Chapter 12

Moody studied the efficiency of a GC separation of 2 -butanone on a dinonyl phthalate packed column. \(^{16}\) Evaluating plate height as a function of flow rate gave a van Deemter equation for which \(A\) is \(1.65 \mathrm{~mm}\), \(B\) is \(25.8 \mathrm{~mm} \cdot \mathrm{mL} \min ^{-1},\) and \(C\) is \(0.0236 \mathrm{~mm} \cdot \min \mathrm{mL}^{-1}\) (a) Prepare a graph of \(H\) versus \(u\) for flow rates between \(5-120 \mathrm{~mL} / \mathrm{min}\). (b) For what range of flow rates does each term in the Van Deemter equation have the greatest effect? (c) What is the optimum flow rate and the corresponding height of a theoretical plate? (d) For open-tubular columns the \(A\) term no longer is needed. If the \(B\) and \(C\) terms remain unchanged, what is the optimum flow rate and the corresponding height of a theoretical plate? (e) Compared to the packed column, how many more theoretical plates are in the open-tubular column?

A mixture of \(n\) -heptane, tetrahydrofuran, 2 -butanone, and \(n\) -propanol elutes in this order when using a polar stationary phase such as Carbowax. The elution order is exactly the opposite when using a nonpolar stationary phase such as polydimethyl siloxane. Explain the order of elution in each case.

Loconto and co-workers describe a method for determining trace levels of water in soil. \(^{19}\) The method takes advantage of the reaction of water with calcium carbide, \(\mathrm{CaC}_{2}\), to produce acetylene gas, \(\mathrm{C}_{2} \mathrm{H}_{2}\). By carrying out the reaction in a sealed vial, the amount of acetylene produced is determined by sampling the headspace. In a typical analysis a sample of soil is placed in a sealed vial with \(\mathrm{CaC}_{2}\). Analysis of the headspace gives a blank corrected signal of \(2.70 \times 10^{5} .\) A second sample is prepared in the same manner except that a standard addition of \(5.0 \mathrm{mg} \mathrm{H}_{2} \mathrm{O} / \mathrm{g}\) soil is added, giving a blank-corrected signal of \(1.06 \times 10^{6} .\) Determine the milligrams \(\mathrm{H}_{2} \mathrm{O} / \mathrm{g}\) soil in the soil sample.

The amount of camphor in an analgesic ointment is determined by GC using the method of internal standards. \({ }^{21}\) A standard sample is prepared by placing \(45.2 \mathrm{mg}\) of camphor and \(2.00 \mathrm{~mL}\) of a \(6.00 \mathrm{mg} / \mathrm{mL}\) internal standard solution of terpene hydrate in a \(25-\mathrm{mL}\) volumetric flask and diluting to volume with \(\mathrm{CCl}_{4}\). When approximately \(2-\mu \mathrm{L}\) sample of the standard is injected, the FID signals for the two components are measured (in arbitrary units) as 67.3 for camphor and 19.8 for terpene hydrate. A 53.6-mg sample of an analgesic ointment is prepared for analysis by placing it in a \(50-\mathrm{mL}\) Erlenmeyer flask along with \(10 \mathrm{~mL}\) of \(\mathrm{CCl}_{4}\). After heating to \(50^{\circ} \mathrm{C}\) in a water bath, the sample is cooled to below room temperature and filtered. The residue is washed with two \(5-\mathrm{mL}\) portions of \(\mathrm{CCl}_{4}\) and the combined filtrates are collected in a \(25-\mathrm{mL}\) volumetric flask. After adding \(2.00 \mathrm{~mL}\) of the internal standard solution, the contents of the flask are diluted to volume with \(\mathrm{CCl}_{4}\). Analysis of an approximately \(2-\mu \mathrm{L}\) sample gives FID signals of 13.5 for the terpene hydrate and 24.9 for the camphor. Report the \(\% \mathrm{w} / \mathrm{w}\) camphor in the analgesic ointment.

Haddad and associates report the following retention factors for the reversed- phase separation of salicylamide and caffeine. \({ }^{25}\) \(\begin{array}{ccccccc}\% \text { methanol } & 30 \% & 35 \% & 40 \% & 45 \% & 50 \% & 55 \% \\ k_{\text {sal }} & 2.4 & 1.6 & 1.6 & 1.0 & 0.7 & 0.7 \\\ k_{\text {caff }} & 4.3 & 2.8 & 2.3 & 1.4 & 1.1 & 0.9\end{array}\) (a) Explain the trends in the retention factors for these compounds. (b) What is the advantage of using a mobile phase with a smaller \(\% \mathrm{v} / \mathrm{v}\) methanol? Are there any disadvantages?

Suppose you need to separate a mixture of benzoic acid, aspartame, and caffeine in a diet soda. The following information is available. \begin{tabular}{lcccc} & \multicolumn{3}{c} {\(t_{\mathrm{r}}\) in aqueous mobile phase of \(\mathrm{pH}\)} \\ compound & 3.0 & 3.5 & 4.0 & 4.5 \\ \hline benzoic acid & 7.4 & 7.0 & 6.9 & 4.4 \\ aspartame & 5.9 & 6.0 & 7.1 & 8.1 \\ caffeine & 3.6 & 3.7 & 4.1 & 4.4 \end{tabular} (a) Explain the change in each compound's retention time. (b) Prepare a single graph that shows retention time versus \(\mathrm{pH}\) for each compound. Using your plot, identify a pH level that will yield an acceptable separation.

The composition of a multivitamin tablet is determined using an HPLC with a diode array UV/Vis detector. A \(5-\mu L\) standard sample that contains 170 ppm vitamin C, 130 ppm niacin, 120 ppm niacinamide, 150 ppm pyridoxine, 60 ppm thiamine, 15 ppm folic acid, and 10 ppm riboflavin is injected into the HPLC, giving signals (in arbitrary units) of, respectively, \(0.22,1.35,0.90,1.37,0.82,0.36,\) and \(0.29 .\) The multivitamin tablet is prepared for analysis by grinding into a powder and transferring to a \(125-\mathrm{mL}\) Erlenmeyer flask that contains \(10 \mathrm{~mL}\) of \(1 \%\) \(\mathrm{v} / \mathrm{v} \mathrm{N} \mathrm{H}_{3}\) in dimethyl sulfoxide. After sonicating in an ultrasonic bath for \(2 \mathrm{~min}, 90 \mathrm{~mL}\) of \(2 \%\) acetic acid is added and the mixture is stirred for \(1 \mathrm{~min}\) and sonicated at \(40^{\circ} \mathrm{C}\) for \(5 \mathrm{~min}\). The extract is then filtered through a \(0.45-\mu \mathrm{m}\) membrane filter. Injection of a \(5-\mu \mathrm{L}\) sample into the HPLC gives signals of 0.87 for vitamin C, 0.00 for niacin, 1.40 for niacinamide, 0.22 for pyridoxine, 0.19 for thiamine, 0.11 for folic acid, and 0.44 for riboflavin. Report the milligrams of each vitamin present in the tablet.

The amount of caffeine in an analgesic tablet was determined by HPLC using a normal calibration curve. Standard solutions of caffeine were prepared and analyzed using a \(10-\mu L\) fixed-volume injection loop. Results for the standards are summarized in the following table. \begin{tabular}{cc} concentration \((\mathrm{ppm})\) & signal (arb. units) \\ \hline 50.0 & 8354 \\ 100.0 & 16925 \\ 150.0 & 25218 \\ 200.0 & 33584 \\ 250.0 & 42002 \end{tabular} The sample is prepared by placing a single analgesic tablet in a small beaker and adding \(10 \mathrm{~mL}\) of methanol. After allowing the sample to dissolve, the contents of the beaker, including the insoluble binder, are quantitatively transferred to a \(25-\mathrm{mL}\) volumetric flask and diluted to volume with methanol. The sample is then filtered, and a \(1.00-\mathrm{mL}\) aliquot transferred to a \(10-\mathrm{mL}\) volumetric flask and diluted to volume with methanol. When analyzed by HPLC, the signal for caffeine is found to be \(21469 .\) Report the milligrams of caffeine in the analgesic tablet.

Bohman and colleagues described a reversed-phase HPLC method for the quantitative analysis of vitamin \(\mathrm{A}\) in food using the method of standard additions. \({ }^{27}\) In a typical example, a \(10.067-\mathrm{g}\) sample of cereal is placed in a 250 -mL Erlenmeyer flask along with \(1 \mathrm{~g}\) of sodium ascorbate, \(40 \mathrm{~mL}\) of ethanol, and \(10 \mathrm{~mL}\) of \(50 \% \mathrm{w} / \mathrm{v} \mathrm{KOH}\). After refluxing for \(30 \mathrm{~min}, 60 \mathrm{~mL}\) of ethanol is added and the solution cooled to room temperature. Vitamin \(\mathrm{A}\) is extracted using three \(100-\mathrm{mL}\) portions of hexane. The combined portions of hexane are evaporated and the residue containing vitamin A transferred to a \(5-\mathrm{mL}\) volumetric flask and diluted to volume with methanol. A standard addition is prepared in a similar manner using a \(10.093-\mathrm{g}\) sample of the cereal and spiking with \(0.0200 \mathrm{mg}\) of vitamin \(\mathrm{A}\). Injecting the sample and standard addition into the HPLC gives peak areas of, respectively, \(6.77 \times 10^{3}\)and \(1.32 \times 10^{4}\). Report the vitamin \(\mathrm{A}\) content of the sample in milligrams/100 g cereal.

Ohta and Tanaka reported on an ion-exchange chromatographic method for the simultaneous analysis of several inorganic anions and the cations \(\mathrm{Mg}^{2+}\) and \(\mathrm{Ca}^{2+}\) in water. \({ }^{28}\) The mobile phase includes the ligand 1,2,4 -benzenetricarboxylate, which absorbs strongly at \(270 \mathrm{nm}\). Indirect detection of the analytes is possible because its absorbance decreases when complexed with an anion. (a) The procedure also calls for adding the ligand EDTA to the mobile phase. What role does the EDTA play in this analysis? (b) A standard solution of \(1.0 \mathrm{mM} \mathrm{NaHCO}_{3}, 0.20 \mathrm{mM} \mathrm{NaNO}_{2}, 0.20\) \(\mathrm{mM} \mathrm{MgSO}_{4}, 0.10 \mathrm{mM} \mathrm{CaCl}_{2},\) and \(0.10 \mathrm{mM} \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\) gives the following peak areas (arbitrary units). \(\begin{array}{lcccc}\text { ion } & \mathrm{HCO}_{3}^{-} & \mathrm{Cl}^{-} & \mathrm{NO}_{2}^{-} & \mathrm{NO}_{3}^{-} \\ \text {peak area } & 373.5 & 322.5 & 264.8 & 262.7 \\\ \text { ion } & \mathrm{Ca}^{2+} & \mathrm{Mg}^{2+} & \mathrm{SO}_{4}^{2-} & \\\ \text { peak area } & 458.9 & 352.0 & 341.3 & \end{array}\) Analysis of a river water sample (pH of 7.49 ) gives the following results. \(\begin{array}{lcccc}\text { ion } & \mathrm{HCO}_{3}^{-} & \mathrm{Cl}^{-} & \mathrm{NO}_{2}^{-} & \mathrm{NO}_{3}^{-} \\ \text {peak area } & 310.0 & 403.1 & 3.97 & 157.6 \\ \text { ion } & \mathrm{Ca}^{2+} & \mathrm{Mg}^{2+} & \mathrm{SO}_{4}^{2-} & \\ \text { peak area } & 734.3 & 193.6 & 324.3 & \end{array}\) Determine the concentration of each ion in the sample. (c) The detection of \(\mathrm{HCO}_{3}^{-}\) actually gives the total concentration of carbonate in solution \(\left(\left[\mathrm{CO}_{3}^{2-}\right]+\left[\mathrm{HCO}_{3}^{-}\right]+\left[\mathrm{H}_{2} \mathrm{CO}_{3}\right]\right) .\) Given that the \(\mathrm{pH}\) of the water is \(7.49,\) what is the actual concentration of \(\mathrm{HCO}_{3}^{-}\) ? (d) An independent analysis gives the following additional concentrations for ions in the sample: \(\left[\mathrm{Na}^{+}\right]=0.60 \mathrm{mM} ;\left[\mathrm{NH}_{4}^{+}\right]=0.014\) \(\mathrm{mM}\); and \(\left[\mathrm{K}^{+}\right]=0.046 \mathrm{mM}\). A solution's ion balance is defined as the ratio of the total cation charge to the total anion charge. Determine the charge balance for this sample of water and comment on whether the result is reasonable.