Isao Matsuzaki,l Robert B. Alexander, and Herman A. ~ ~ e b ~ a f ~ k y * Department of Chemistry, Texas A d M Unieersify, College Station, Texas 77843 The advantages of: the mass flowmeter make it attractive for measuring rates of gas evolution in the aaalytical laboratory, but i t was not possible to predict on the basis of available information whether a mass flowmeter-recorder ~ o ~ ~ ~ could ~ a serve t i o satis~ factorily when gas was being evolved at highly variable rates in systems with appreciable free volume not all at the same temperature. it was shown by investigating a reaction system with periodic gas evolution that the combination could give satisfactory results, provided the necessary corrections are properly made. Wider use of the Combination is recommended.
IN THE PERIODIC decomposition of hydrogen peroxide by the iodine-iodate couple in acid solution, strong pulses in iodide concentration have recently been discovered ( I ) to accompany the pulses in rate of oxygen evolution found about fifty years ago (2). The relationship of these two kinds of pulses must be known before the reaction can be understood. To establish this relationship, one must have the most detailed information possible about oxygen pulses, the time at which they begin and the peak rate of oxygen evolution being particularly important. It i s not easy to measure satisfactorily these transient rates of oxygen evolution. Such rates may increase almost tenfold within a minute and fall as rapidly to the background rates from which they started. The integral information given by a gas buret (3) (see Figure 1) needs to be supplemented by direct measurements of the rate during the pulses.
we believe that of the Type F-20 transducer to be near the lower end of the range. Response of the meter to a change in flow rate is described as logarithmic ( 4 ) : 67% of a change in flow rate will appear on the meter 5 sec after the rate is changed from one constant value to another. Other Apparatus and Experimental Detail. Throughout, mass flow rates are expressed in scc/min. The scc is the mass of gas contained in 1 cc at 1 atni and 273.16 OK. All experiments were done in simulated reaction system shown schematically in Figure 2. Because conditions in the gas space are complex, the “effective volume,” Ve*f,of this space was determined as follows. With the reaction system at atmospheric pressure and the temperature as indicated in Figure 2, the transducer was replaced by a reservoir of known volume containing oxygen at room temperature T,, and known pressure above atmospheric. The oxygen was permitted to expand into the reaction system, and Vefi was calculated from the ideal gas law, T,, and the measured final pressure being used in the calculation. In most experiments, the output of the transducer was recorded on a Hewlett-Packard Strip Chart Recorder Model 7100l3, with Plug-in Module 17501A, of response time 0.6 sec full scale. This corresponds in our work to a response time of 0.1 sec or less. Flow rates thus measured will usually be expressed in millivolts. The following mass-flow rates are pertinent (all in sccjmin): f i , flow rate of gas entering Vetf or evolved in reaction
system
A, true flow rate of gas through transducer j P , flow rate of gas through transducer as shown by
CALIBRATION EXPERIMENT
The Mass Flowmeter. The most convenient way of measuring and recording these rates directly is by use of a mass flowmeter, but it was necessary to establish whether such an instrument could meet the severe demands. We have found that the Matheson Company LF-20 Mass Flowmeter ( 4 ) can do so, but that the recorded results require an important correction. In this meter, gas flows through an electrically heated tube (transducer channel) surrounded by an arrangement of thermocouples. Heat transfer to the gas generates a d.c. voltage proportional to the rate of mass flow, which means that pressure and temperature of the flowing gas need not be known. Flow can be read in scc/min (see below} on an indicating meter, which we shall usually call the meter. Transducer channels are 3 inches long and range in diameter from 0.003 (0.0076 cm} to 0.125 inch (0.318 cm). Further information about channel diameters is proprietary ( 5 ) ; On leave from Dept. of Chemistry, Faculty of Science, Hokkaido University, Sapporo, Japan. To whom correspondence is to be sent.
(1) J. H. Woodson and N. A. Liebhafsky, Nature, 224, 690 (1969). (2) (a) W. C. Bray, 1.Amer. Chem. SOC., 43, 1262 (1921); (b) W. C. Bray and H. A. Liebhafsky, ibid., 53, 38 (1931). (3) H. A. Liebhafskv. results. University of California. _ ,unmblished Berkeley, 1928. (4) \ , Instruction Manual No. 8110-0121. The Matheson Company. - East Rutherford, N. J., June 16, 1967( 5 ) Letter dated Oct. 13, 1969, J. Okladek, Matheson Gas Products, East Rutherford, N. J. 07073, to H. A. Liebhafsky. _
indicating meter flow rate of gas through transducer as given by recorder
fiR,
Steady-State Flow. For such flow
The data in Figure 3, which were obtained at a series of constant pressures, P, in the reaction system, show that
,/in
e
ANALYTICAL CHEMISTRY, VOL. 42,
( E in mV)
and fi21f =
99(P
- P,,) (pressures in atmospheres)
(3)
where E is the output of the transducer and Prmis the atmospheric pressure in the room. For steady-state flow, P
- P,,
=
8.0 Ei99
(4)
Equation 4 shows that the recorder can be used to measure P at a steady state so long as P,, is constant. Equation 3 suggests that steady-state flow through the transducer obeys Poiseuille’s equation (see below). Transient Flow. General. For transient flow, the continuity equation for the simulated reaction system reads Ji
I
1690
= 8.0 E
-fi
= =
dB { 273 Vn(P - Pao)niTn ] /dt (273Vcri/Tr,) (dPjdt)
(5)
where t is time, PH~O is the pressure of water vapor, and n = 1 , 2 , or 3 ; the summation is taken over the three sections
NO. 14, DECEMBER 1970
Time ( m i n ) 4
Time ( m i d +
Figure 1. Periodic (pulsed) oxygen evolution from an acid reaction mixture containing iodate ion and hydrogen peroxide (3) Gas-buret (integral) data on left. Derived rate (differential) data on right. The shape and height of the pulses on the right are highly uncertain: it is probable that all three pulses had about the same true peak heights. The reaction mixture was shaken violently enough to make varying supersaturationunlikely
Figure 3. Experimental data for steady-state flow
-
ansducer indicating mV meter recorder
Note that the precision is high except at very low flow rates,
where slight deviations occur. Open circles, Equation 2. Solid circles, Equation 3
Matheson mass flowmeter
2
I 0,cylinder 2 Pressure adjuster
4 Reaction vessel
3 Hg manometer
6 Heating plats
7 Rotary magnet
5 Magnetic stirrer
Figure 2. Experimental apparatus used of the reaction system shown in Figure 2. Equation 5 shows why it is expedient to use the empirically determined Veif. For a system with instantaneous response, $2
= A M = hR
(6)
and Equations 2 , 4 (differentiated), and 5 give
+ (273 Veri/Trm)(8.0/99) (dl3ldt) = 8.0 E + kdE/dt
j; = 8.0 E
Figure 4. Comparative response of indicating meter (Curve 3) and recorder (Curve 2)
(7)
(7a) Equations 7 and 7a describe how jP (measured in millivolts) will vary with time when P (and fi) are changed, and there is no time lag in the measuring system. Curve I in Figure 4 was calculated from Equation 7 for the following experiment: (1) P was increased by lowering the tube in the pressure regulator at constant rate for 5 seconds. ( 2 ) P was maintained constant for several minutes. (3) P was lowered by raising the tube in the pressure regulator at constant rate for 5 seconds. Curve 2 is the recorder trace (jP) for the experiment. Curve 3 was obtained by converting into millivolts in accord with Equations meter readings (p) 2 and 3. Curve 3 shows a considerably slower response than Curve 2, and the difference is greater when Pis increased. Slow response can exist in the transducer and in the indicating meter; the response or" the recorder is for our purposes instantaneous (see above). Figure 4 shows that one gains considerably by using the recorder for transient flow, and this was done henceforth.
Response on Change to Constant f i . Transducer response to increased flow rates was established as follows. At t =.O, fi was suddenly increased from zero to one of three constant values (8.2, 20, and 55 scc/min), the constant fi for each experiment having been established manometrically when the gas flowed into a known volume. The response was computed from values offiR by Equation 7a. The results are given on a master plot in Figure 5. The construction of this plot is clear from Equation 7a. For instantaneous transducer response, Equation 7a prescribes a straight line with dE/dt equal to j l / k at E = 0 (ordinate in Figure 5 ) , and E equal to f i / 8 at dE/dt equal to zero (abscissa). If transducer response is slow, the experimental values will lie below the calculated line. Figure 5 shows that dE/dt is too small by 15 at its maximum value, which is reached at t = 0 when the change from zero flow rate to constant Jl is made. The experimental curve merges with the calculated line in about 3 minutes. Response to Decreasing Flow Rate. With steady-state flow achieved, j 1 was reduced to zero at t = 0, and the response was computed as for Figure 5 from values of f i R when fi had been 3.72, 7.39, or 11.3 scc/min. Theresults, inFigure 6, resemble those in Figure 5 except that dE/dt is negative,
ANALYTICAL CHEMIISTRY, VOL. 42, NO. 14, DECEMBER 1970
0
1691
4)
f,- 8.2
5
-
0
E(mV)
10-8
t
f, 10
Figure 5. Detailed response of mass flowmeter-recorder combination when gas flow was suddenly changed a t t = 0 from zero to the constant fi values (sccimin) shown in the figure Niunerisal values of ordinate and abscissa are proportional to fi. E x p e r i ~ e points ~ ~ a ~computed from values of hRby Equation 7a. Other data: V,ff = 278.6 cc; T,, = 297 O K ; k = 20.7
1
.-C
9 f,= 3.72
)
Tima-
E \
,
Time e-
>
Figure 7. Relationship of iodide and oxygen pulses
F
Only the corrected oxygen pulse (b) shows a logical relationship to the concomitant iodide pulse. Within the experimental error, the corrected pulses start and stop at the same time, and the relative decrease in the iodide concentration approaches the relative increase in the rate of oxygen evolution
E
W w
i
The correction is made by using Equation 7 with numerical values inserted as follows: Figure 6. Detailed response (computed from values of JT]to decreasing P when fi was changed to zero at t = 0 from constant value listed in figure. Other data: Veff = 278.6 T,, = 297 OK; k = 20.7.
z
and its maximum value is only 5 low. With both indicating meter and recorder, therefore, it appears that the transducer adjusts more rapidly to a decreasing than to an increasing flow rate. APPLICATION TO AN OXYGEN PULSE The final (and most severe) test of preceding considerations is their application to an oxygen pulse taken at random from a series formed during a reaction carried out by one of us (I. M.) with J. W. Woodson. A similar series (uncorrected) appears in Reference 1. The uncorrect,ed pulse is Curve I , Figure 7a. An estimate O € the effect of delayed transducer response was made for one point on each branch of the curve by using as is shown in Figure "a, the information from Figures 5 and 6. As this effect is negligible, it will be dismissed with the statement that the delayed transducer response may be regarded roughly as delaying oxygen evolution by about 1 second. By contrast, the correction based on Equation 7 is vital, 1692
e
dOz/dt
=
j i = 8.0 E
+
(273 X 8.0 X 120/99 X 298) (dE/dt) (8) It was shown that both the areas below the f L R (corrected)time and 5-time curve in Figure 7 coincided within 3 z between the start of pulse and the time which gave the same A" value as at the start; the reason this time interval was used for the purpose of comparison is that the amount of oxygen passing through the transducer in the interval is equal to that evolved in the reaction system. The importance of the correction is clear from a comparison of oxygen pulses with concomitant pulses in iodide concentration (6), as in Figure 7. The inverse proportionality of [I-] and dOz,'dt, which the corrected data shows, is logical on the basis of chemical kinetics, as is the occurrence of iodide and oxygen pulses over the same interval. To support this statement, we turn briefly to the reaction system, which contains IO3-, HIO2, H21203,WIO, Iz, and I- as principal iodine species. Some of these can react with each other (2b), andior with H202. Hydrogen peroxide can act either as oxidizing or reducing agent. Free radicals also need to be considered. What makes this unique reaction system worth reinvestigating despite this complexity is the ( 6 ) J. H. Woodson and H. A. Lielshafsky, ANAL.CHEW,41, 1894 (1969).
ANALYTICAL CHEMISTRY, VOL. 42, NO. 14, DECEMBER 1970
periodic character, discovered over 50 years ago (2a) and unexplained today. Our hope is that the use of modern tools will bring success. The iodide-selective electrode fulfilled our expectations in revealing iodide pulses of remarkable regularity (1, 6). The mass flowmeter, on the other hand, was initially disappointing because each recorded oxygen pulse-though each began simultaneously with the accompanying pulse in iodide concentration-continued long after this iodide pulse had ended ( I ) . This could have meant that the pulses in oxygen were due to more than one reaction, of which only one was simply related to the iodide concentration-a highly discouraging prospect. The expected and logical relationship to iodide concentration is this. With the equilibrium Iz
K + HzO e H+ + I- + H I 0
(9)
maintained, the oxygen pulses result from an increase in the rate of the reaction
HI0
+ H s O z A 0 2+ El+. + I- + HzO
(10)
owing to the increased [HIO] that follows the decrease in [I-] during the iodide pulse. For the rate of Reaction 10, Liebhafsky (7) found at 25 "C -d[HzOz]jdt
=
dOL/dt = 6.6(10-10)([Iz]j[H-][~-])
X [HzOz] = Kk([I~I~[H+][I-])[Hz0~1 (11 ) For the reaction mixture of Figure 7, the calculated rate of oxygen evolution is 0.6 scc/min at 25 "C. Values of K and k at 50 "C are not available. A reasonable, but necessarily uncertain, estimate is that K will increase 10-fold and k 6-fold during the transition from the lower to the higher temperature. Accordingly, the peak rate is 36 sccimin at 50 "(7; Figure 7 shows about 35. Reaction 10 thus seems to be responsible for the oxygen pulses, and this brightens the prospects for an eventual understanding of the reaction system. Visual examination of many pulses supports these conclusions. GENERAL SIGNIFICANCE OF RESULTS Because mass flowmeters of the present type deserve wider application in physical chemistry, we conclude with a brief general discussion. We consider here a system with volume V at pressure P between gas source and transducer inlet, fi and .f; being meamred in scc/min. The temperature throughout is 273 OK. According to Equation 3 (for steadystate flow)
fi
= kidP
- Prm)
(7) H. A. Liebhafsky, J . Amer. Chem. SOC.,54, 3499 (1932).
Poiseuille's equation governs the volume rate of laminar flow for an incompressible fluid through a cylindrical channel. To apply it here, we must consider that gases are compressible, that volume flow is involved, and that temperature and pressure in our channel are unknown. Compressibility is compensated for by using the Poiseuille's equation in the form (8) dVldt
=
+
{ n(P - P,,)r4/8Z~)(P Pr,)/2P,, (cgs units) (13)
By taking 7 and the volume flow sate at 0 "C, our mass units, SCC,may be used in Equation 13. For the approximate calculation of the diameter of the transducer channel, the pressure and temperature uncertainties may be disregarded. With 7 = 192 x 10-5 poises, the value for oxygen at 0 "C, Equations 3 and 13 yield r = 0.0087 cm for the radius of the transducer channel, which corresponds to a diameter (perhaps nominally 0.007 inch) near the lower end of the range. Clearly, it should be possible to calculate klz for a cylindrical channel from Poiseuille's equation if the necessary data were available. The general continuity equation is
fi + VdPjdt
(14)
dfi,ldt = kizdP/dt
(15)
fi
=
From Equation 9, whence Equation 14 becomes
fi = f i
+ (Vlkiz) (dfildt)
(1 6 )
Equation 16 shows that the m a s flowmeter gives the value of
fi only when the product in the equation is negligible. The easiest way to bring this about is to keep V small. Forfi constant, Equation 16 can be integrated to give
In [ f i j ( f i - fill
= kl2tiV
(17)
for fi = 0 at t = 0. This equation then givesfi at time t and can be used to calculate how long it will take fi to approach fi at given values of k12and V. This response is obviously logarithmic. A measured slower response indicates an instrumental lag. No general integration is possible when fi varies. Because its readings do not need to be corrected according to Equation 16, the gas buret may under certain conditions be preferable to the mass flowmeter. The two devices complement each other.
RECEIVED for review May 25, 1970. Accepted September 1, 1970. Work supported by the Robert A. Welch Foundation.
(12) (8) W. 9. Moore, "Physical Chemistry," 2nd ed., Prentice-Hall, Englewoods Cliffs, N. J., 1955, p 175.
ANALYTICAL CHEMISTRY, VOL. 42, NO. 14, DECEMBER 1970
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