Concentrometer-The Minimum Version of a Continuous, Real Time, Automatic, Direct- Reading Tit r imete r Tomas Hirschfeld Block Engineering. i n c . , 79 Biackstone Street. Cambridge, Mass. 02739
The basic operation of titration is the continuous variation of the sample-titrant ratio until the equivalence point is reached. This point is detected through the response of an added indicator. For a continuous sample stream, this may be accomplished by mixing it with a continuously increasing proportion of titrant and indicator solution as it travels along, and observing the distance downstream a t which the color shift takes place. This can be implemented by turbulent flowing the sample down a thin dialysis fiber suspended in a reservoir of the titrant-indicator solution. A supporting member holding the fiber along one side, curved so as to provide magnification and having a n engraved scale, completes the basic system. For laboratory use, a long-stemmed funnel t o provide constant head (and therefore constant velocity for all sample fluids of similar viscosities) or a positive displacement pump is also required. In a process controller, the fluid pressure inside the process piping can be used. For process fluids showing considerable viscosity variations, a flow restrictor can be used as t h e driving pressure source. Then the driving pressure will be proportional to the sample viscosity with precisely t h e inverse relationship of the viscosity flow rate one, and a constant flow rate independent of viscosity will result. The readout is identical to that of a thermometer; the scale position a t the color change point can be calibrated in terms of concentration or the scale can be engraved in concentration units to start with (provided the fiber properties are predictable enough). An indicator that is colorless before the equivalence point is convenient for readout simplicity; if the titrant solution is also colored, a second support must be contacted to the hollow fiber for illumination, or the one support must be used for reflex viewing. The first alternative may make the fraction of the fiber t h a t is exposed vary erratically; the second may require artificial illumination. To achieve turbulent flow, flow velocities past the critical Reynolds number may be employed, but these imply considerable flow rates and therefore large diffusion speed and titrant reservoir volume requirements. Packing the column with a powdered material (closely index matched for transparency) to randomize the flow p a t h is a superior alternative. To study the behavior of such a system, let us assume t h a t concentrations are everywhere low enough t h a t solution volumes and flow rates are constant along the tube. Furthermore, the sample and titrant are supposed to react to completion with negligible delay and the concentration of titrant in the reservoir is assumed to be constant. We can then define: D = the capillary diameter. cm; 1 = the capillary lzngth, cm; F , = the fractional free volume in capillary lumen; u = the flow velocity, cm X sec-1; CT = t h e titrant concentration, equiv cm-3; us = the sample diffusivity across wall, cm sec-l; g',- = the titrant diffusivity across wall, cm sec-l; and C,(1) = the sample concentration as a function of length, equiv cm-3. Over a n infinitesimal sequence dl of capillary, we now have
dC.(I) 2156
=
dW ~
1'
ANALYTICAL CHEMISTRY, VOL. 45,
in which
(2)
u = (ir/4)D2F,dl
and
dW
=
dl
dl
- a , C , ( l ) y PirDd - aTCT; 2irDdl
(3)
where d W = the change in sample quantity, and dC,(I) = the change in sample concentration. By substitution and rearrangement, we get
This linear first order differential equation has a solution
C,(l)
=
C,(O)e - (8a,)/iDuF,) -
whose root, corresponding to the equivalence point, is given by
The measurement scale, giving C,(O)$lo, will have spacings proportional to
dl,, dC.(O) ---=
DuF, ~ [ u ~ C T u,C,(O)]
+
(7)
Because of the finite mixing length along the capillary and visual resolution limitations, there exists a minimum discernible variation in lo to which a minimum discernible change in C,(O) corresponds. From Equation 7, this is
where ( A l 0 ) ~ = l ~the minimum discernible variation in ~ ~ minimum equivalence distance, cm, and ( l C s ) =~ the discernible concentration change, equiv cm - 3 . By differentiation we find a minimum for Equation 8 when (9)
giving
and
1, = (DcF,)/(8a,) The transit time through the system in seconds
(11)
(12) is thus independent of the velocity, whose reduction then reduces lo and also t h e pressure drop, given by t h e Kozeny Carman equation ( I ) as ( 1 ) H . Purnell, 'Gas Chromatography," Wiley, New York, N . Y . , 1962, pp
64-65.
NO. 12, OCTOBER 1973
TO ELEVATED FUNNEL,WMP, OR PIPE BLEED-OFF
fi /VENT
CAPILLARY
POINT
STOPPER
I
I
0
2,o
1.0 CONCENTRATION ( N )
TO DRAIN +
Concentrorneter accuracy as a function of sample concentration at various titrant concentrations
Figure 1.
Figure 2.
Construction of concentrorneter
For accuracy, of course, the titrant must flow past the outside of t h e tube a t a rate large compared with G,r, from which where A p = t h e pressure head, cm; q = the sample solution viscosity, poise; d, = the packing particle diameter, c m ; go = the acceleration of gravity, cm sec-l; and p = the sample density. g cm-3. Finally, we have for the sample flow rate in cm3 sec-I (14) and for the consumption rate of titrant in the same units 7r(e GT
- 1) D ~ ~ F , , ~ , --
=
4
(15)
UT
where D = 200 fi (the smallest diameter allowing adequate visibility with magnification); F, = 50% (a reasonable packing level for uniform spherical particles); u = 1.0 cm sec-I; C,(O) N 1.ON; ( - 1 1 0 ) ~ 1 =~ 0.5 m m (determined by visibility requirements and t h e need for a few D’s to achieve mixing); q = 1.0 cp (dilute aqueous solution); d, = 10 fi (larger diameters would reduce Ah but as d, D flow randomization suffers, making ( A 1 0 ) ~ l increase); l~ p = 1.0 g cm - 3 (dilute aqueous solution); a n d d, = 25 f i z . Then ‘is = UT = 1.75 X 10- 4 cm/sec (for existing fibers (2)); C,r = 0.582N; i o = 7.14 cm; t = 7.14 sec; { [.1C,(O)]~vrr~/C,(O)iopr = 0.16%; Ah = 13.10 cni HzO; G, = 1.57 X cm3 sec-l; and G1 = 2.70 X cm3 sec-l. While this accuracy of course seems very high, it degrades as C,(O) moves away from t h e value for which C r has been optimized, as shown in Figure 1, which also shows the much larger effect of changing CT. However, larger Cl’s might sometimes be advantageous to reduce GT, when long term monitoring from a reasonable sized reservoir is intended. Here even small values of GT become significant, since as soon as a noticeable fraction of the reservoir’s titrant content is consumed, lo changes and the readings become erroneous.
-
where u t = t h e mean transversal velocity of titrant, which in our example becomes u t >> 1.51 x 10-3 cm sec-l. Velocities of this order will always exist in a tube that has been moved recently and, for stationary devices, even minimal temperature gradients will produce enough motion by convection. The existence of such gradients is assured by the interaction of diurnal temperature changes with the local fluctuation of heat exchange rates between the reservoir a n d the atmosphere. A feasibility experiment was done using a single fiber from a n Amicon HlDPlO Diafiber cartridge (molecular weight cutoff 10000, diameter 200 f i , wall thickness -50 f i ) . The titrant was a solution of 0.6N NaOH in 609’0 ethanol, while the sample was a 0.05% phenolphthalein and 1N HC1 solution in 60% ethanol. Powdered cryolite (sodium aluminum fluoride) was used as a tube filling, after passage through a 200-mesh sieve. T h e tube was held by two stoppers in the center of a glass tube cut out from a graduated pipet as shown in Figure 2. The sample solution head was adjusted to a 1.2 cm/sec flow rate, and lo was observed to be 9.1 f 0.1 cm by the sudden increase in the red color intensity on the fiber. Strong illumination was required for this purpose, as the fiber was only translucent. A weak pink color could be observed along the fiber before the equivalence point, possibly because of the outward diffusion of the indicator. This was reduced by repeating the experiment a t lower ethanol concentrations. in which the indicator precipitated as a suspension of much reduced diffusivity. At these alkali concentrations, the life of fibers of this type was not very prolonged. When measuring over prolonged periods, no fluctuation in the readings could be observed; reproducibility is t h u s better than the measurement resolution. The same was true of experiments in which t h e flow was stopped and
A N A L Y T I C A L C H E M I S T R Y , VOL. 45, NO. 1 2 . OCTOBER 1973
2157
z 0
!$
s
1.00
z
V 0
0.5
5.0 10.0 NEUTRALIZATION LENGTH (CM)+
Figure 3. Concentrometer experimental calibration curve
restarted between readings (a wait of more than a time constant was used to allow the system to come to equilibrium). In all these experiments, the pressure head was constant to better than 1% and the ambient laboratory temperature ranged over no more than 5 "C. The resolution in this experiment was about 0.01N (la),limited by the 1-2 mm width of the color change zone. A series of measurements done with different standard solutions is shown in Figure 3. The individual points,
while reproducible to less than the resolution interval, are not on a smooth curve. On examination of the fiber, considerable diameter variations were observed; up to 10% variations being common for commercial fibers (2). In order to have the accuracy match the precision, one must use the measured points to generate a calibration curve. Later on, fiber selection or more rigid manufacturing control will be most desirable. Concentrometer's principal applications would seem to lie in the area of process indicators or (in combination with a syringe pump, a quick exchange fitting, and a suction probe) as a very rapid laboratory titrator for repetitious titration. However, it should be noted that difficulties in end-point detection associated with visual observation of indicators are not removed by its use (except insofar as spatial color contrast may be easier to detect than temporal color contrast). Sample consumption is exceedingly low; less than a drop being consumed for one determination. The titrant consumption is correspondingly small, and will allow prolonged operation without titrant refills with a reasonable sized reservoir. Received for review December 1, 1972. Accepted April 18, 1973. (2) W. F. Blatt. L. Helsen, E. M . 271 (1972).
Zipilivan, and
M. Porter. Separ. Sci.. 7,
Mercury Leveling Device for McLeod Vacuum Gauges J. H. Vorachek and G. G. Meisels Department of Chemistry, University of Houston, Houston, Texas 77004 Adjustment of the mercury level in a standard McLeod vacuum gauge is usually accomplished by admitting atmospheric air to the lower portion of the gauge. The mercury is returned to the reservoir by removing the air with the aid of a vacuum pump. In addition to the health hazard created by expelling mercury vapor into the laboratory atmosphere, this procedure monopolizes a moderately expensive vacuum pump. To eliminate the requirement for a vacuum p u m p and prevent contamination of the laboratory atmosphere by mercury vapor, a device (see Figure 1) was constructed whereby the vapor pressure of a condensable gas is used to adjust the level of the mercury. Return of mercury to the reservoir is accomplished by condensation of the working gas using either a Dry Ice slush or liquid nitrogen as the refrigerant.
EXPERIMENTAL The seat sealing sidearm of a 4-mm Teflon (DuPont) vacuum stopcock was attached to the wall of a section of %-inch heavy wall Pyrex (Corning) tubing. The tubing was sealed at each end to form a cold finger approximately 8 cm long. The three-way stopcock on the mercury reservoir was replaced by the Teflon stopcock assembly. A second stopcock was attached between the reservoir and the Teflon stopcock. To facilitate the later removal of the second stopcock, a constriction was left in the sidearm below the stopcock and the completed assembly annealed. The gauge was filled with mercury, attached to the vacuum line, and both sections were evacuated. Evacuation of the lower 2158
section was accomplished by means of a temporary connection to the vacuum line. The working gas was admitted to the lower section until the mercury level was sufficient for pressure readings. After closing the stopcock on the filling line, the working gas was condensed into the cold finger with liquid nitrogen, and the filling stopcock removed by sealing the constriction with a handtorch.
RESULTS AND DISCUSSION There are a number of acceptable choices available for the working gas. The few restrictions on the choice of compound to act as the working gas are that the compound must be nonreactive with the materials present, have a vapor pressure greater than 700 mm of Hg a t room temperature but not so great as to present a danger of explosion when confined in the cold finger, and have a vapor pressure of no more than a few centimeters a t the temperature of the refrigerant. We found isobutane performs quite well as the working gas. The time required to raise or lower the mercury level by vaporization or condensation of isobutane is comparable to the time required when atmospheric air and a vacuum pump are used. When compounds of lower volatility, e.g:, n-butane, were used as the working gas, the time required for vaporization was significantly longer. An additional advantage in using a working gas is a gradual slowing of the rate of vaporization as the remaining liquid is cooled by evaporation. This slowing of the rising mercury level as the reference mark is approached facilitates adjustment of the mercury level.
ANALYTICAL CHEMISTRY, VOL. 45, NO. 1 2 , OCTOBER 1973
