Calculation of uncertainty in titrimetry Ivan Špánik

Transcription

1 Calculation of uncertainty in titrimetry Ivan Špánik Problem A solution of hydrochloric acid (HCl) is standardised against a solution of sodium hydroxide (NaOH). The NaOH is titrated against the titrimetric standard potassium hydrogen phthalate (KHP). It is assumed that the NaOH concentration is known to be of the order of 0.1 mol L 1. The end-point of the titration is determined by an automatic titration system using a combined ph-electrode to measure the shape of the ph-curve. Procedure Approximately g of the previously dried KHP is weighed to achieve a titration volume of 19 ml NaOH. The KHP is dissolved in 50 ml of DI water and then titrated using the NaOH solution. A titration is performed using automated burette with potentiometric indication of endpoint. 15 ml of the HCl solution is transferred by volumetric pipette. The HCl solution is diluted with de-ionised water to volume 50 ml solution in the titration vessel. The same automatic titrator performs the measurement of HCl solution. 1

2 Uncertainty sources Uncertainty model Uncertainty sources 2

3 m(khp) mass KHP Measured value of weight: g Non-linearity of the balance (declaration): ± 0.15 mg Conversion to a standard deviation using a rectangular distribution P(KHP) purity of KHP Is given by producer. He declares purity 100 % ± 0.05% We have to consider rectangular distribution Uncertainty sources 3

4 V(NaOH) Standardisation (consumption of 19 ml) Calibration: given by producer. He declares ucertainty of volume 0.03 ml. We have to consider triangular distribution Temperature: possible temperature variation is ± 4 C and is treated by rectangular distribution V(NaOH) Standardisation (consumption of 19 ml) End point detection: error can be caused by oxidation of atmospheric CO 2. Titration is performed in Argon atmosphere so no error is observed. V(NaOH) Titration (consumption of 15 ml) Calibration: given by producer. He declares ucertainty of volume 0.03 ml. We have to consider triangular distribution Temperature: possible temperature variation is ± 4 C and is treated by rectangular distribution 4

5 V(NaOH) Titration (consumption of 15 ml) End point detection: error can be caused by oxidation of atmospheric CO 2. Titration is performed in Argon atmosphere so no error is observed. Uncertainty sources M(KHP) Molecular weight sum formula: C8H5O4K Assumption: triangular distribution M KHP = g/mol 5

6 Uncertainty sources V(HCl) taken by pipette 15 ml Calibration: given by producer. He declares ucertainty of volume 0.02 ml. We have to consider triangular distribution Temperature: possible temperature variation is ± 4 C and is treated by rectangular distribution Calculation Uncertainty evaluation 6

7 Calculation Uncertainty evaluation Uncertainty evaluation Expanded uncertainty 7

8 Calculation of uncertainty in HPLC determination of caffeine in coca cola Ivan Špánik Problem A simazine is determined using HPLC. Since suggested concentrattion in waste waters is high, no sample preconcentration is required. The concentration is determined using calibration curve. Simazine Measurand: Uncertainty sources The specification of the measurand is according the SOP, DIN/ISO methods or laboratory methods. Identification of sources of uncertainty For the identification of the sources of uncertainty a cause effect diagram is very useful. From this diagram the relation between the sources of uncertainty can also be seen. 8

9 Uncertainty sources The uncertainty consists of three parts: The determination of the mass of simazine; The purity of the chemical; The measurement of volume - depends on the fabrication tolerance, the temperature and the repeatability. Uncertainty net weight of simazine According to the specification of the manufacturer of the balance the tolerance amounts to g (standard deviation). u mass = 0.1mg 9

10 Uncertainty purity of chemicals According to the specification of the manufacturer the purity amounts to 98.5% ± 1.5% (equal to ± 0.015). If a normal distribution and a confidence interval of 95% are assumed these result in u purity = 0.015/1.96 = Uncertainty volume measurement This uncertainty (100-ml graduated flask) consists of three parts: 1. Calibration by the manufacturer. According to the manufacturer s instructions the tolerance at 20 C is 100 ± 0.1 ml. With the assumption of a rectangular distribution (declared by the manufacturer) the uncertainty is Uncertainty temperature in the laboratory. If the graduated flask with the solution is not kept at 20 C the influence of temperature has to be considered. The coefficient of thermal expansion g of water amounts to 1.806x10-4 / C; therefore, With the assumption of a rectangular distribution the uncertainty is 10

11 The combined uncertainty of the volume measurement (100-ml graduated flask) is: Relative uncertainty of the stock solution and relative individual contributions: 1 stock, 2 purity, 3 mass, 4 volume. The concentration of the stock solution is: 11

12 The combined uncertainty of the stock solution is: Uncertainty sources Pipette Analogous to volumetric flask: 12

13 Uncertainty sources Calibration curve Five concentrations (125, 250, 350, 500, 600 mg/l) were used, each solution was injected three times. The result of the linear regression is Y= R= Uncertainty is expressed as uncertainty of slope and intercept Total combined uncertainty 13

14 Expanded uncertainty Expanded uncertainty A coverage factor k =2 is selected: U expanded = 2 x 13.5 = 27 mg/l Presence of Simazine equals to (500 ± 27) mg/l Uncertainty Relative uncertainty of the stock solution and relative individual contributions: 1 total, 2 stock, 3 pipette, 4 calibration curve 14