Titrimetic Analysis of Mixtures

Shown below is a titration curve for a mixture of two monoprotic weak acids, HA and HB, where pKa,HA = 4.00 and pKa,HB = 8.00.  The titrant is 0.200 M NaOH.

(a) Briefly explain how you can tell that this is the titration curve for a mixture of weak acids and not the titration curve for a diprotic acid, such as H2A.

(b) Supplement your answer to part (a) by sketching the expected titration curve for the diprotic weak acid H2A (for simplicity just superimpose your sketch on the titration curve for the mixture). Assume that pKa1 = 4.00, pKa2 = 8.00 and that the concentration of H2A is the same as that for HA in the titration curve shown above. Don’t worry about accurately estimating the pH levels after the second equivalence point.

(c) Using the titration curve, estimate the concentration of the weaker of the two acids (be sure to show you arrived at the volume of NaOH used in this part of the titration).

(d) The sample being titrated was prepared by adding 0.311 g of HA and 0.258 g of HB to 50.00 mL of water. Estimate the equivalent weight of HA.

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Titration Curve for Amino Acid

Shown below is a potentiometric titration curve for a 0.050-g sample of an amino acid dissolved in water and titrated with 0.100 M NaOH. Based on this titration curve, answer the following questions:

(a) How many titratable acid/base sites does the amino acid have?

(b) Estimate the pKa for each of the acid-base sites you  identified.

(c) Estimate the gram equivalent weight of the amino acid?

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Titrimetric Analysis of Amino Acids

The quantitative titrimetric analysis of amino acids often is complicated by the high pKa of the —NH4+ group, which produces a titration break that is too small for the effective use of a visual indicator. There are several ways to overcome this complication, including a back-titration, changing to a non-aqueous solvent, or using a derivative titration curve.  For each of these methods, discuss how it might improve the experimental determination of the titration’s endpoint. Be sure to explain how the method enhances your ability to locate the endpoint, and how the volume of titrant needed to reach the end point is related to the concentration of amino acid.

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Complexometric Titration of CaO in Limestone: Analysis of Procedure

In the EDTA titration for CaO in limestone, the pH of the sample is made sufficiently basic so any magnesium thatis present will precipitate as Mg(OH)2. The adjustment of pH is fairly critical, as complications  arise if the solution is either too basic or not basic enough.  Briefly explain  these complications and how each affects the accuracy of the analysis.

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Gravimetric Method for Analysis of Phosphorous: Analysis of Procedure

Once upon a time, a common method for determining phosphorous was to convert it to phosphate, precipitate it as magnesium ammonium phosphate, MgNH4PO4, and ignite it to form magnesium pyrophosphate, Mg2P2O7.  The solubility reaction for MgNH4PO4 is

MgNH4PO4(s) ↔ Mg2+(aq) + NH4+(aq) + PO43-(aq)

for which the Ksp is 2.51 x 10-13.  Additional equilibrium constants of interest are listed below.

H3PO4: pKa1 = 2.33, pKa2 = 7.22, pKa3 = 12.33

NH4+: pKa = 9.25

(a) Le Châtelier’s principle suggests that the solubility of MgNH4PO4 will decrease if we add an excess of NH4+.  Experimental work, however, shows that the solubility actually increases.  Explain why the solubility increases when NH4+ is added in excess.  You may approach this using a ladder diagram, or by combining appropriate equilibrium constant expressions.

(b) The procedure calls for dissolving the sample in HCl and HNO3.  Solutions of NH4+ and Mg2+ are added along with additional HCl to ensure an acidic solution. The precipitate is then formed by adding NH3 dropwise until the pH is neutral, followed by adding 2 mL in excess.  Clearly explain why the solution is initially made acidic, why the precipitant is added dropwise, and why the precipitant is added in excess.

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Sampling Plan for Cadmium Leeching from Strip Mine

One of the hazards of strip mining is that water passing through the mine’s “tailings” (the piles of discarded material) is often very acidic and contains high concentrations of metal ions, such as Pb2+ and Cd2+.

(a) Suppose you are involved in a study to determine whether a strip mine is responsible for the high concentrations of metal ions in a local stream.  Your first task is decide on where to collect samples of sediment.  Shown below is a map of the area from which you are planning to collect samples.  You are limited to six sampling locations due to time and budget constraints.  Which of the six sampling strategies (random, systematic, judgmental, systematic/judgmental, stratified or convenience) would you use to select your sites?  Please note that more than one strategy may be appropriate, but that some strategies are clearly inappropriate.  Show, using dots (•), where you might place these sampling locations, being sure that your locations are consistent with your sampling strategy.

(b) Four replicate 1-g samples of sediment are collected from a single location and analyzed for Cd, giving results of 5.09, 6.29, 6.64 and 4.63 ppb.  Assuming that sampling is the only significant source of indeterminate error, report the percent relative standard deviation due to sampling.

(c) The next step in the sampling plan is to determine the minimum sample size needed to obtain results of acceptable precision.  Although the concentration of Cd may vary significantly from location-to-location, the soil at any single location is reasonably homogeneous. What size samples should be collected if you want the relative standard deviation due to sampling to be 5%?

(d) The final step in the sampling plan is to determine the number of samples to collect at each location. Assuming that you are looking to achieve results with a relative error of no more than ±3%, what is the minimum number of samples that you should collect from each location?

(e) In question (b) we assumed that sampling was the only important source of indeterminate error. Briefly explain how you would verify that the method does not significantly contribute to the indeterminate error.

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Extraction and Analysis of Gingko Leaves

You may know that there is a growing interest in the ginkgo tree because herbal supplements using extracts of ginkgo are believed to aid in fighting memory loss.  A recent paper [Lang, G.; Wai, C. M. Anal. Chem. 1999, 71, 2929-2933] describes a method for extracting ginkgolides and bilobalides (the pharmacologically active species) from ginkgo leaves.

To accomplish the separation a 1-g portion of powdered ginkgo leaves is placed in 15 mL of distilled water and boiled for 2 minutes. The solid residue is removed by filtration, placed in 10 mL of 0.1% w/v Na2HPO4 and boiled for 15 minutes.  After filtering, the filtrate is adjusted to a pH of 4.5-5.0 using H3PO4 and NaOH, and diluted to a final volume of 50 mL. A 5-mL portion of the diluted extract is transferred to a 50–mL separatory funnel and 5 mL of CH2Cl2 added.  After shaking and allowing the two phases to separate the amount of ginkgolides and bilobalides in the CH2Cl2 are determined using GC-MS.

(a) The Ka value for ginkgolide B, which we can represent as HG, is 4.82 x 10-8.  Explain why a pH of 4.5-5.0 is used for the extraction.

(b) Why are the combined extracts diluted to 50 mL?

(c) The authors report that a single extraction, as described above, results in an 80-86% extraction of ginkgolide B.  What is the minimum number of extractions needed to ensure that at least 98% of ginkgolide B is removed?

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Developing a Sampling Plan for Lead in Soil

When leaded gasoline was available, automobiles were a significant source of the total yearly environmental emission of Pb.  During internal combustion lead in gasoline, which was present as tetraethyl lead, was vaporized.  The lead, now present as Pb0, adsorbed to small aerosol particulates, which were then released with the exhaust.  Eventually these particulates settled out as “dry rain,” and were incorporated in local soils.  One of the ways that this source of pollution was identified was through studies showing that the concentration of Pb in soils near highways decreased with distance from the highway.

(a) Suppose you are involved in a study to determine the effect of leaded gasoline on lead in the environment, and that you are to design the sampling plan.  Your first task is decide where to collect samples. Shown below is a map of the area from which you are planning to collect samples. You are limited to six sampling locations due to time and budget constraints.  Which of the six sampling strategies (random, systematic, judgmental, systematic/judgmental, stratified or convenience) would you use to select your sites.  Please note that more than one strategy may be appropriate, but that some strategies are clearly inappropriate.  Show, using X’s, where you might place these sampling locations, being sure that your locations are consistent with your sampling strategy.

(b) After selecting your sampling locations, the next step in the sampling plan is to determine whether the collection of samples, or the subsequent analysis of the samples will limit your study’s overall precision. Four replicate 1.0-g samples of soil are collected from a single location and analyzed for Pb, giving results of 5.09, 6.29, 6.64 and 4.63 ppb.  When a NIST standard soil sample was analyzed by the same method the concentration of lead was found to be 11.49, 11.57, 11.72 and 11.77 ppb.  Using these results, report estimates for the standard deviation due to sampling and the standard deviation due to the method.

(c) The next step in the sampling plan is to determine the sample size needed to obtain results of acceptable precision.  Although the concentration of Pb may vary significantly from location-to-location, the soil at any single location is reasonably homogeneous. Using the information given above, what size samples should be collected if you want the relative standard deviation due to sampling to be 5%?

(d) The final step in the sampling plan is to determine the number of samples to collect at each location, and the number of replicate analyses to perform on each. Assuming that you are looking to achieve results with a relative error of no more than ±3%, what is the minimum number of samples that you should collect from each location?  Is there a need to analyze any single sample more than one time?  Explain.

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Separating a Weakly Acidic Analyte from a Weakly Basic Interferent

Imagine  you have an aqueous sample containing a weak acid analyte, HA, and a weak base interferent, HI.  The following information about HA, HI, the method of analysis, and the sample are available to you:

Ka,HA = 1.00 x 10-3 Kb,HI = 1.00 x 10-7 KHA,HI = 0.500   [HI]o/[HA]o = 10

(a) What is the expected percent relative error for the quantitative analysis of HA if no attempt is made to separate the analyte and interferent?

(b) One way to separate the analyte and interferent is to use a liquid-liquid extraction.  As a starting point, evaluate the efficiency of a single extraction using 50.0 mL of sample buffered to a pH of 5.0, and 50.0 mL of an organic solvent for which KD,HA is 50.0 and KD,HI is 100.0.  Be sure to calculate the extraction efficiency for both the analyte and the interferent.

(c) In which phase is the analyte preferentially found?  This is the phase in which we will isolate and analyze the analyte.

(d) Calculate the recoveries for the analyte and interferent in the phase in which the analyte is enriched.  What is the percent relative error for the quantitative analysis after this extraction?

(e) To improve the separation you might consider the following modifications: make the pH of the aqueous phase more acidic; make the pH of the aqueous phase more basic; use a larger portion of organic solvent; use a smaller portion of organic solvent; use more sample; use less sample; perform more extractions.  Which of these do you think will improve the separation.  Be sure that you have good reasons for your decisions.

(f) Based on your answer to the previous question, design a modified separation that will produce a percent relative error of less than 5%.

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Sampling M & Ms

Carry out the following “experiment” to test the validity of the sampling constant equation

mR2 = Ks

where m is the sample’s mass, R is the relative standard deviation for sampling, and Ks is the sampling constant.

Obtain a package of M&M’s, or other candy that comes in several colors.  Select five M&M’s at random, recording the percentage that are brown (note: for this sample, m = 5).  Return the M&M’s to the bag and repeat for a total of 7 trials.  Continue in this manner using samples of 10, 15, 20, and 25 M&M’s.  To analyze your data, do the following:

(a) Gather your data together in a table with column headings of “sample size”, “% Brown”, “average % Brown”, “standard deviation”, “R”, and “Ks”.  Note that second and third columns will each have seven entries for each sample size, whereas the remaining columns will have but one entry per sample size.

(b) Examine your results for Ks and comment on the validity of the sampling constant equation for this population of M&M’s.

(c) Prepare a graph showing the average % Brown per trial on the y-axis and the sample size on the x-axis (a total of 35 data points).  Using your average value for Ks, calculate the expected standard deviation for sample sizes of 1 – 10 and add points to your graph of ± 1 standard deviation about the global mean value (the average % Brown for all 35 trials).  Connect these points with two smooth lines (one for +1 standard deviation and one for –1 standard deviation) and comment, again, on the validity of the sampling constant equation for this population of M&M’s.

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