Endpoint drift correction for automatic titrations

An apparatus and method are described for automatically correcting drift in automatic titrations, such as coulometric titrations of water. An endpoint detector provides a signal indicative of the state of the titration mixture and the detector signal is monitored by two comparators, responsive to titration mixture states on opposite sides of the endpoint and connected to means for controlling forward and back titration. At the end of a titration, the titration time and amount of titrant are stored in memory elements, and circuitry including an array of gates monitors the comparator signals during two post titration time periods to determine both the direction and rate of drift, and to correct the titration results for the amount of drift detected.

CROSS-REFERENCE TO RELATED APPLICATION 
A more detailed description of a filter used in the apparatus of the 
invention is in a concurrently filed application of James K. Kroeger, Ser. 
No. 910,173, now abandoned. 
BACKGROUND OF THE INVENTION 
This invention relates to automatic titrations and titration apparatus, and 
in a preferred embodiment the invention is concerned with coulometric 
titration of water using the Karl Fischer reaction with apparatus of the 
type described in U.S. Pat. No. 3,726,778 to Levy and Seltzer. As 
described in that patent, such titrations are subject to positive and 
negative baseline drift, that is, drift away from the endpoint condition 
not resulting from sample addition. Such drift can be caused by a variety 
of factors, including side reactions in the titration mixture which either 
generate or consume the substance being titrated. In coulometric titration 
of water, aldehyde or ketones in samples will react to produce water. 
While U.S. Pat. No. 3,726,778 provides one approach to compensation for 
drift, it would be desirable to provide an apparatus and method adapted 
for determining accurately the actual amount of drift in each titration 
and automatically correcting the titration results. 
SUMMARY OF THE INVENTION 
The invention relates to a method and apparatus for coulometric titration. 
More particularly, the invention relates to a method and apparatus for 
accurate and precise determination of the results of a coulometric 
titration and compensation for drift. In a particularly preferred 
embodiment the invention concerns an improved method and apparatus for the 
coulometric titration of water by the Karl Fischer reaction. 
As with coulometric titrations generally, the method and apparatus of the 
invention involve a titration compartment, with means for introducing a 
titration reagent and sample, an electrolysis anode and cathode in the 
compartment to pass current through the titration mixture and generate a 
titrant from the reagent; a detector for determining the condition of the 
titration mixture relative to a predetermined endpoint; and a source of 
electrolysis current for the electrolysis electrodes and means for 
measuring the amount of electric charge passed through the titration 
mixture. The apparatus can also include additional components, such as an 
auxiliary electrolysis current source of opposite polarity to the main 
source for back titration, appropriate filters, buffers, amplifiers and 
control circuitry to allow the detector to control the titration, display 
elements for displaying the results in various convenient forms, such as 
coulombs, titration time, concentration units, etc. The basic structure 
and use of coulometric titrators is known and conventional. See, for 
example, Levy and Seltzer, U.S. Pat. No. 3,726,778. 
In colulometric titrations, and particularly in coulometric titration of 
water by the Karl Fischer reaction, the endpoint can be subject to drift, 
due to a variety of factors such as side reactions, leakage of atmospheric 
conatminants into the titration compartment, etc. Depending on the 
chemistry of different samples, drift due to side reactions can vary in 
both direction and amount, adversely affecting the results of the 
titration. The invention provides a method and apparatus for compensating 
for the actual drift occuring during the titration, so that the drift 
elements in each titration can be accounted for. 
In the process of the invention, an electrolysis current is passed through 
a titration mixture of reagent and sample to generate titrant therein, 
until the titration mixture first reaches a predetermined endpoint as 
indicated by an endpoint signal provided by a detector. After the endpoint 
signal is first reached, electrolysis current is again passed through the 
mixture whenever the detector signal exceeds the endpoint level, until the 
mixture is titrated back to the endpoint. The amount of electric charge 
(Q) used for electrolysis is measured, and the titration time (T) is also 
measured. After the endpoint condition is reached for the first time, the 
mixture is monitored and held without measurements being taken for a first 
predetermined short time period to allow to mixture to stabilize. During 
this period, the mixing of the titration mixture is continued so that any 
heterogeneity, due to localized conditions at the titration electrodes or 
detector electrodes, will be eliminated. Monitoring is then continued for 
a second, longer time period. If the detector signal does not depart from 
the endpoint level during the second time period, the amount of sample is 
determined from the amount of electrolysis current passed through the 
mixture until the initial endpoint. If, during the second period, the 
titration mixture departs from the endpoint level the monitoring is 
continued over a third time interval, beginning with a return to the 
endpoint condition, continuing for a predetermined time period and ending 
with another departure from and subsequent retitration to the endpoint 
condition. 
The first post-titration time interval is relatively short, e.g. 5-10 
seconds, being only long enough to ensure that localized differences in 
the titration mixture are eliminated. The second post-titration time 
interval is generally longer; e.g., 30-60 seconds, when there is no 
forward or back titration of drift. The predetermined time duration of the 
second time interval is selected in relation to system time response and 
titration rate to correspond to, or to exceed the ordinary duration of the 
initial titration so that absence of forward or back titration during this 
period will indicate absence of drift during the initial titration. The 
first period and the predetermined time duration of the second period can 
be preselected and controlled by a timer. When titratable drift occurs, 
the end of the second period, and the beginning and end of the third 
period are in response to the state of the titration mixture. The third 
time period must begin and end with departures from, or retitrations 
returning to, the predetermined endpoint condition in order to obtain an 
accurate determination of the drift rate. 
Since the first period is merely to allow stabilization of the titration 
mixture, the second and third periods are the two time intervals during 
which drift measurements and corrections occur. In titrations for which no 
post-endpoint stabilization is required, for example, with rapid mixing 
and a slow titration rate, the stabilization period can be eliminated. 
Electrolysis current passed through the mixture periodically during the 
third time interval, and the total duration of the third time interval are 
measured and the average drift rate is determined from the amount of 
charge used during the third period to maintain the endpoint, and the 
duration of the third period. The amount of sample titrated is determined 
from the amount of charge used until the end of the titration adjusted by 
the drift rate and the measured titration time. Periodically the detector 
signal is monitored and reverse polarity back titration current is passed 
through the mixture when the signal reaches a predetermined level beyond 
the endpoint, and the reverse current is also measured as stated above, 
and used to determine and adjust for negative drift. 
The apparatus of the invention includes conventional elements of a 
coulometric titrator including electrolysis electrodes, current source, 
titration compartment, and a detector for detecting the condition of the 
titration mixture relative to a predetermined endpoint. The detector 
output signal is connected through a variable low pass filter to a 
comparator means for comparing the detector output to the predetermined 
endpoint level. The filter is adapted to vary in response to the 
comparator between a short time constant condition above the endpoint and 
a long time constant, high damping condition at or beyond the endpoint. 
The comparator is also connected to means for controlling the titration 
current. 
The apparatus also includes means for measuring the titration electric 
charge, and a timer for measuring titration time, and gate means 
responsive to the time and the comparator for controlling the first 
post-titration period; second gate means responsive to the first gate 
means, the timer and comparator for connecting the charge measuring means 
to output means such as a display when the second post titration time has 
elapsed without a departure from the endpoint, and for transmitting the 
measurements of titration time (T.sub.titr) and titration charge 
(Q.sub.titr) at the end of the titration and the time and charge 
measurements (T.sub.co and Q.sub.co) at the beginning of the third 
post-titration period to first and second memory means; third gate means 
responsive to the second gate means, the timer and the comparator for 
transmitting the measurements of titration electric charge (Q.sub.cl) and 
time (T.sub.cl) from the measuring means and timer when the selected 
retitration occurs at the end of the third time period; means responsive 
to the third gate means and connected to the and second memory means for 
generating a signal corresponding to (Q.sub.cl -Q.sub. co /T.sub.cl 
-T.sub.co), which thus corresponds to the average drift rate (D.R.) during 
the third time interval; multiplier means connected to the 
subtractor/divider means and the first reader/memory means for generating 
a signal corresponding to the amount of drift taking place during the 
titration, (D.R..times.T.sub.titr =Q.sub.titr); and adder and subtractor 
means connected to the first reader/memory and the multiplier means for 
connecting the titration result Q.sub.titr by subtracting or adding the 
amount of electric charge Q.sub.corr attributable to titration of positive 
or negative drift. 
The titration time measured in the process and apparatus of the invention 
is the total of (a) a relatively brief sample introduction period (during 
which the sample to be titrated is introduced into the titration reagent), 
(b) the time between the end of the sample introduction period and 
beginning of titrant introduction by switching on the main electrolysis 
current source; and (c) the time during which titration current is passed 
through the mixture until the endpoint condition is first reached. Period 
(a) is a relatively brief period, e.g. 5-10 seconds to allow time for the 
introduction of sample. Period (b) can be eliminated, however, it is 
preferred in the case of certain samples to allow a delay of 10 to as long 
as 3600 seconds, to permit complete mixing, or extraction of materials 
from solid samples into the titration mixture. This can be provided by 
including a convention delay timer to delay operation of the current 
source for selected times. Since drift due to side reactions, atmospheric 
contamination, etc. can occur during periods (a) and (b), it is necessary 
to include such periods in the titration time.

DETAILED DESCRIPTION 
As illustrated in the embodiments of FIGS. 4 and 5, the apparatus comprises 
electrolysis electrodes 34,36 connected to a main electrolysis current 
source 35, and an endpoint detector 39, including electrometric sensing 
electrodes 40, 41, and indicator current source 42. A negative drift 
auxiliary current source 56 is also provided, connected to electrodes 34, 
36 with opposite polarity to main current source 35. These basic elements 
are conventional and described, for example, in U.S. Pat. No. 3,726,778 in 
reference to Karl Fischer titrators. 
Endpoint detector 39 is connected through conventional buffer and voltage 
limiter circuits 43 to a variable low pass filter 10, and the output of 
filter 10 (the filtered detector signal) is connected to endpoint 
comparator 24 and negative drift comparator 52. A predetermined endpoint 
reference voltage source 28 is connected to endpoint comparator 24 to 
provide a reference voltage corresponding to the titration endpoint. The 
output signal of comparator 24 (indicated as S, in FIG. 5) is connected to 
a light actuated switch, LAS 33, which controls the operation of the main 
current source 35 while electrically isolating the comparator 24 from 
current source 35 and titration counter and drift correction circuitry 60, 
62, 64, 65. In a coulometric Karl Fischer titrator embodiment with an 
amperometric sensing electrode as detector 39, the detector signal is 
voltage, which decreases during the titration as water is consumed, to an 
endpoint value of, for example, about 70 millivolts. Comparator 24 and LAS 
33 are connected to activate electrolysis current source 35 when the 
signal from detector 39 indicates the presence of untitrated sample and to 
switch off current source 35 when the detector signal reaches the endpoint 
reference level provided by voltage source 28. The current source 35 
remains switched off at LAS 33 until the detector signal at comparator 24 
returns to the endpoint level (due to drift, untitrated sample, new sample 
addition, etc.). As best shown in FIGS. 2 and 3, the electrolysis current 
source 35 will be activated periodically after the endpoint is first 
reached. 
As illustrated in FIG. 1, the unfiltered output from detector 39 is an 
extremely noisy signal. The filtered signals of FIGS. 2 and 3 illustrate 
more typical titrations. As best shown in FIG. 2, a titration continues 
for an initial titration time T.sub.titr, beginning with the start of a 
sample introduction period, continuing through a period during which the 
constant current source operates, and ending when the titration reaches 
its initial endpoint, at T-T.sub.titr =0 in FIG. 2. (The signal 
illustrated is voltage limited to a maximum shown at (a) in FIG. 2.) 
Although the electrolysis current is switched off at the endpoint, at 
T-T.sub.titr =0, the detector signal exceeds the endpoint, to (f) then 
begins to return during an initial post titration stabilization period. 
The second post titration period ends and the third period begins at 
T-T.sub.titr =10 seconds, when the titration current is switched on and 
off, giving rise to a retitration "spike" (b). With the retitration at 
(b), the signal again goes beyond the endpoint, then gradually drifts 
upward at (g) during the third time period. The upward drift is followed 
by another retitration spike (c), an "overshoot" and upward drift (h) to 
another retitration spike (d). With a third time period having a minimum 
time duration of, for example, 30 to 50 seconds, the third time period 
would be 55 seconds long, from the beginning of spike (b) at T-T.sub.titr 
=10 seconds to the beginning of spike (c) at T=65 seconds. With a minimum 
third period duration of 60 seconds, the third period would continue until 
the beginning of spike (d) at T-T.sub.titr =102 seconds, making the third 
period 92 seconds long (from T-T.sub.titr =10 to T-T.sub.titr =102). 
As best shown in FIG. 2, the drift cycles, (f), (g), (h), and (i) are not 
uniform in duration. It is necessary for the third time period to begin 
and end with a post titration spikes, preferably with the beginnings of 
spikes. The third time periods in different titrations, will not 
necessarily be of the same duration. 
To provide a quick shut off of titration current at the endpoint, together 
with adequate filtering of the detector signal so that return to the 
endpoint can be reliably detected, filter 10 comprises capacitor 12, 
connected in series through resistors 15, 17 to the detector input, and 
connected to amplifier 22. Two additional resistors 14, 16 are switchably 
connected in parallel with one of resistors 15, 17 via switches 18, 20. 
Switches 18, 20 (both shown open in FIG. 4 are controlled by actuator 26 
connected to the output of comparator 24, so that both the switches 18, 20 
are closed or both switches are opened substantially simultaneously. 
Resistors 14, 16 are selected to provide different resistances in the RC 
filter circuit, and thus different cut off frequencies and time constants 
depending on whether resistors 14 and 16 are switched into or out of the 
circuit. Switch actuator 26 is connected to comparator 24 to provide 
short-time-constant/high-pass filtering during the titration and 
long-time-constant/low-pass filter characteristics when the endpoint is 
met or exceeded. Further details of the filter 10 are described in a 
copending commonly assigned application, concurrently filed herewith by 
James K. Kroeger, Ser. No. 910,173, hereby incorporated by reference. 
As shown in FIG. 4 the filtered detector signal is also connected a 
negative drift comparator 52, which is also connected to a reference 
voltage source 55. This reference voltage is a predetermined level 
corresponding to negative drift of the detector signal below the endpoint 
level. For example, in Karl Fischer titrator with an endpoint reference of 
70 millivolts, a suitable negative drift reference level can be 55 
millivolts. Comparator 52 is connected to an LAS 54 which switches the 
negative drift auxiliary current source on or off, in response to the 
output signal S.sub.2 of comparator 52. 
The outputs of comparators 24, 52 are connected through the respective 
light activated switches 33, 54 to a resettable titration counter 64, 
which measures the electric charge used to titrate or to correct drift, 
and to a drift correction/readout circuit 65. When both current sources 
35, 56 are constant current sources, for example, the main electrolysis 
source preferably provides +100.35 milliamperes when switched on, and 
negative drift source 56 provides -25.09 milliamperes. With constant 
current electrolysis, titration counter 64 is preferably a clock or timer, 
which records the time during which the current sources operate. A clock 
60 is connected to both titration counter 64 and real time clock 62 to 
provide uniform timing measurement. 
DRIFT CORRECTOR AND READOUT 65 
As shown in FIG. 5, main titration comparator 24 through LAS 33 provides a 
signal S.sub.1, which corresponds to the endpoint status of the detector 
signal and the main electrolysis current from source 35. Similarly, a 
signal S.sub.2 from comparator 52 and its LAS 54 indicates the negative 
drift status of the detector signal and negative drift correction current 
source 56. Titration counter 64 provides a signal Q, which corresponds to 
electric charge used in titration, the signal Q being a measurement of the 
time that either current source 35 or source 56 has been switched on. 
Clock 62 provides a signal T, which corresponds to the actual duration of 
the titration procedure independently of switching on and off of sources 
35 and 56 before and after the endpoint is first reached. 
For simplicity, signals S.sub.1, S.sub.2, T and Q are shown repeatedly as 
inputs or connections to various elements in FIG. 5. It is understood that 
the apparatus includes appropriate connections between the comparators 24, 
52, LAS 33 and LAS 54, counter 64 and clock 62 to supply these signals. 
The drift corrector and readout circuits 65, include a series of gate 
systems (gates 70, 71, 73, 74); reader/memory elements 75, 76, 77, 78 for 
signals T and Q at various times controlled by clock 62 and comparators 
24, 52 through the gates 70, 71 72 and 73; signal function manipulators 
(80, 81, 82, 83, 84) connected to certain of the reader/memory elements 
75, 76, 77, 78 and gate 74 and a readout circuit 85. The readout circuit 
85 includes conventional display apparatus for displaying the results, 
recorder, etc., and associated conventional apparatus, e.g. converter 94 
for converting the results to a desired numerical units, such as coulombs, 
moles, millimoles, micrograms, etc. and desired numerical base, such as 
binary, octal, decimal, etc. Such apparatus is well known and the 
particular type of readout apparatus is not critical. 
A reset element 86 is connected to clock 62 and counter 64 to reset the 
clock and counter and clear the memories when a start signal from a start 
switch 90 is produced. 
The gates, reader/memory elements, and function manipulators 70-84, follow 
the titration and any post titration drift, correct the result for drift 
(if any) and transmit the final result to the readout 85. When the readout 
85 receives the final result, reset element 86 resets the titration 
counter 64 and clock 62. In a further embodiment, the device includes 
additional circuits to monitor drift periodically in the apparatus between 
titrations, and to apply the most recent drift correction to the readout 
during subsequent titrations until the first endpoint. 
The apparatus is controlled at several points by signals S.sub.1 and 
S.sub.2 from comparators 24, 52. Each comparator signal corresponds to one 
of two states of the detector signal and current sources 35, 56. For 
brevity, the two signal states are hereinafter referred to as OFF and ON, 
corresponding to the following; 
S.sub.1 =OFF, detector signal below endpoint, main titration current source 
35 off; 
S.sub.1 =ON, detector signal at or above endpoint, main titration current 
source on; 
S.sub.2 =OFF, detector signal above predetermined negative drift limit 
(which is below the endpoint level); auxiliary current source off; and 
S.sub.2 =ON, detector signal below negative drift limit; auxiliary current 
source on. 
OPERATION 
A titration is started, e.g., by actuating a "start" switch 90 just prior 
to adding a sample to the titration reagent, clearing the display and 
actuating reset element 86. Reset element 86 resets and starts the clock 
62, and resets counter 64 to zero, and briefly inhibits operation of the 
current source 35 for a predetermined sample introduction period. If the 
sample contains water detected by indicator 39, S.sub.1 goes to the ON 
state, and starts counter 64. When the titration first reaches the 
endpoint, the signal S.sub.1 from comparator 24 goes to OFF, stopping the 
titration counter 64 but not the clock 62; and T and Q are transferred to 
memory elements 75, 76. These signals are T.sub.titr (titration time) and 
Q.sub.titr (titration charge). The "5-second" gate 70 follows the signal T 
from clock 62 for 5 seconds after S.sub.1 first goes to OFF, then 
activates the "30-second" gate 71. The 30 second gate monitors the clock 
signal T, and S.sub.1 and S.sub.2. If both S.sub.1 and S.sub.2 remain OFF 
for the entire period, gate 71 transmits the signal Q.sub.titr from memory 
75, through subtractor 82 to the display 85 and converter/multiplier 94. 
S.sub.1 and S.sub.2 both remain OFF only if there is no detectable drift 
during this period, therefore Q.sub.corr in subtractor 82 is zero. 
In the usual case, some drift will occur and either S.sub.1 or S.sub.2 will 
switch ON during the period controlled by gate 71, as the device either 
titrates positive drift back to the endpoint or back titrates negative 
drift back to the pre-set limit. When either S.sub.1 or S.sub.2 goes to ON 
during this period, the 30 second gate transmits the clock 62 and counter 
64 signals T and Q to memory elements 77. T and Q at this time can be 
designated as T.sub.Co, and E.sub.Co the subscript "Co" denoting the 
beginning of the drift correction measurements. Gate 71 also activates 
gate 72, and, in response to which comparator signal (S.sub.1 or S.sub.2) 
is ON, activates correction selector gate 74 to connect function elements 
81, 82 for S.sub.1 =ON or function elements 83, 84 for S.sub.2 =ON. 
Once activated by S.sub.1 or S.sub.2 going to ON, the 45 second gate 
monitors the time signal T from clock 62 and then activates the C.sub.1 
Gate 73 after 45 seconds. The activated C.sub.1 Gate monitors T.sub.1, 
S.sub.1 and S.sub.2, and when either S.sub.1 or S.sub.2 goes to ON again, 
or if neither S.sub.1 or S.sub.2 go ON for 30 seconds gate 73 transfers Q 
and T at that time to Q.sub.C.sbsb.1, T.sub.C.sbsb.1 reader/memory element 
78. The subscript "C.sub.1 " denotes the end of the correction measurement 
period. 
The apparatus has thus determined the titration charge Q.sub.titr and time 
T.sub.titr until S.sub.1 first reached OFF; delayed 5 seconds; then 
monitored S.sub.1 and S.sub.2 during a second time interval, and 
determined T and Q at the beginning (T.sub.Co, Q.sub.Co) and end 
(T.sub.C.sbsb.1, Q.sub.C.sbsb.1) of a third time interval which started 
with S.sub.1 or S.sub.2 switching On after the 5 second delay and ended 
with the next ON state of S.sub.1 or S.sub.2 which occured after the 
expiration of 45 seconds from the start of the third time interval or, if 
there is no subsequent ON state within the 30 seconds of the C.sub.1 gate 
73, which ended after the 45 seconds of gate 72 plus the 30 seconds of 
gate 73. 
Gate 73 also activates the drift rate calculator function element 80, which 
uses Q.sub.Co and T.sub.Co from memory 77 and Q.sub.C.sbsb.1 and 
T.sub.C.sbsb.1 from reader/memory element 78 to generate a drift rate 
signal corresponding to: 
EQU (Q.sub.C.sbsb.1 -Q.sub.Co /T.sub.C.sbsb.1 -T.sub.Co) 
Element 80 thus comprises subtractors and a divider element. 
If S.sub.1 was ON during the post titration period, correction selector 
gate 74 transmits the drift rate signal from calculator 80 to correction 
multiplier 81 which multiplies the drift rate signal by T.sub.titr stored 
in memory element 76 to produce a drift correction value signal 
Q.sub.corr, corresponding to the amount of titration charge Q.sub.corr 
which was consumed during the titration by drift compensation rather than 
by titrating sample water. Q.sub.corr is transmitted from multiplier 81 to 
subtractor 82, which receives Q.sub.titr from memory 75. Subtractor 82 
subtracts Q.sub.corr from Q.sub.titr and transmits the resulting signal, 
now corresponding to the titration result corrected for drift (Q.sub.titr 
-Q.sub.corr), to display 85 via converter/multiplier 94. 
If negative drift occured, S.sub.2 was ON during the post titration period. 
Gate 74 transmits the drift rate from calculator element 80 to correction 
multipliers 83, A and B which multiply the drift rate by T.sub.titr (83B) 
and divide (83A) by a factor K.sub.1 corresponding to the ratio of main 
titration current to negative drift auxiliary current. E.g. when the main 
current is 100.35 ma and the auxiliary current is -25.09 ma, the drift 
rate from calculator 80 must be reduced by a factor of 4, since 
Q.sub.C.sbsb.1 -Q.sub.Co is actually only a measurement of time, not 
current. The resulting correction value Q.sub.corr corresponds to the 
amount of additional charge which would have been used in the titration if 
negative drift had not occurred. Multiplier 83 transmits Q.sub.corr to 
adder 84 which adds Q.sub.corr to Q.sub.titr (transferred from memory 75) 
and transmits the resulting signal to the readout 85. 
It will be apparent from the foregoing that the corrected result signal 
from either subtractor 82 or adder 84 (or from counter 64 via gate 71 when 
there is no drift) is a measurement of titration charge in terms of 
titration time at constant titration current. The display element 85 
preferably includes a conventional converter/multipliers 94 and unit 
factor memory 98 to convert the corrected Q to coulombs, or to moles, or 
micrograms of water or other desired units. 
In an alternative embodiment of the invention the display elements 85 can 
be supplied with a partially corrected Q signal during the titration and 
before the drift correction process is completed. This allows the operator 
to observe approximate results as the titration progresses, so that 
unusual conditions, such as sample addition errors, etc. can be signalled 
early. This can be done for example, by providing an additional memory 
element (not shown) to store the most recently determined drift rate DR 
(or DR/K.sub.1 in case of negative drift) and correcting the Q display 
using the most recent drift rate correction. 
The invention has particular applicability in coulometric titration of 
water by the Karl Fischer reaction, in apparatus of the type described by 
Levy and Seltzer in U.S. Pat. No. 3,732,778, the disclosure of which is 
hereby incorporated by reference. Such apparatus includes electrolysis 
electrodes 34, 36 in contact with the titration mixture for passing 
current through the mixture to generate iodine which is consumed in the 
Karl Fischer reaction, and indicator or detector electrodes 40, 41 in 
contact with the reaction mixture for detecting the endpoint of the 
titration electrometrically. The amount of electric charge required by the 
electrolysis electrodes in order to reach the endpoint state is measured 
to give a measurement of water titrated. By using a constant electrolysis 
current, the coulometric measurement can utilize a timer. Coulometric 
water titrators of this type are described in the above U.S. Pat. No. 
3,726,778, and are commercially available, e.g., Aquatest II Karl Fischer 
Titrator, Photovolt Corporation, New York, N.Y.. 
In such an apparatus, the signal from the detector is inherently a rather 
noisy signal. With conventional filtering methods the signal-to-noise 
ratio is improved by using a long time-constant RC filter system, but the 
titration control is delayed, which can allow the titration to progress 
beyond the endpoint. Back titration must then be employed. In addition 
baseline drift frequently occurs after titration of sample water is 
complete, necessitating both positive and negative stabilization. 
DISPLAY OF RESULTS 
The interaction of the drift correction circuits, drift monitor circuitry 
and display 85 is illustrated in FIG. 5. 
As shown in FIG. 5, readout 85 comprises a digital display panel 85b 
controlled by a counter 85a. The result signals Q.sub.titr +Q.sub.corr, 
Q.sub.titr -Q.sub.corr or Q.sub.titr, from the adder 84 or subtractor 82 
are, as noted above, in units corresponding to time at constant current. A 
convertor/multiplier 94 is provided to multiply the Q signals by the 
appropriate conversion factor (from a conversion factor memory 95) so that 
the display 85b is in desired units such as micrograms of water. In 
construction and operation the titration counter may be counting time at a 
much higher rate than is desired for the display counter. (E.g., if clocks 
60 and 62 and titration counter 64 are counting at 600 Hertz, it may be 
desirable to have the display counter operate at 1 hertz or less, 
particularly when it is desired to display Q during the titration.) 
Converter/multiplier 94 thus can use two conversion factors, a display 
factor to convert titration counter time units to display counter time 
units, and a second conversion factor proportional to the main 
electrolysis current (coulombs/time) to provide a display in units such as 
coulombs, moles, micrograms of water, etc. 
When it is desired to display a corrected Q value continuously during the 
titration, the apparatus can be modified to provide an additional memory 
element (not shown) to store the drift rate (DR, or DR' for negative 
drift) from the most recent titration, and multiplier elements to 
continuously apply that drift rate factor to the Q signal to be displayed. 
If desired, a drift correction factor used for continuous Q displays can 
be revised periodically between titrations by resetting clock 62 and 
counter 64, and clearing memory elements 75, 76, 77, 78 at the end of a 
titration correction sequence, and using the gates 70, 71, 72, 73, 74, 
memories 77 and 78 and element 80 to monitor drift conditions between 
titrations. Such modifications add to the complexity of the apparatus and 
method, and do not improve accuracy, since the drift rate correction 
employed for continuous Q display is ultimately revised by the correction 
process after the actual titration is completed. 
Elements 70-84, 94 and 98 can be assembled using separate integrated 
circuit chips, e.g., gates, memories, adders, subtractors, multipliers, 
etc., or preferably using a conventional arithmetic logic unit for the 
arithmetic operations. Preferably, these elements as well as clocks 60, 62 
and counter 64 are memory locations in a microprocessor. Commercially 
available units such as an Intel microprocessor No. 8085, with two 
programmable read-only memory units (Intel No. 2716) and a random access 
memory (Intel No. 8156), Intel Corp., Santa Clara, California are used in 
a preferred apparatus. It will be apparent, also, that the Q.sub.titr 
memory 75, T.sub.titr memory 76, and Q.sub.Co and T.sub.Co and 
Q.sub.C.sbsb.1, T.sub.C.sbsb.1 memory elements 77 and 78 can be 
constructed using separate display elements, or an appropriate printer, to 
provide the necessary values of Q.sub.titr, T.sub.titr, Q.sub.Co, 
T.sub.Co, Q.sub.1 and C.sub.1, so that the correct computations can be 
carried out separately, either manually or on a separate, appropriately 
programmed digital computer, for example. Also the time periods applied by 
the various gates 70, 71, 72, and 73 can be varied. 
The invention has been described with respect to coulometric Karl Fischer 
titration of water, with an endpoint condition sensed as voltage and 
approached during the titration from a higher endpoint detector voltage so 
that positive drift corresponds to increasing voltage and negative drift 
corresponds to negative voltage. It will be apparent, however, that the 
method and apparatus can be readily adapted to other titrations and other 
endpoint detection systems, such as, for example, the system described by 
Dahms in U.S. Pat. No. 3,723,062. 
An apparatus of the type described was constructed using a 100.35 
milliampere titration current, a-25.09 ma negative drift titration 
current, and a 70 millivolt endpoint in a general construction as 
disclosed in the above-mentioned patent to Levy and Seltzer and the 
application of Kroeger, with the above-mentioned Intel microprocessor and 
memory components, using a 5 second stabilization period at gate 70, a 30 
second period for gate 71, a 45 second period at gate 72 and a 30 second 
period for gate 73. In representative titrations of a sample containing 
450 micrograms of water, with no drift, the mean result was 450 micrograms 
with a standard deviation of .+-.5. With a 450 microgram sample and 
positive drift (due to acetone in the sample) of about 300 
micrograms/minute, the mean result corrected by the invention was 468 
micrograms with a standard deviation of .+-.13. The uncorrected mean 
result was 745 .+-.18. In a similar operation with moderate drift, the 
uncorrected mean Q.sub.titr of replicate samples containing 608 .+-.8.9 
micrograms water was 2200 micrograms, while the apparatus and method of 
the invention gave a mean corrected result of 575 micrograms with a 
standard deviation of .+-.25.6 micrograms. It will be apparent that the 
invention not only provides improved results in coulometric titrations, 
but allows coulometric titrations under drift conditions in which 
coulometric titration was previously impractical.