D. Harvey - Modern Analytical Chemistry (794078), страница 68
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In this problem you will collect and analyze data in asimulation of the sampling process. Obtain a pack of M&M’sor other similar candy. Obtain a sample of five candies, andcount the number that are red. Report the result of youranalysis as % red. Return the candies to the bag, mixthoroughly, and repeat the analysis for a total of 20determinations.
Calculate the mean and standard deviationfor your data. Remove all candies, and determine the true %red for the population. Sampling in this exercise shouldfollow binomial statistics. Calculate the expected mean valueand expected standard deviation, and compare to yourexperimental results.13. The following two experiments were conducted in developinga sampling plan for determining the concentration of theherbicide diaquat in soil.
First, eight samples, each with amass of 1.50 g, were analyzed, giving a sampling variance of0.013. In the second experiment, eight samples, each with amass of 3.00 g, were analyzed, giving a sampling variance of0.0071. (a) If samples of 1.00 g are to be collected, how manyare needed to give a sampling variance of 0.0100? (b) If fivesamples are to be collected, how much should each sampleweigh?14. Determine the error (α = 0.05) for the following situations. Ineach case, assume that the variance for a single determinationis 0.0025 and that the variance for collecting a single sample is0.050.
(a) Nine samples are collected, each of which isanalyzed once. (b) One sample is collected and analyzed ninetimes. (c) Five samples are collected, each of which is analyzedthree times.15. Which of the sampling schemes in problem 14 is best if youwish to have an overall error of less than ±0.25, and the costof collecting a single sample is 1 (arbitrary units), and the costof analyzing a single sample is 10? Which is best if the cost ofcollecting a single sample is 7, and the cost of analyzing asingle sample is 3?16. Maw, Witry, and Emond evaluated a microwave digestionmethod for Hg against the standard open-vessel digestionmethod.28 The standard method requires a 2-h digestion andis operator-intensive, whereas the microwave digestion iscomplete in approximately 0.5 h and requires littlemonitoring by the operator. Samples of baghouse dust fromair-pollution-control equipment were collected from ahazardous waste incinerator and digested in triplicate by eachmethod before determining the concentration of Hg in partsper million (ppm).
Results are summarized in the followingtable.Parts per Million Hg FollowingMicrowave DigestionSample12345678Replicate 1Replicate 27.1216.14.899.646.766.199.4430.87.6615.74.629.037.226.619.5629.0Replicate 37.1715.64.288.447.507.6110.726.2Parts per million Hg FollowingStandard DigestionSample12345678Replicate 1Replicate 25.5013.15.396.596.206.2515.020.45.5412.85.126.526.035.6513.916.1Replicate 35.4013.05.367.205.775.6114.020.0Evaluate whether the microwave digestion method yieldsacceptable results in comparison with the standard digestionmethod.1400-CH07 9/8/99 4:04 PM Page 229Chapter 7 Obtaining and Preparing Samples for Analysis22917.
Simpson, Apte, and Batley investigated methods forpreserving water samples collected from anoxic (O2-poor)environments containing high concentrations of dissolvedsulfide.29 They found that preserving the water samples byadding HNO3 (which is a common preservation method foraerobic samples) gave significant negative determinate errorswhen analyzing for Cu2+. When samples were preserved byadding H2O2 followed by HNO3, the concentration of Cu2+was determined without a determinate error. Explain theirobservations.24.
A solute, S, has a distribution ratio between water and ether of7.5. Calculate the extraction efficiency if a 50.0-mL aqueoussample of S is extracted using 50.0 mL of ether as (a) a singleportion of 50.0 mL; (b) two portions, each of 25.0 mL;(c) four portions, each of 12.5 mL; and (d) five portions, eachof 10.0 mL. Assume that the solute is not involved in anysecondary equilibria.18.
In a particular analysis the selectivity coefficient, KA,I, is 0.816.When a standard sample known to contain an analyte-tointerferent ratio of 5:1 is carried through the analysis, theerror in determining the analyte is +6.3%. (a) Determine theapparent recovery for the analyte if RI = 0. (b) Determine theapparent recovery for the interferent if RA = 1.26. What must a solute’s distribution ratio be if 99% of the solutein a 50.0-mL sample is to be extracted with a single 50.0-mLportion of an organic solvent? Repeat for the case where two25.0-mL portions of the organic solvent are used.19. The amount of Co in an ore sample is to be determined usinga procedure for which Fe is an interferent.
To evaluate theprocedure’s accuracy, a standard sample of ore known to havea Co/Fe ratio of 10.2:1 is analyzed. When pure samples of Coand Fe are taken through the procedure, the followingcalibration relationships are obtainedSCo = 0.786 × number of grams CoSFe = 0.699 × number of grams FeWhen 278.3 mg of Co is taken through the separation step,275.9 mg is recovered.
Only 3.6 mg of Fe is recovered when a184.9-mg sample of Fe is carried through the separation step.Calculate (a) the recoveries for Co and Fe; (b) the separationfactor; (c) the error if no attempt is made to separate the Coand Fe before the analysis; (d) the error if the separation stepis carried out; and (e) the maximum recovery for Fe if all theCo is recovered and the maximum allowed error is 0.05%.20.
The amount of calcium in a sample of urine was determinedby a method for which magnesium is an interferent. Theselectivity coefficient, KCa,Mg, for the method is 0.843. When asample with a Mg/Ca ratio of 0.50 was carried through theprocedure, an error of –3.7% was obtained. The error was+5.5% when a sample with a Mg/Ca ratio of 2.0 was used.(a) Determine the recoveries for Ca and Mg.
(b) What isthe expected error for a urine sample in which the Mg/Caratio is 10.0?21. Show that F– is an effective masking agent in preventing areaction of Al3+ with EDTA. Assume that the only significantforms of fluoride and EDTA are F– and Y4–.22. Cyanide is frequently used as a masking agent for metal ions.The effectiveness of CN– as a masking agent is generally betterin more basic solutions. Explain the reason for this pHdependency.23.
Explain how an aqueous sample consisting of Cu2+, Sn4+,Pb2+, and Zn2+ can be separated into its component parts byadjusting the pH of the solution.25. What volume of ether is needed to extract 99.9% of the solutein problem 24 when using (a) one extraction; (b) twoextractions; (c) four extractions; and (d) five extractions.27. A weak acid, HA, with a Ka of 1.0 × 10–5, has a partitioncoefficient, KD, between water and an organic solvent of 1200.What restrictions on the sample’s pH are necessary to ensurethat a minimum of 99.9% of the weak acid is extracted in asingle step from 50.0 mL of water using 50.0 mL of theorganic solvent?28.
For problem 27, how many extractions will be necessary if thepH of the sample cannot be decreased below 7.0?29. A weak base, with a Kb of 1.0 × 10–3, has a partitioncoefficient, KD, between water and an organic solvent of 500.What restrictions on the pH of the sample are necessary toensure that a minimum of 99.9% of the weak base is extractedfrom 50.0 mL of water using two 25.00-mL portions of theorganic solvent?30.
A sample contains a weak acid analyte, HA, and a weak acidinterferent, HB. The acid dissociation constants and partitioncoefficients for the weak acids are as follows: Ka,HA = 1.0 × 10–3,Ka,HB = 1.0 × 10–7, KD,HA = KD,HB = 500. (a) Calculate theextraction efficiency for HA and HB when 50.0 mL of sample,buffered to a pH of 7.0, is extracted with 50.0 mL of theorganic solvent. (b) Which phase is enriched in the analyte?(c) What are the recoveries for the analyte and interferent inthis phase? (d) What is the separation factor? (e) Aquantitative analysis is conducted on the contents of thephase enriched in analyte. What is the expected relative errorif the selectivity coefficient, KHA,HB, is 0.500 and the initialratio of HB/HA was 10.0?31.
The relevant equilibria for the extraction of I2 from anaqueous solution of KI into an organic phase are shown in thefollowing diagram.I2OrganicKDAqueousI2 + I–KfI3–(a) Will the extraction efficiency for I2 be greater for higher orlower concentrations of I–? (b) Derive an expression forthe distribution ratio for this extraction.1400-CH07 9/8/99 4:04 PM Page 230230Modern Analytical Chemistry32. The relevant equilibria for extracting a neutral metal–ligandcomplex from an aqueous solution into an organic phase areshown in the following diagram.ML2OrganicKDM2+ + 2L–β2AqueousML2(a) Derive an expression for the distribution ratio for thisextraction. (b) Calculate the extraction efficiency when50.0 mL of an aqueous solution that is 0.15 mM in M2+and 0.12 M in L– is extracted with 25.0 mL of the organicphase.
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