How to Calculate MU By Sanjay Tiwari Chief

How to Calculate MU? By Sanjay Tiwari Chief Chemist Central Agmark Laboratory Nagpur

Uncertainty • “A parameter associated with the result of a measurement, that characterizes the dispersion of values that could reasonably be attributed to the measurand. ” • In general use the word uncertainty relates to the general concept of doubt. Knowledge of the uncertainty implies increased confidence in the validity of a measurement result.

Uncertainty components • In estimating the overall uncertainty, it may be necessary to take each source of uncertainty and treat it separately to obtain the contribution from the source. • Each of the separate contributions to uncertainty is referred to as an uncertainty component. When expressed as a standard deviation, an uncertainty component is known as standard uncertainty.

Error and uncertainty • It is important to distinguish between error and uncertainty. Error is defined as the difference between the result and the true value of the measurand. • As such, error is a single value. In principle, the value of a known error can be applied as a correction to the result. • Uncertainty on the other hand, is a quantification of the doubt about the measurement result. • In general the value of uncertainty can not be used to correct a measurement result.

Ways to estimate uncertainties • No matter what are the sources of uncertainties, there are two approaches of estimating them: • ‘Type A’ and ‘Type B’ evaluations. In most measurement situations, uncertainty evaluations of both types are needed.

Ways to estimate uncertainties contd. • Type A evaluations - uncertainty estimation using statistics (usually from repeated readings) • Type B evaluations - uncertainty estimation from any other information. This could be information from past experience of the measurements, from calibration certificates, manufacturer’s specifications, from calculations, from published information, and from common sense.

EVALUATION AND EXCPRESSION OF UNCERTAINTY IN THE DETERMINATION OF ACID VALUE IN MUSTARD OIL 1. Method BIS 548 Part I 1961 Weigh Sample 25 ml Alcohol Result Add few drops of 1% Phenolphthalein indicator Titrate with. 1 Nao. H Soln

2. Mathematical Model Acid Value = 56. 1 x. Vx N Where V = Volume in ml of standard Nao. H required for sample N = Normality of standard Nao. H Solution W = Weight in grams of the oil for the test

3. Identification of sources of uncertainty (fishbone diagram) Weighing Balance Calibration certificate Repeatability Acid Value Repeatability Temp. Purity Burette Pipette Standard Titration for (Potassium Sodium Pthalate) Sample

4. Information Available • Uncertainty of Weighing Balance • Tolerance of Burette at 27 degree Celsius • Tolerance of pipette at 27 degree Celsius • Purity of Standard Potassium Sodium Pthalate

5. Set of values from previous analysis Acid Value Mass Of Sample Titration Value 10. 0470 1. 10 0. 64 10. 0380 1. 10 0. 64 10. 0500 1. 10 0. 64 10. 2100 1. 15 0. 66 10. 1182 1. 15 0. 67 10. 1212 1. 05 0. 61 10. 0986 1. 10 0. 64 10. 0202 1. 05 0. 62 10. 0790 1. 10 0. 64 10. 0480 1. 15 0. 67 SUM 100. 8302 11. 05 6. 43 Mean 10. 08302 1. 105 0. 643 S. D. Standard Uncertainty 0. 056436273 0. 036893239 0. 019465068 0. 01785958 0. 011675076 0. 006

• Uncertainty associated with Weighing balance: (1)From Calibration Certificate of weighing balance no. Axis LCGC AGN 204, calibrated on 24. 06. 2011 by STQC, Mumbai. Uncertainty = 0. 0002 gm Std. uncertainty = 0. 0002/ 3 = 1. 15 x 10 -4………………. . (i) (ii) From Repeatability(n=10) Standard Deviation = 0. 056436273 Standard Uncertainty = 0. 01785958 = 1. 78 x 10 2 …………(ii) Combined Uncertainty of balance for (i) and (ii) 4)2 + (1. 78 x 10 2)2 (1. 15 x 10 1. 78 x 10 -2

7. Uncertainty associated with Titration of Sample: (i) Burette (ii) Temperature (iii) Repeatability (i) Burette: Cap 50 ml Uncertainty = 0. 002 Standard Uncertainty = 0. 002/ 6 = 8. 16 x 10 -4 ………………. . (1) (ii) Temperature: Temp at the time of titration = 240 C here the equation of x t x v is used Where is the sensitivity coefficient for expansion of water, t is the difference in temp and v is the mean volume for titration of sample. = 2. 1 x 10 -4 ml /0 C t = 30 C (burette is calibrated at 270 C whereas titration is done at 240 C) v = 1. 105 ml Std Uncertainty = 2. 1 x 10 -4 x 3 x 1. 105 3 = 4. 02 x 10 -4 ………………. (2)

(iii) Repeatability of titration No of titrations (n=10) Titration values = 1. 1, 1. 15, 1. 05, 1. 10, 1. 15 Mean = 1. 105 ml Standard Deviation = 0. 03689 Standard Uncertainty = 0. 01167 = 1. 17 x 10 ‑ 2……………. (3) Combined uncertainty of (i), (ii) and (iii) = (8. 16 x 10 -4)2 + (4. 02 x 10 -4) +(1. 17 x 10‑ 2) = 1. 17 x 10 -2

8. Uncertainty associated with Standard Potassium Hydrogen Phthalate (KHP) Purity of Potassium Hydrogen Phthalate Standardization of Sodium Hydroxide solution Must be dried at 1200 C for 2 hrs Weigh KHP Titration with Nao. H Purity = 99. 96 % Uncertainty = 0. 05% (Coverage factor K = 2, confidence level 95%) Standard Uncertainty = 0. 0005/ 3 = 2. 9 x 10 -4

11. Summary Table Sl. No. Uncertainty Source Mean Estimated Standard Value Uncertainty Ux Std Uncertainty/Mean Ux/Mean 1 Sample Mass 10. 08302 gm 1. 78 x 10 -2 1. 77 x 10‑ 3 2 Titration Sample 1. 105 ml 1. 17 x 10 -2 1. 06 x 10 -2 3 Purity of Potassium 0. 1 N Hydrogen Pthalate 2. 9 x 10 -4 2. 9 x 10 -3

12. Overall Combined Uncertainty Uc/0. 643 = (1. 77 x 10 -3)2 + (1. 06 x 10 -2)2 + ( 2. 9 x 10 -3)2 Uc/0. 643 = 1. 11 x 10 2 Uc = 0. 643 x 0. 011 Uc = 0. 0070 13. Expanded Uncertainty at coverage factor K = 2 = 0. 0070 x 2 = 0. 014 14. Reporting of results Acid Value = 0. 64 0. 014 Coverage factor (k) = 2 at 95% confidence level.