E V A L U A T I N G M E T R O L O G I C A L C H A R A C T E R I S T I C S

V I S C O S I M E T R I C T I T R O M E T E R S

Yu. A. G a b u n i y a

OF

UDC 389.0 : 543.24

Analytical instruments are normally checked by means of calibrated test compounds or physical equivalents of their compositions and by comparison with reference instruments.

Automatic analytical instruments for measuring the composition of high-molecular compounds often cannot be calibrated or tested by means of these methods, since suitable specimens of such compounds cannot be prepared owing to their instability. Physical equivalents of compositions which fully simulate the measured quantity and ref- erence test instruments are normally not available. Therefore, the automatic instruments are tested by comparing their readings with the results obtained from a parallel chemical analysis carried out under working conditions, or else by calibrating and checking separate units and calculating the total error.

The titration equation has the form of

C~,= kC B V ' (1)

where C A is the concentration of the component measured with the instrument; k is the constant which accounts for the stoichiometric coefficients of the A and B titration reaction A + B ~ C + D; C + D is the concentration of the titrating solution; C B is the amount of the titrated solution (volume, mass); V is the quantity of the sample (vol- ume, mass). The error in determining C a is effected by ACB, AV, and Av. The error Av consists of Av' due to the inaccurate determination of the equivalent titration point and Av- due to inaccurate measurement of the vol- ume or mass of the supplied titrating solution.

In analyzing the titration process it should be noted that quantities figuring in the titration equation are inde- pendent of each other, the functional relationship between them and the measurement result does not change through- out the measurement range, and the vaIues of C B and V change in the titration process only within the limitsoftheir errors.

The measurements ambiguity range C A can be represented by the two-term formula

Ao 7 - +Ts, (2)

CA

where 7 = ACA/CA is the relative error's current value; A 0 = 70CA2 is the zero error (here 70 is the effective error or the additive component); 7s is the sensitivity error (mulfiplicative component).

The effect of AC B and AV on AC A changes proportionately, since they are multiplied by the variable value of v and determine the expression

The error in determining the amount of the supplied titrating solution does not normally change and 7 0 = Av/v z.

(3)

Translated from Izmeritel,naya Tekhnika, No. 7, pp. 69-70, ~uly, 1973.

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The relative errors ACB/CB, AV/V, and Av /v do not differ in their value and amount normally to 0.5-2%, thus making it possible to consider the distribution law of AC A as normal.

Let us determine separate components of the error in measuring concentrations by the titration method. Let us plot a titration curve for Av ' / v , with a quantity v of the supplied titer plotted along the axis of abscissas and the measured property, in this case viscosity ~, plotted along the axis of ordinates. Having found by means of measur- ing instruments the viscosity sensitivity iX 7/, it is possible to determine from the graph the corresponding value of Av'. It is possible to determine iXv'/v analytically by simulating a titration curve, for instance, with the equation

kj v _k.ov_ rl - - ~1o - - - ~ _ [ _ v -[- B - - v ' (4)

where ~ is viscosity; 7/0 is the initial viscosity; v' is the quantity of the titer; k 1 and k z are coefficients; A and B are constants which characterize the titration of the viscose.

By differentiating this equation, we obtain

dr I le~ B kl A

dv ( B - - v ) ~ ( A - k v ) 2 (5)

Having determined the coefficients and the constants and solved (5) with respect to the final v' we obtain the values of Z~v' and ixv ' /v ' . The latter is the relative error due to the inaccurate finding of the equivalent titration point.

If the titer is supplied discretely in drops, the value of ixv' cannot be smaller than the volume of a drop. If the computed value of Av' is smaller than that, it should be rounded off to the volume of a drop. The value of ixv ' /v ' can be effected in addition to the error due to viscous insensitivity, also by the incomplete titration reac- tion which is affected by the rate of the titrating solution supply and the intensity of its mixing. The task of e l imi- nating these errors arises at the development stage, and they usually do not exist in the instrument.

The value of ACB/C B represents the relative error in preparing the titrating solution by an analytical chem- ist. The main sources of the error C B consist of the inaccuracies of laboratory burettes and of rounding off the solu- tion level,s reading to the nearest burette division. The value of AV represents the error in measuring the mass of separate doses of the tested quantity batched by an automatic Titrimeter. This error can be evaluated by weighing and statistical analysis of the results thus obtained. The value of Av represents the deviations of the instrument's readings from the quantity of the actually supplied titer and it is determined by comparing the instrument's read- ings with the quantity of titer measured with a laboratory burette or by weighing.

In the course of an instrument, s utilization it is more convenient not to check the error of its separate units, but to compare its readings with the results of a parallel chemical analysis, i.e., by comparing CAinst and CAchra.

By subtracting these values we obtain ACAsum , which is affected by the errors of both analyses and by Ca.

Having analyzed the difference ACAsum , it is possible to determine C~sum, the deviation o clam, and the in-

strument,s root-mean-square deviation

= ]fOsum- Ochre (6) The value of AC A can be found from the expression

AC A -~- kcr, (7)

where k is the entropy coefficient. For a normal distribution k = ~ = 9.07, By rounding it o f f to integers we obtain k n = 2.

The obtained value of AC A can be compared with

ACA = A0 + ~s CA (8)

thus checking the validity of the adopted definitions.

The values figuring in (8) can be found by the above-mentioned method of adding up particular errors.

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In computing o it is preferable to determine C A not only for a single concentration, but for a group of various values, since in the course of the instrument's utilization the value of CA changes continuously.

We have considered the random errors of viscosimetric titration. System errors can be reduced by calibration to a minimum and considered as random ones. Since titrimeters of the above type are discrete ins~uments, they can measure only slowly-changing quantities. For determining possible dynamic errors it is necessary to have data on the tested quantity's rate of change.

LITERATURE CITED

1. "fu. A. Gabuniya and K. S. Lyapin, in: Automation of Chemical Production [in Russian], No. 1, NIITEKhIM, Moscow (1970).

2. Yu. A. Gabuniya, K. S. Lyapin, and V. P. Dobrovol'skii, Author's Certificate No. 174430, Byui1. Izobr., No. 17 (1968).

3. P.V. Novitstdi, Foundations of Measuring Devices, Information Theory [in Russian], ~nergiya, Leningrad (1968).

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