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Towards a Procedural-Instrumental Discourse on Quantitative Chemical Analysis:Chemistry Insights into the Validity of Objective Investigations and Student Evaluations

Paper URL:

Published in: Research Journal of Contemporary Concerns, (Cotton College, Guwahati–781001, Assam, India) Vol. 3, page 46 (2005)

Rituraj Kalita

Department of Chemistry, Cotton College, Guwahati-781001, Assam, India

Presentation Finalized on: August 20, 2006

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Errors in Quantitative Chemical Analysis (QCA)

  • Quantitative chemical analysis is the branch of science dealing with measurements of the amounts and the concentrations of chemical substances.

  • It is prone to diverse kinds of errors: determinant errors such as reagent errors, instrumental errors, errors of method (procedure), personal and operational errors, and also the so-called indeterminate (random) errors of unknown origin.

  • The errors due to reagents, volumetric instruments, weights & balances are all due to errors in our tools of measurement; so can be considered as generalized instrumental errors.

  • Errors of method (procedural errors) are errors inherent in the formally adopted procedure (e.g., incomplete precipitation), and are thus distinguished from the personal & operational errors arising from the incompetence of the individual analyst.

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Extent of Such Errors Faced by You & Me

  • The random (indeterminate) errors are very small in most cases

  • The personal & operational errors (either small or large) depend on the competence, care & expertise of the individual analysts; so avoidance of such errors is their own responsibility

  • As chemistry students and researchers/ teachers in South Asia, we all have however encountered very significant extent of generalized instrumental errors, due to faulty reagents, volumetric instruments, weights and balances. Such errors are, thus, not only a subject matter of philosophical deliberations.

  • It’s here common for burettes & pipettes to show difference of 0.5-0.6 mL (even 1.0 mL being not unusual) while measuring a volume of 25 mL; a 2% - 4% error being introduced thereby!

  • In weighing 1.0 g of a reagent, weighing error of 50 mg is not at all unusual, introducing some 5% error thereby!

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The Procedural-Instrumental Errors: Sabotaging beyond the Scope of the Individual Analyst

  • Personal and operational errors, such as due to parallax error, overheating or overcooling, bumping of solutions etc., can be eliminated by care in manipulations and through experience.

  • The instrumental & reagent-origin (generalized instrumental) and procedural errors (here both clubbed as PI errors) in the analysis, however, sabotage the accuracy of results in ways out of reach of the usual care & expertise of the individual analyst.

  • These errors must be corrected by specific techniques (such as pipette-burette volume comparison, weight-comparisons with reference weights) that go beyond the care and expertise of the individual analyst in the given chemical-analytical process

  • Students’-evaluations in QCA aims to measure the students’ ability to avoid personal-operational errors. So, influence of procedural-instrumental errors must be nullified beforehand.

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What Corrective Measures Do We Actually Need? The Impracticality of Complete Corrective-Measures

  • Naturally, we might be inclined to think that a complete set of corrective-measures are necessary: all burette-readings and pipette-readings must be converted to international-standard millilitres, all measured-weights must be converted to IUPAC-standard grams, all weighed-solid weights be multiplied by their percentage purities and so on. It’d be a very big exercise.

  • Unfortunately, such a complete correction is also practically impossible. Sitting in a small South Asian college/ university, it is just impossible to tell which burette (if any at all) has the actual millilitre markings, or which 1g wt. is actually 1.000 g.

  • Fortunately, no such complete correction is necessary. We’ll show that only a small set of corrective measures are enough.

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Procedural-Instrumental Discourse (PID): Deciding the Bare Minimum of Procedural-Instrumental Corrective Measures for the Analysis in Hand

  • Similar corrective measures are necessary also for quantitative measurements in non-chemical sciences, such as in physics

  • Thus there is a necessity to have a branch of science that would work towards finding the minimum requirement of corrective measures for any given quantitative determination experiment.

  • PID, this branch of science, would give the mathematical deduction (may also be called PID), performed about the given quantitative experiment, using which we can find this required bare minimum of procedural-instrumental corrective measures.

  • Thus, PID shows that if the aim of the experiment is to find just the ratio of concentration of an acid solution neutralising a base solution, finding the burette-measured volume of the pipette suffices as the lone PI-corrective measure (assuming BUA).

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Procedural-Instrumental Discourse (PID): Not an Issue of Novelty, but of Systematisation

  • This is not meant here that the knowledge coming within this proposed branch of science didn't already exist in earlier scientific discussions within physical and chemical sciences.

  • However, its resulting decisions were mostly assumed or considered as understood, and hardly were formally and rigorously derived. It’s in spite of the possibility of rigorous, mathematical derivations in this field, as has been shown here.

  • Thus, there has been a lack of formalisation in the area of knowledge pertaining to suchdiscourses;a recognition of this area as a branch of science should certainly help.

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Inside-View of Procedural-Instrumental Discourse: Linearity Assumptions such as BUA & WBPA

  • To actually work with PID, it is best for us to assume some linearity assumptions, which, even though not perfectly valid themselves for most instruments and analytical procedures, offers a sea of improvements over a no PI-correction situation

  • For example, for many burettes (particularly when we’re measuring a small range of volume such as 22-30 ML) we can safely assume the Burette Uniformity Assumption (BUA), which states that the values of volumes (say, 20.4 mL & 30.6 mL) measured by asingle burette being used are proportional to their actual volumes (say, 20.2 mL & 30.3 mL).

  • Safely valid for most calibrated weight-balance systems, the Weight-Balance Proportionality Assumption (WBPA) stresses a similar proportionality between reported & actual weights.

  • In a solid, pc. purity may be assumed to be uniform throughout

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Inside-View of Procedural-Instrumental Discourse: PID Derivation for Ratio-Determn. of Acid-Base Conc.

  • Let Va, Vb are the solution volumes of the acid and base respectively (having basicity & acidity unity for each), and Sa, Sb are their molarities. So Va Sa = Vb Sb + d, where d is the additive indicator (procedural) error. As d is considered negligible, so we have Va Sa = Vb Sb .  Hence the concentration ratio  Sa / Sbis actually equal to Vb / Va (where Vb & Va are actual volumes, not necessarily the instrument-measured volumes).

  • Let acid volume be measured with a definite burette, and base volume with a definite pipette. Assuming BUA, let b (let's call it the burette-factor) be the ratio of the burette-marked mL and the actual (true) mL value. So Vb = b V'b , where V'b is the burette-measured volume-value. Similarly let p (let's call it the pipette-factor) be the ratio of the pipette-marked mL and the actual mL value. So Vb = p V'b , where V'b is the pipette-measured volume-value (For single-mark pipettes, there's no need of a pipette uniformity assumption).Thus we get,  Sa / Sb = (b V'b) / (p V'a) = (b / p).(V'b / V'a) 

  • Now, if the pipette volume is calibrated in terms of the burette volume, i.e., if the pipette filled up to its mark is discharged into the burette so as to measure the pipette volume (e.g., 24.6 mL instead of the manufacturer-defined 25.0 mL) in terms of burette readings, then the corresponding newly defined pipette-marked mL will become exactly same as the burette-marked mL, which means that the factor p will now have identical value with b. Thus (b / p) will now equal unity, and Sa / Sb equals simply (V'b / V'a). Thus, by this simple corrective procedure the instrumental error has been completely eliminated (provided BUA is valid for the burette used). 

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PID Concept in Student Evaluations: Evaluator-Evaluated Harmony (EEH) as PID-Comparison Desirability Requirement for the Teacher & the Student

  • Other than in the search for the exact truths about nature, another, much more down to earth application of the concepts of PID is in the case of student evaluations, such as in (chemistry or othersciences) practical examinations.

  • Applying PID to the teacher's (evaluator's) determination experiment, we may know how the evaluator’s result will be influenced by the PI-shortcomings. Again applying PID to the student’s experiment, we may similarly know howthe resultfound by the evaluated will be influenced by the PI-factors.

  • So, the evaluator must plan her own procedural-instrumental (PI) corrections and instruct the evaluated (s) to perform their PI-corrections as well,in such a way so that in absence of personal, operational and indeterminate errors, the evaluator and the evaluated gets (practically) the same result.

  • Such sort of a planning may be said to contain Evaluator-Evaluated Harmony (EEH). Thus, application of the PID concept to the field of student evaluationsgive rise to the concept of EEH. EEH is a must in any examination process.

  • In a practical examination, one tests student’s expertise in avoiding personal, operational & indeterminate errors. Unless PI-sabotage dies, it’s impossible.

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Inside-View of Evaluator-Evaluated Harmony: An EEH-Theorem for Titrimetric Glucose-Estimation

  • (a) In student's determination of the amount of glucose supplied (in the form of its solution) to the student (evaluated person) by the teacher (evaluator), EEH is preserved from the procedural side if the teacher finds the glucose amount from weighing and the student prepare an standard glucose solution of comparable concentration by weighing using the same glucose source, then standardize the Fehling solution with that, and then finds the unknown glucose by a similar titration with the Fehling solution.

  • (b) Following this procedure, EEH is preserved from the instrumental side if (i) the weight-balance system has an uniformly proportional error (i.e., obeys WBPA), (ii) this WBPA-proportionality of error being equal for both the teacher & the student, (iii) the student's lone burette obeys BUA (even if the lone pipette-volume is not burette-measured), (iv) the student's volumetric-flask volume must be volume-measured (or newly volume-marked) using the student's burette, and (v) the solid glucose source has an uniform purity in all its samples (providedthe Fehling solution is measured with the burette only &the glucose solutions by the lone pipette only)

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Inside-View of Evaluator-Evaluated Harmony: EEH Derivation for Titrimetric Glucose-Estimation Expt.(may see

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Inside-View of Evaluator-Evaluated Harmony: EEH Derivation for Titrimetric Glucose-Estimation Expt.(may see

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Chemistry Insights into Evaluations in General: Is the Generalized-EEH Conserved in All Examinations?

  • The concept of EEH may be generalised to discuss exams on qualitative determinations, and even theory examinations!

  • Thus, in a qualitative determination exam, the students find what constituents are present in a given sample. The teacher generally knows this constitution from the manufacturer, who might specifywrongly! Is generalised-EEH preserved there?

  • Similarly, a solution of Pb(NO3)2 as an unknown salt, unexpectedly gives a ppt. with BaCl2 reagent, insoluble in dil. HNO3, confirming SO42–. Is the student taught to deal with it?

  • In a theory exam for school students can we, as the evaluators, expect them to go beyond the mistakes (PI-errors) in their school textbooks (instruments), and still write correct answers?

  • Something akin to EEH must be missing in those situations!

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Chemistry Insights into Knowledge in General: Are We Predisposed to Arrive at the Actual Truths?

  • Some philosophical generalisation seems to be possible also for the concept of PID dealing with search for the objective truth.

  • Recognition of and discourse on the procedural-instrumental drawbacks of quantitative determinations naturally lead us to doubt our qualitative knowledge (in chemistry and other natural sciences) as well; there may be cases where such doubt is true!

  • Qualitative knowledge on some social science fronts may be similarly blocked or corrupted by generalised-PI problems!

  • Some sort of procedural-instrumental drawbacksmight be existing, within our minds and within the social institutions inhabited by us, hindering our quest of truth or of knowledge in the social, socio-political and socio-economic fronts as well, thereby affecting our day-to-day decisions & actions in life!

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1. “A Text-Book of Quantitative Inorganic Analysis”, 3rd ed.; Vogel, A. I.; Longman Group Limited, London, 1972

2. “Errors, Measurements and Results in Chemical Analysis”; Eckschlager, K.; Van Nostrand Reinhold, London, 1961

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Supplementary Materials:

The two PID-EEH derivations overviewed here are being stored (for space and time constraints) on the web, in the complete and rigorous form, at

(This presentation is also accessible therefrom)

Tip: Type the complete URL above before pressing Enter

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My Acknowledgements goes to:

  • Biological Evolution and Nucleic Acids etc.: for providing me with a human life & thought processes

  • The Human Civilization: for providing me with the inquisitiveness and the spirit of systematic enquiry

  • Department of Chemistry, Cotton College, Guwahati: for allowing me to apply EEH concepts on student evaluations during chemistry-practical examinations