THE USE OF Z FACTORS IN GRAVIMETRIC VOLUME MEASUREMENTS Author: T. Mautjana NMISA Private Bag X 34 Lynwood Ridge; 0040 Email: tmautjana@nmisa.org Phone: 012 841 4798; Fax: 012 841 2131 Abstract Using gravimetric method to determine volume is based on the determination of mass with a balance of water delivered or contained. This method requires monitoring of the environmental conditions. There is a need to convert mass of the liquid to volume which must take into account the density of the liquid and evaporation during the cycle time. The Z factor must take into account the air density and density of the mass pieces used to calibrate the balance and the density of water adjusted to local temperature and pressure. This paper discusses the equation for calculating volume conversion factors (Z) and gives typical examples for different liquids. 1. Introduction Volume measurements are important in industrial and analytical measurements operations. The instruments are common in field like chemistry, pharmacy, biology (biochemistry, microbiology), etc. It is important that these instruments give reliable and accurate results during operation to give the end user confidence in measurement results. The instrument would normally get calibrated using gravimetric method which links them directly with the SI unit of mass [1]. It is therefore vital that possible errors be eliminated through the use of correct method and it is important to understand formulae (their conditions) and any applicable correction factors which might be necessary to give accurate results. 2. Gravimetric method The standard method used by NMI s and accredited laboratory to determine volume of high accurate instrument is to weigh the liquid. The method requires the weighing of empty and full volumetric measure or the content of the measure/instrument can be emptied into a weighing vessel following a specified procedure [1]. This method should be carried out in a laboratory with stable environmental conditions. Temperature control is recommended as temperatures of liquid and the measure/instrument must be stabilized, and monitored.
The method requires liquid of high purity to be used as density has a large influence on the calibration result. Thus high accuracy of temperature measurement is also important [2]. Volume measurements using gravimetric method require weighing the contents of a liquid of known temperature and density. The liquid mass measurements need to be converted into volume from the knowledge or determination of densities of the liquid. The conversion from mass to volume must take into account the density of the liquid, air buoyancy as well as the evaporation during the weighing cycle [4]. Volume at the measured temperature can be calculated from V i = (M i + e)z (1) Where M i e Z is the mass as read on the balance or differences in balance indication average evaporation loss during the weighing cycle is a conversion factor incorporating density of water, air density at test temperature and barometric pressure Evaporation that occurs during the measurements depends on temperature, humidity and cycle time. It has noticeable effect on small volume measurements less than 50 µl [5]. Volume measurements require that reference temperature (generally 20 o C) be reported as volume depends on the temperature. Reference temperature is normally the temperature at which volume measure is intended to contain or deliver its nominal volume. Thus volume at measured temperature would generally require to be converted to reference temperature such as at 20 o C, therefore equation 1 would become 2.1 Estimation of the Z factor V 20 = (M i + e)z[1 γ(t 20)] (2) The Z factor is not just equal to the density of liquid adjusted to the local temperature and pressure. It also takes into account the air density and density of weights used to calibrate the balance. Z factor is calculated as Where 1 Z = [( )(1 ρ A )] (3) ρ L ρ A ρ B ρ A - density of air ρ L - density of the liquid ρ B - density of the weights used for balance calibration
The air density (ρ A ) to be considered is (in principle) the density of the air inside the volumetric instrument and displaced when the instrument is filled with liquid. It is generally assumed that the ambient air density does not change significantly between and during weighing. This ensures that buoyancy effect exerted on the instrument is constant. If the ambient air changes, the true mass of the instrument must be determined for each weighing [3]. The environmental or ambient conditions influence the air density determination. Density of the liquid can be determined or obtained from formulae given in literature. Batista and Paton [1] detailed differences in volume as a result of using different density formulae which are common in practice. Density of the weights/mass pieces is presented in the calibration certificate of the weights or alternatively according to OIML R111-1, it can be deduced from the weight class used for balance calibration [7]. 3. Typical Examples of Z factor Calculation Values of the conversion factor Z (µl/mg) as a function of temperature and pressure as given in literature is mainly for distilled water. When other liquids other than distilled water are used or measured, correction factors (Z factors) for the specific liquid would have to be determined. The conversion factors presented in tables 1 to 4 below present typical examples of corrections to be applied for different liquids at specific temperatures and atmospheric pressure. Table 1: Values for Z factor as a function of temperature and pressure for distilled water Distilled water ρ w (999.10 to 997.04)kg/m 3 15 1.0017 1.0018 1.0020 1.0020 20 1.0026 1.0027 1.0029 1.0029 25 1.0038 1.0039 1.0040 1.0041 Table 2: Values for Z factor as a function of temperature and pressure for sea water Sea water ρ w (1026.021 to 1023.3873)kg/m 3 15 0.9754 0.9755 0.9757 0.9757 20 0.9766 0.9766 0.9768 0.9768 25 0.9779 0.9780 0.9781 0.9782 ρ w sourced from [6]
Table 3: Values for Z factor as a function of temperature and pressure for Toluene Toluene ρ w (869 to 862.3)kg/m 3 15 1.1545 1.1546 1.1549 1.1549 20 1.1547 1.1547 1.1550 1.1550 25 1.1608 1.1609 1.1611 1.1612 Table 4: Values for Z factor as a function of temperature and pressure for Benzene Benzene ρ w (884 to 873.8)kg/m 3 15 1.1323 1.1324 1.1326 1.1327 20 1.1387 1.1388 1.1390 1.1391 25 1.1455 1.1456 1.1458 1.1459 Effect of Z factor on the volume measurement indicated as the difference from nominal; where positive indicate an increase in volume while negative sign indicate a decrease in volume. Table 5 below provides various volume measures at a temperature of 20 o C and atmospheric pressure of 864 hpa corrected with respective Z factors. Table 5: Effect of Z factors on volume Measurement Z (Distilled Z (Sea H 2 0) Z (Toluene) Z (Benzene) H 2 0) (M i + e) V (ml) V (ml) V (ml) V (ml) 0.01 0.000027-0.000234 0.001547 0.001388 0.05 0.000135-0.00117 0.007735 0.00694 0.1 0.00027-0.00234 0.01547 0.01388 0.25 0.000675-0.00585 0.038675 0.0347 0.5 0.00135-0.0117 0.07735 0.0694 50 0.135-1.17 7.735 6.940 100 0.27-2.34 15.470 13.88 250 0.675-5.85 38.675 34.7 500 1.350-11.7 77.350 69.4 4. Conclusions It could be seen in table 5 above that incorrect use of correction factor can have a significant influence in volume determination. Table 5 also showed that the effect increases with an increase in nominal volume. It is therefore critical for one to ensure that the volume correction factors applied are correct for the intended liquid.
5. References: 1. Batista E and Paton R (2007). The selection of water property formulae for volume and flow calibration. BIPM and IOP Publishing Ltd, Metrologia 44 (2007) 453 463. 2. B F van der Merwe, Calibration of volume standards, November 2008, NML06-0122 3. EURAMET cg-19. Calibration guide: Guidelines on the determination of uncertainty in gravimetric volume calibration, version 2.1 (03/2012), ISBN 978-3-942992-24-4 4. Gilson guide to pipetting, Second Edition. 5. ISO 8655-6:2002(E), International Standard, Piston-operated volumetric apparatus, Part 6: Gravimetric methods for the determination of measurement error 6. ITTC- Recommended Procedures: Fresh water and Seawater properties.(2011) Revision 02 7. OIML R111-1. Edition 2004 (E). International Recommendation. Weights of class E 1, E 2, F 1, F 2, M 1, M 1-2, M 2-3, and M 3. Part 1: Metrological and technical requirements