the flow velocity reaches 90 % of that on the reactor axis already at a distance of 4-5 mm from the tip, The simple approximate expression that desoribee the diatribution of the reagent concentrations in the diffusion cloud may be obtained when the relative change in the flow velocity, the concentration of the ac;tive particles and the conversion depths in the "diffusion length" (1D = D/V) are small, i.e. when the following conditions (ref.41 are observed, v'(x)*lD/v(xM~l, ~A(x)~'.lD/[A(x)~~
(6)
0
where nor n P the concentration distributfon of the molecules delivered into the diffusion cloud in the absence and presence of the reaction; k P the reaction rate constant; WC = the mass flow rate of the molecules through the capillary into the reactor; D= the diffusion coefficient of the molecules. As it is clear from (ref.3) the concentration distribution of the atoms A in the diffusion cloud is set out by the expression: [A(x)] = [A]o.Cl - ,&&
l
exp[&&&x-=)I)
(8)
,
where [Ao]= concentration of atoms at a large distance from the capillary tip. The contact timeC(x) can be most conveniently determined experimentally from the kinetic data tith the help of relation (9) C'(x) =Qx(x)EV whereAx = determined from the dependence, ln(n,/n>=f(xI, as
126
it
is
shown
in Fig.3
for
the reactions
H + X02,
0 + Br2,
P f C2D4.
allows to obtain the quantitative data at the small lengths of the diffusion cloud as well, what of particular significance for the determination of the reaction rate constants of the chemically active particles formed in the reactions of atoms with molecules, The distribution of the intermediate product concentrations along the reactor axis fog the succession of reactions A+B 'P,, A+P., 1 P,, can be obtained by analogy of the derivation of formula (6). in case of equal diffusion coefficients (DB=Dp =D pg ) the following expressions are valid at limitations for th& experimental conditiona: The use
#+
of the
‘[l
= *
"contact
time"
in the MPDCF
- exp((k-kl )*[A],.Ux))]
(10)
(11) the reaction zone we took the average rate in it. For example the following rate constants were obtained (cm3/s), which could include systematic errors of the origin considered in this paper: 0 + "2k !L 0 + CS L
H2(V,
products
k4(298K)=(2.1+0.2).10-"
co +kS
5) + NO 2
k3(298K)=(2.4~0.24).10-12
IIN0 + H
k5(295K)=(2'1).10-"
k6
k6(295K)=(1.2'0.5).10-'" H+HNOH2 + NO Measurings by a more recent method described above result in the following values: k3=(3.3~0.3).10"', k4=(2.1~0.2).10-'I, kgP(l.l-+0.2).10-", k6=~l.3~0.2).10"o, REFERENCES
V.L,Talrose, G,K.Lavrovskaya, A,F.Dodonov, I.I.Morozov, Recent Development in Maas Spectrosoopy, Tokyo, Utiverslty of Tokyo Press, 1970, p.1022. 2 A.F.Dodonov, V,V.Zelenov, V.P,Strunin, V.L.Talrose, Kinetika i kataliz, 1981, t.22, v.4, 888-897 pp. 3 A.P,Dodonov, V,V.Zelenov, G.N,Sargsyan, V.L.Talrose, DAN SSSR, 1980, t.252, No.2, str. 391-394. 4 V.L,Talroae, N.I.Butkovskaya, M.N.Larichev, I.O.Leipunskii, I.I.Morozovi A.P,Dodonov, B.V,Kudrov, V.V.Zelenov, V.V.Raenikov, Advances in Mass Spectrometry, ed. Daly N.D., London, 1978, v.7, 693 p. V.V,Zelenov, V,L,Talrose, DAN SSSR, 1980, t-252, 5. A.F,Dodonov, str.642. 1
International Journal of Mass Spectromeby and Ion Physics, 46 (1983) 123-126 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
EXACT
DFTERMINATION OF CHEMICAL REACTION RATE CONSTANTS SPECTROFc0?TRICPROBING THE DIFFUSION CLOUD Ihi FLOW
I3Y MASS
V.L,TALHOSE, A.F,DODONOV, Y,V.ZELENOV and V,P,STRUNIN Institute of Chemical Physics, Academy of Sciences of the USSR, 777334 l’/Ioscow (USSR)
ABSTRACT The improvements in measurisg and calculating technique of m&s8 spectrometric probing the diffusion cloud in flow are described, They make it possible to exclude systematic error8 arising due to the influence of the carrier gas flow from capillary and its retardation on the capillary outer surface upon the rate fields. The theoretical grounds and experimental application of the improved technique are given. The rate constants of the reactions of atoys and radicals are reported with the qccuracy of higher than -10 % instead of the earlier accepted -30 %, The mass spectrometric probing of the diffusion cloud (MPDCFF), devised earlier (ref.71 (see Fig.11, finds ever greater application nowadays. Before when treating the experimental data, the flow velocity and the concentration of the active particlea were supposed to be constant ower.the all cloud, The present paper describes the improvements in the measuring and calculating technique. It enables ua to exclude systematic errors arising due to the effect of capillary 2 and sampler 3 on the gas flow velocity as well as due to the inconstancy of the active particles concentration in the reaotion Bone, The relative change in the velocity by the capillary is (ref.2): (1)
where Q. P g& flow through the capillary; $ 0: kiqematic viscosity; ri and r, P inner and outer radii of the capillary; 1 = the capillary tip length; V = the flow velocity in the absence of the capillary; x,r = point references in the reactor (Fig.1). The distortion of the velosities profile by the capillary will be minimal wpen the flow through the capillary equals to l Kr oi r V (2) QE = 1.04 -VI&
l l
0020-736l/63/000~000/$03.00
0
0
1983 Elsevier Scientific Publishing Company
124
A+Ee
to
ion
source
B+He -
Fig. mary
1. Reactor with free radicals),
Fig.2 reaction
shows zone
the diffusion
B = molecules,
the distribution near
the inlet
cloud in flow. A q atoms Fe - carrier gas
of the gas flow
velocity
(prf-
in the
cone,
obtained by experimental Curves O-6 represent the distribution of the modelling technique. relative velocity of gas flow along the reactor redius, 0,7,2,3,4, 5,6
mm from the inlet cone tip measured at Reynolds number of 6.5, The distribution of the relative flow velocity along the reactor
Ax(x)
2. The distribution of the gas flow velocfty Fig, cone ‘* Fig. 3. On the contact time determination,
near
the inlet
125
axis near the inlet hole can be perfectly approximated by the relation: V(x>/f = 2[1 - exp(-ax)] (3) where 7 P a mean flow velocity in the reactor; x = a distance from the inlet cone tip; the factor "an equals to 4.7-+0,25, 4.920,25, 520.25 for Reynolds numbers of 6.5, 11, 22 respectively, That ie the factor 1,aIrdepends but slightly on the flow velocity, From the shape of the curve8 of Mg,2 and equation (3) we can draw two conclusions: 1. near the reactor axis the inlet cone has a zone where the velocJity alightly changes by the radius; 2, by the tip of the inlet cone the flow velocity reaches 90 % of that on the reactor axis already at a distance of 4-5 mm from the tip, The simple approximate expression that desoribee the diatribution of the reagent concentrations in the diffusion cloud may be obtained when the relative change in the flow velocity, the concentration of the ac;tive particles and the conversion depths in the "diffusion length" (1D = D/V) are small, i.e. when the following conditions (ref.41 are observed, v'(x)*lD/v(xM~l, ~A(x)~'.lD/[A(x)~~
(6)
0
where nor n P the concentration distributfon of the molecules delivered into the diffusion cloud in the absence and presence of the reaction; k P the reaction rate constant; WC = the mass flow rate of the molecules through the capillary into the reactor; D= the diffusion coefficient of the molecules. As it is clear from (ref.3) the concentration distribution of the atoms A in the diffusion cloud is set out by the expression: [A(x)] = [A]o.Cl - ,&&
l
exp[&&&x-=)I)
(8)
,
where [Ao]= concentration of atoms at a large distance from the capillary tip. The contact timeC(x) can be most conveniently determined experimentally from the kinetic data tith the help of relation (9) C'(x) =Qx(x)EV whereAx = determined from the dependence, ln(n,/n>=f(xI, as
126
it
is
shown
in Fig.3
for
the reactions
H + X02,
0 + Br2,
P f C2D4.
allows to obtain the quantitative data at the small lengths of the diffusion cloud as well, what of particular significance for the determination of the reaction rate constants of the chemically active particles formed in the reactions of atoms with molecules, The distribution of the intermediate product concentrations along the reactor axis fog the succession of reactions A+B 'P,, A+P., 1 P,, can be obtained by analogy of the derivation of formula (6). in case of equal diffusion coefficients (DB=Dp =D pg ) the following expressions are valid at limitations for th& experimental conditiona: The use
#+
of the
‘[l
= *
"contact
time"
in the MPDCF
- exp((k-kl )*[A],.Ux))]
(10)
(11) the reaction zone we took the average rate in it. For example the following rate constants were obtained (cm3/s), which could include systematic errors of the origin considered in this paper: 0 + "2k !L 0 + CS L
H2(V,
products
k4(298K)=(2.1+0.2).10-"
co +kS
5) + NO 2
k3(298K)=(2.4~0.24).10-12
IIN0 + H
k5(295K)=(2'1).10-"
k6
k6(295K)=(1.2'0.5).10-'" H+HNOH2 + NO Measurings by a more recent method described above result in the following values: k3=(3.3~0.3).10"', k4=(2.1~0.2).10-'I, kgP(l.l-+0.2).10-", k6=~l.3~0.2).10"o, REFERENCES
V.L,Talrose, G,K.Lavrovskaya, A,F.Dodonov, I.I.Morozov, Recent Development in Maas Spectrosoopy, Tokyo, Utiverslty of Tokyo Press, 1970, p.1022. 2 A.F.Dodonov, V,V.Zelenov, V.P,Strunin, V.L.Talrose, Kinetika i kataliz, 1981, t.22, v.4, 888-897 pp. 3 A.P,Dodonov, V,V.Zelenov, G.N,Sargsyan, V.L.Talrose, DAN SSSR, 1980, t.252, No.2, str. 391-394. 4 V.L,Talroae, N.I.Butkovskaya, M.N.Larichev, I.O.Leipunskii, I.I.Morozovi A.P,Dodonov, B.V,Kudrov, V.V.Zelenov, V.V.Raenikov, Advances in Mass Spectrometry, ed. Daly N.D., London, 1978, v.7, 693 p. V.V,Zelenov, V,L,Talrose, DAN SSSR, 1980, t-252, 5. A.F,Dodonov, str.642. 1