Chapter 7

The data in the following table were collected during a preliminary study of the \(\mathrm{pH}\) of an industrial wastewater stream. $$ \begin{array}{cccc} \text { Time }(\mathrm{hr}) & \mathrm{pH} & \text { Time }(\mathrm{hr}) & \mathrm{pH} \\ \hline 0.5 & 4.4 & 9.0 & 5.7 \\ 1.0 & 4.8 & 9.5 & 5.5 \\ 1.5 & 5.2 & 10.0 & 6.5 \\ 2.0 & 5.2 & 10.5 & 6.0 \\ 2.5 & 5.6 & 11.0 & 5.8 \\ 3.0 & 5.4 & 11.5 & 6.0 \\ 3.5 & 5.4 & 12.0 & 5.6 \\ 4.0 & 4.4 & 12.5 & 5.6 \\ 4.5 & 4.8 & 13.0 & 5.4 \\ 5.0 & 4.8 & 13.5 & 4.9 \\ 5.5 & 4.2 & 14.0 & 5.2 \\ 6.0 & 4.2 & 14.5 & 4.4 \\ 6.5 & 3.8 & 15.0 & 4.0 \\ 7.0 & 4.0 & 15.5 & 4.5 \\ 7.5 & 4.0 & 16.0 & 4.0 \\ 8.0 & 3.9 & 16.5 & 5.0 \\ 8.5 & 4.7 & 17.0 & 5.0 \end{array} $$ Prepare a figure showing how the pH changes as a function of time and suggest an appropriate sampling frequency for a long-term monitoring program.

The distinction between a homogeneous population and a heterogeneous population is important when we develop a sampling plan. (a) Define homogeneous and heterogeneous. (b) If you collect and analyze a single sample, can you determine if the population is homogeneous or is heterogeneous?

In this problem you will collect and analyze data to simulate the sampling process. Obtain a pack of M\&M's (or other similar candy). Collect a sample of five candies and count the number that are red (or any other color of your choice). Report the result of your analysis as \% red. Return the candies to the bag, mix thoroughly, and repeat the analysis for a total of 20 determinations. Calculate the mean and the standard deviation for your data. Remove all candies from the bag and determine the true \(\%\) red for the population. Sampling in this exercise should follow binomial statistics. Calculate the expected mean value and the expected standard deviation, and compare to your experimental results.

Determine the error \((\alpha=0.05)\) for the following situations. In each case assume that the variance for a single determination is 0.0025 and that the variance for collecting a single sample is 0.050 . (a) Nine samples are collected, each analyzed once. (b) One sample is collected and analyzed nine times. (c) Five samples are collected, each analyzed twice.

Simpson, Apte, and Batley investigated methods for preserving water samples collected from anoxic \(\left(\mathrm{O}_{2}\right.\) -poor \()\) environments that have high concentrations of dissolved sulfide. \({ }^{27}\) They found that preserving water samples with \(\mathrm{HNO}_{3}\) (a common method for preserving aerobic samples) gave significant negative determinate errors when analyzing for \(\mathrm{Cu}^{2+}\). Preserving samples by first adding \(\mathrm{H}_{2} \mathrm{O}_{2}\) and then adding \(\mathrm{HNO}_{3}\) eliminated the determinate error. Explain their observations.

In a particular analysis the selectivity coefficient, \(K_{A, I}\), is 0.816 . When a standard sample with an analyte-to-interferent ratio of 5: 1 is carried through the analysis, the error when determining the analyte is \(+6.3 \%\). (a) Determine the apparent recovery for the analyte if \(R_{I}=0\). (b) Determine the apparent recovery for the interferent if \(R_{A}=0\).

The amount of Co in an ore is determined using a procedure for which Fe in an interferent. To evaluate the procedure's accuracy, a standard sample of ore known to have a Co/Fe ratio of 10.2 is analyzed. When pure samples of Co and Fe are taken through the procedure the following calibration relationships are obtained $$ S_{\mathrm{Co}}=0.786 \times m_{\mathrm{C}_{\mathrm{o}}} \text { and } S_{\mathrm{Fe}}=0.699 \times m_{\mathrm{Fe}} $$ where \(S\) is the signal and \(m\) is the mass of Co or Fe. When \(278.3 \mathrm{mg}\) of Co are taken through the separation step, \(275.9 \mathrm{mg}\) are recovered. Only \(3.6 \mathrm{mg}\) of Fe are recovered when a \(184.9 \mathrm{mg}\) sample of \(\mathrm{Fe}\) is carried through the separation step. Calculate (a) the recoveries for Co and Fe; (c) the selectivity ratio; (b) the separation factor; (d) the error if no at- (e) the error if the separation tempt is made to separate the Co and Fe; step is carried out; and (f) the maximum possible recovery for Fe if the recovery for Co is 1.00 and the maximum allowed error is \(0.05 \%\).

Cyanide is frequently used as a masking agent for metal ions. Its effectiveness as a masking agent is better in more basic solutions. Explain the reason for this dependence on \(\mathrm{pH}\).

A solute, \(S\), has a distribution ratio between water and ether of \(7.5 .\) Calculate the extraction efficiency if we extract a 50.0 -mL aqueous sample of \(S\) using \(50.0 \mathrm{~mL}\) of ether as (a) a single portion of \(50.0 \mathrm{~mL} ;\) (b) two portions, each of \(25.0 \mathrm{~mL} ;(\mathrm{c})\) four portions, each of \(12.5 \mathrm{~mL} ;\) and \((\mathrm{d})\) five portions, each of \(10.0 \mathrm{~mL}\). Assume the solute is not involved in any secondary equilibria.

A weak acid, HA, with a \(K_{\mathrm{a}}\) of \(1.0 \times 10^{-5}\) has a partition coefficient, \(K_{\mathrm{D}}\), of \(1.2 \times 10^{3}\) between water and an organic solvent. What restriction on the sample's \(\mathrm{pH}\) is necessary to ensure that \(99.9 \%\) of the weak acid in a \(50.0-\mathrm{mL}\) sample is extracted using a single \(50.0-\mathrm{mL}\) portion of the organic solvent?

A weak base, \(\mathrm{B}\), with a \(K_{\mathrm{b}}\) of \(1.0 \times 10^{-3}\) has a partition coefficient, \(K_{\mathrm{D}}\), of \(5.0 \times 10^{2}\) between water and an organic solvent. What restriction on the sample's \(\mathrm{pH}\) is necessary to ensure that \(99.9 \%\) of the weak base in a 50.0 -mL sample is extracted when using two 25.0 -mL portions of the organic solvent?

A sample contains a weak acid analyte, HA, and a weak acid interferent, \(\mathrm{HB}\). The acid dissociation constants and the partition coefficients for the weak acids are \(K_{\mathrm{a}, \mathrm{HA}}=1.0 \times 10^{-3}, \mathrm{~K}_{\mathrm{a}, \mathrm{HB}}=1.0 \times 10^{-7},\) \(K_{\mathrm{D}, \mathrm{HA}}=K_{\mathrm{D}, \mathrm{HB}}=5.0 \times 10^{2}\). (a) Calculate the extraction efficiency for HA and HB when a 50.0 -mL sample, buffered to a pH of 7.0 , is extracted using \(50.0 \mathrm{~mL}\) of the organic solvent. (b) Which phase is enriched in the analyte? (c) What are the recoveries for the analyte and the interferent in this phase? (d) What is the separation factor? (e) \(\mathrm{A}\) quantitative analysis is conducted on the phase enriched in analyte. What is the expected relative error if the selectivity coefficient, \(K_{\mathrm{HA}, \mathrm{HB}}\), is 0.500 and the initial ratio of \(\mathrm{HB} / \mathrm{HA}\) is \(10.0 ?\)

The following information is available for the extraction of \(\mathrm{Cu}^{2+}\) by \(\mathrm{CCl}_{4}\) and dithizone: \(K_{\mathrm{D}, \mathrm{c}}=7 \times 10^{4} ; \beta_{2}=5 \times 10^{22} ; K_{\mathrm{a}, \mathrm{HL}}=3 \times 10^{-5}\) \(K_{\mathrm{D}, \mathrm{HL}}=1.1 \times 10^{4} ;\) and \(n=2 .\) What is the extraction efficiency if a 100.0 -mL sample of an aqueous solution that is \(1.0 \times 10^{-7} \mathrm{M} \mathrm{Cu}^{2+}\) and \(1 \mathrm{M}\) in \(\mathrm{HCl}\) is extracted using \(10.0 \mathrm{~mL}\) of \(\mathrm{CCl}_{4}\) containing \(4.0 \times 10^{-4}\) \(M\) dithizone (HL)?