Interactive Study Guide: Calibration Standard Solutions Produced by Graham Currell and Kevin Sudlow, University of the West of England, Bristol in association with: Royal Society of Chemistry, 'Discover Maths for Chemists' website, and Essential Mathematics and Statistic for Science, 2nd Edition Graham Currell and Antony Dowman, Wiley-Blackwell, 2009 Case Study: Preparing Standard Solutions for the Calibration of an AA Spectrophotometer You are required to use an Atomic Absorption Spectrophotometer (AAS) to measure the concentration of copper within a test solution. Previous measurements suggest that the concentration of this test solution is approximately 25 ppm. You will calibrate the AAS by preparing five standard 100 ml (cm 3 ) solutions of known concentrations of copper. The solvent for the solution will be 5% nitric acid to match the acidified matrix of the test solution. Note that you do not want to produce larger volumes of your final standards because these will be in acidified solutions, and you do not want to prepare an unnecessary volume of acidified solvent. As part of the process for producing the standard solutions, you will prepare 1000 ml (= 1.0 dm 3 ) of an initial stock solution with an approximate copper concentration of about 1000 ppm which you will keep for later use. The reason for preparing a relatively strong stock solution is that a small amount of copper will leach into the container wall over time, but the effect on the concentration will be proportionally less for a more concentrated solution. You will use copper sulphate as an easy source of copper in this example, although an alternative method would be to dissolve copper metal directly in nitric acid. You will need to know the following performance specifications of the instruments being used: Linear range of the AA Spectrophotometer for measuring copper: 0 to 5 ppm Accuracy of balance: +/- 0.5 mg The following analysis leads you through the types of decisions/calculations that you will have to make, although the exact details of preferred options may depend on the exact situation being considered, available glassware, etc. Decision / Calculation 1 You must first calculate the mass of copper that must be present in 1000 ml (= 1.0 dm 3 ) of solution to produce a copper concentration of 1000 ppm. Select the correct mass from the following options: (A) 10.0 g (B) 1.00 g (C) 0.01 g (D) 0.001 g
Option (B) is correct A concentration of1.0 ppm can be produced as follows: 1.0 µg of solute in each 1.0 ml (cm 3 ) of solution gives a concentration of 1.0 ppm, or 1.0 mg of solute in 1000 ml (= 1.0 dm 3 ) also gives a concentration of 1.0 ppm. Hence 1.0 g (= 1000 mg) in 1000 ml gives a concentration of 1000 ppm. You have calculated that it requires 1.0 g of copper in 1000 ml of solution to obtain a concentration of 1000 ppm. Decision / Calculation 2 It is now necessary to calculate the mass of copper sulphate that will contain 1.0 g of copper (use the following relative atomic masses Cu:63.5, S:32.1, O:16.0 and H:1.0). Select the correct mass from the following options: (A) 249.6 g (B) 159.6 g (C) 3.931 g (D) 2.513 g Option (C) is correct. The molar mass of copper sulphate pentahydrate, CuSO 4.5H 2 O, is calculated by combining the relative atomic masses to give 1 63.5 + 1 32.1 + 4 16 + 5 (2 1 + 1 16) = 249.6 The molar mass of 249.6 g of copper sulphate pentahydrate will contain the atomic mass of 63.5 g of copper. Hence to get 1.0 g of copper we must divide the total amount by 63.5: 249.6/63.5 = 3.931 g of copper sulphate will contain 63.5 /63.5 = 1.0 g of copper For help in similar calculations see Moles, Concentrations and Dilutions You have calculated that 3.931 g of copper sulphate contains 1.0 g of copper. Note that if you are asked to weigh out accurately 3.931 g of material, you may find that, due to crystal size or static electricity, you are unable to obtain exactly 3.931 g on the balance pan. It is only expected that you will weigh out an amount close to 3.931 g, and that you will record the actual weight as accurately as appropriate - normally to 4 figures, e.g. 3.920 g. You will then use the actual weight in your calculations. For the remaining calculations, we will assume that you weigh out accurately 3.931 g of copper sulphate pentahydrate and dissolve in 5% nitric acid in a 1.0 L (dm 3 ) volumetric flask to obtain a 1000 ppm stock solution.
Decision / Calculation 3 You must now plan your calibration of the AA Spectrophotometer. Note that previous measurements of the test solution give an expected concentration of about 25 ppm. Working from your initial 1000 ml of 1000 ppm stock solution, do you then prepare your five standard solutions with concentrations between (select the best option): (A) 10 and 50 ppm to compare directly with the test solution (B) 20 and 30 ppm to compare directly with the test solution (C) 1 and 5 ppm, but you will need to dilute the test solution by a factor of 5 (D) 1 and 5 ppm, but you will need to dilute the test solution by a factor of 10 Option (D) This is the best option as the calibration range coincides with the linear range of the instrument, allowing a linear best-fit calibration line to be used, and the proposed dilution should give a test measurement of approximately 2.5 ppm, which is in the middle of the calibration range. You have decided to produce 100 ml (cm 3 ) of each of five standard solutions of concentration, 1, 2, 3, 4 and 5 ppm of copper. Decision / Calculation 4 You must now decide what overall method you will now adopt to produce your five standards. You must consider carefully the accuracies of the available volumetric glassware with which you would make the dilutions. You have available the following class B glassware, listed with quoted accuracies: Volumetric flask volumes in ml (cm 3 ) with class B tolerances: 1000 ±0.8 500 ±0.5 200 ±0.3 100 ±0.2 50 ±0.12 20 ±0.08 10 ±0.05 Bulb pipette volumes in ml (cm 3 ) with class B tolerances: 100 ±0.15 50 ±0.1 20 ±0.06 10 ±0.04 5.0 ±0.03 2.0 ±0.02 1.0 ±0.015 Will you (select the best option): (A) make five direct dilutions of the 1000 ppm stock solution to obtain 100 ml of each of the required concentrations, 1, 2, 3, 4 and 5 ppm. (B) first dilute the 1000 ppm stock solution by a factor of 10 to obtain 100 ml of a 100 ppm intermediate working solution and then make five further dilutions to obtain
(C) first dilute the 1000 ppm stock solution by a factor of 100 to obtain 100 ml of a 10 ppm intermediate working solution and then make five further dilutions to obtain (D) first dilute the 1000 ppm stock solution by a factor of 100 to obtain 1000 ml of a 10 ppm intermediate working solution and then make five further dilutions to obtain Option (D) is the best option. The two stage dilution from a volume V1 (=1000 ml) of the 1000 ppm stock solution to a final volume, V5 (= 100 ml) of 1.0 ppm (for example) solution can be obtained by first transferring (dilution factor = 100): volume, V2 (= 10 ml), of the stock solution by pipette into volume, V3 (= 1000 ml), of the 1000 ppm working solution in a volumetric flask and then transfer (dilution factor = 10): volume, V4 (= 10 ml), of the working solution by pipette into volume, V5 (= 100 ml), of the final standard solution in a volumetric flask You can link to tutorials (+ video) on 'Dilutions' and 'Uncertainties in concentrations and dilutions' by clicking here: Moles, Concentrations and Dilutions You can also use the Excel file UncertCuStands.xls to calculate the uncertainty in the overall dilution due to the class B tolerances. You need to enter the relevant data into the cells shaded in yellow. Note that these calculations do not include uncertainties due to human error in using the glassware. For option (D), the relative uncertainty in the final concentration (1.0 ppm) is 0.0.366 %. This is the lowest uncertainty of the given options. In addition, the effect of human error will probably be less because 10 ml is the smallest pipette volume transferred instead of 1 ml. You have decided to use a bulb pipette to take 10 ml of the initial 1000 ppm stock solution, transfer to another 1000 ml (1.0 dm 3 ) volumetric flask, adding further solvent up to the mark to obtain your 100 ppm working solution. You then use bulb pipettes to transfer selected volumes to 100 ml (cm 3 ) volumetric flasks for the five standard solutions. For your: 1 ppm standard, use a 10 ml bulb pipette to transfer 10 ml. 2 ppm standard, use a 20 ml bulb pipette to transfer 20 ml. 3 ppm standard, use a 10 ml and a 20 ml bulb pipette to transfer 30 ml. 4 ppm standard, use a two different 20 ml bulb pipettes to transfer 40 ml. 5 ppm standard, use a 50 ml bulb pipette to transfer 50 ml. Practical note: Transfer some of the stock solution into another container before using the pipettes; this reduces the risk of accidental contamination of the main stock solution.
Decision / Calculation 5 Calculate the uncertainties in each of your standard solutions due to the uncertainties in the balance and the class B glassware. For help in understanding the combined effect of uncertainties refer to Moles, Concentrations and Dilutions. You can use the Excel file UncertCuStands.xls to calculate the uncertainty in the overall dilutions. Important note: These uncertainty calculations do not take into account any human (or student) error in the experimental process. The results only show the limiting uncertainty due to the equipment being used in the overall process. Concentration (ppm) Relative uncertainty (%) Standard uncertainty (ppm) 1.0 0.366 0.00366 2.0 0.330 0.00661 3.0 0.312 0.00937 4.0 0.305 0.01219 5.0 0.302 0.01509 Click here to show the above answers Decision / Calculation 6 From your calculations, identify the relative uncertainties in each of the following processes: : Process Relative uncertainty (%) Weighing 3.931 g of copper sulphate 0.008 Using 10 ml bulb pipette 0.240 Using 100 ml volumetric flask 0.120 Using 1000 ml volumetric flask 0.048 Click here to show the above answers From the above results it is possible to see that the most critical stage for accuracy in dilution is in using the pipette to measure out the smallest volumes End of Case Study - You can download here a print-out (pdf) of this page showing full working