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2	Outline Theory Immediate benefits of dilution-by-mass Dilution-by-mass Long term benefits of dilution-by-mass How to achieve long term benefits How dilution-by-mass is applied at IMR Test Labs Summary
3	Theory Dilution-by-mass (DBM) procedures employ the analytical balance for determining the mass of analytical solutions. The mass (m) of the solution is then converted to its corresponding volume (V) via the density equation D = m / V, where the density (D) of the solution is already known. This technique is ideal for wet chemistry techniques which require large dilutions such as ICP-AES.
4	Immediate Benefits of DBM In general, DBM enables better accuracies than volume-to-volume dilutions especially for samples that require high dilutions. Volumetric flasks are not always accurate. Automatic pipettes are efficient but not accurate. Analytical balances are very accurate. A trained technician can produce DBM dilutions in almost the same amount of time as volume-to-volume dilutions.
5	Inaccuracies of Volumetric Flasks We’ve seen as much as 1 mL variation in 100 mL HDPE flasks and 0.5 mL in Class A 100 mL glass volumetric! This could result in as much as 1% error in samples requiring large dilutions.
6	Calibration of Flasks First Step: Mass of clean, dry flask (and lid if used) Record flask ID and mass of flask. OR Permanently mark the flask with this mass. NOTE: The mark cannot change the mass of the flask or if it does the change in mass must be taken into account as the marking occurs.
7	Calibration of Flasks Second Step: Accurate volume of flask (two techniques) Mark a new meniscus at exactly 100.00 mL. Calculate mass of 100.00 mL of DI-water at a constant temperature using density of water (CRC) and density equation D = m/V. Fill the flask with this mass of water and permanently mark new meniscus without affecting flask mass. OR Calculate the actual volume of the flask. Fill the flask to mark and determine the mass of water required. Calculate the actual volume of the flask and permanently mark volume on flask or record with flask ID.
8	Marking Flasks Etch (truly permanent, but changes mass) For mass of clean, dry flask etch 1 significant figure at a time and reweigh. Record 4 significant figures. For meniscus etch a very small mark near the front of the flask. This mark can be circled or colored in with Sharpie marker. Sharpie marker (not so permanent, but does not affect mass) Works well in combination with wax pencils. Can’t use acetone to wash flasks or you’ll loose your marks.
9	HDPE Flasks Volumes of these flasks can change over time. Factors affecting volume Heat Prolonged exposure to concentrated acid Need to recalibrate flasks depending on usage.
10	Density of Undiluted Sample Density is the link between mass and volume of any solution. Density of solution = mass of solution / volume of solution Note: Flask must have clean surfaces so that the mass of clean, dry flask recorded on flask is accurate.
11	Make a Dilution Use an automatic pipette to measure the approximate volume of undiluted solution into a tared flask or container and weigh. Determine the Corrected Aliquot Volume using: D = density of undiluted sample m = mass of aliquot V = m/D Use the Corrected Aliquot Volume for all future calculations of diluted sample. Bring dilution to volume in calibrated flask.
12	Make a Dilution (cont.) No automatic pipette available….no problem! Rather than using an automatic pipette the required mass of solution could be added to the container by a dropper. As long as the mass and density is known, the corrected aliquot volume can be determined.
13	Automatic Pipette Calibration Tolerance Control limits from the manufacturer of a 100 - 1000 µL pipette
14	Effect of Inaccuracy of Pipettes
15	Analytical Balance Calibration Tolerance Control limits from the manufacturer of an analytical balance
16	Effect of Inaccuracy of Balance Inaccurate mass by 0.005 g (50 times higher than repeatability of balance) yields results with less than 0.1% relative error.
17	DBM and Calibration Standards With known densities and concentrations of stock standards the exact concentration of each analyte in the standard can be calculated. Example: Need 100 mL of a standard for Cr at 25 µg/mL. The stock solution is 1000 µg/mL with a density of 1.0297 g/mL. Set pipette to deliver 2.5 mL and weigh the aliquot and calculate. (M₁V₁ = M₂V₂) 1000 µg/mL x 2.5337g = M₂ x 100 mL 1.0075g/mL M₂ = 25.15 µg/mL Cr
18	DBM and Calibration Standards Improved correlation coefficients Analysis of certified reference materials are closer to certified values.
19	Long Term Benefits of DBM Eliminates the need for calibrated flasks. Enables maintenance of similar matrix no matter the sample size provided so as to best match calibration standards. Reduces prep volumes and dilution volumes. Reduces reagent costs Reduces acid waste disposal costs
20	To achieve these benefits… First need to be able to consistently make sample solutions of the same density. Theoretically, digestions of the same mass of sample and same acid combinations and volumes should have the same densities. i.e. all digestions consisting of 0.5 g sample with 15 mL HCl and 5 mL HNO₃ brought to volume in 100 mL flask Collect data for similar digestions and determine an average density for each group.
21	Example Any suitable sized container can be used to make the dilution. No longer need calibrated flasks. Sample solution is still matrix matched to standards.
22	Example (cont) 70 % reduction in volume of reagents used and acid waste produced.
23	Findings on Consistent Densities Amount and type of acids in digestion has largest effect on density. Alloy type has little to no effect on density. Mass of sample has little effect on density. For samples typically prepared with 0.5 g / 100 mL, a mass change of 0.1 g only affects the density in the 3rd decimal place (1.051 g/mL vs. 1.049 g/mL) and has less than 0.2 % relative difference in the sample result. Acid concentrations are very difficult to maintain in open reaction vessels.
24	At IMR Consistent densities were not achieved with hot plate digestions. No current SOP to eliminate calibrated flasks for this portion of the sample prep. We continue to determine the density of each sample. Consistent densities were achieved for dilutions. Now we can make dilutions to 30 mL instead of 100 mL. By decreasing our diluted sample size from 100 mL to 30 mL the amount of acid waste produced is decreased by 35% which saves thousands of dollars in waste disposal fees over a year. Since 1/3 of our dilutions require acid matrix, acid reagent consumption is also reduced by 10% saving hundreds of dollars a year.
25	Summary Improved accuracies for diluted samples ≤ 1% relative at concentrations of 80 wt% Improved accuracies for calibrations curves Better correlation coefficients and CRM readbacks Reduction in reagents and acid disposal Reduced operating costs No loss of time with DBM procedures DBM Training can be provided by IMR Test Labs.
26	Acknowledgements Robert Hall – Consultant ARMI