/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 22 The composition of a multivitami... [FREE SOLUTION] | 91影视

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Chapter 12: Problem 22

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.

Short Answer

Expert verified
Calculate response factors, then use them to find concentrations in the sample. Finally, convert concentrations to milligrams for each vitamin.

Step by step solution

01

Determine Response Factors

To find the concentration of each vitamin in the sample solution, we first need to calculate the response factor (R_F) for each vitamin using the standard signals and concentrations provided. The response factor is calculated as follows:\[R_F = \frac{Signal_{standard}}{Concentration_{standard}}.\]Calculate the response factors for each vitamin.
02

Calculate Concentrations in Sample

Using the response factors calculated in the previous step, we determine the concentrations of each vitamin in the tablet extract. This is done by rearranging the formula for response factors:\[Concentration_{sample} = \frac{Signal_{sample}}{R_F}.\]Using the sample signal for each vitamin, calculate the concentration of each in the sample solution.
03

Convert Concentrations to Milligrams

To find the milligrams of each vitamin in the tablet, use the concentration in the sample solution and convert it to the total amount. The concentrations from the previous step are in ppm, which are equivalent to mg/L in the extract. Since the total volume of the extract is 100 mL, convert the concentration to mg by multiplying by the volume:\[Mass_{vitamin} = Concentration_{sample} \times \text{Total Volume (L)}.\]Convert each vitamin concentration to milligrams in the entire volume.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Vitamin Analysis
High-Performance Liquid Chromatography (HPLC) is an analytical technique used to separate, identify, and quantify individual components in a mixture. It's particularly powerful in vitamin analysis, allowing for precise measurement of vitamins in complex samples like multivitamin tablets. The analyze works by injecting a small volume of the sample solution into the HPLC system, where different vitamins travel at unique speeds through a column under pressure. This method is highly effective for determining the vitamin composition in tablets. In this experiment, vitamins such as vitamin C, niacin, niacinamide, pyridoxine, thiamine, folic acid, and riboflavin are analyzed. Each vitamin's retention time鈥攖he time it takes to pass through the column鈥攈elps in its identification. The diode array UV/Vis detector then measures the absorbance of each vitamin at specific wavelengths. This absorbance is directly related to the concentration of the vitamin present in the solution, which is crucial to find out how much of each vitamin is in the tablet.
Response Factor Calculation
To accurately quantify the vitamins in the multivitamin tablet using HPLC, Response Factor (RF) calculation is essential. Response Factor is a way of correlating the detector signal (from HPLC) to the concentration of the vitamin. It is calculated using standard samples with known concentrations and their corresponding signals. The formula for calculating the response factor for each vitamin is:\[ R_F = \frac{Signal_{standard}}{Concentration_{standard}} \]Using the RF, we can process any sample鈥檚 HPLC data to find the concentration of each vitamin in the sample solution. The concentration is then calculated by rearranging the formula:\[ Concentration_{sample} = \frac{Signal_{sample}}{R_F} \]This calculation is crucial because it allows us to translate the signals obtained from the sample into meaningful concentration values. Without an RF, it would be impossible to precisely quantify the vitamins in the sample based on the signals alone.
Diode Array UV/Vis Detection
Diode Array UV/Vis Detection is an integral part of HPLC, especially useful in the detection of vitamins. This detection method utilizes a diode array to measure the absorbance of light by the compounds as they elute off the HPLC column. The spectrum is recorded, providing not only the concentration of the analyte but also aiding in the identification of each compound. A diode array detector allows for the simultaneous collection of data at multiple wavelengths, making it a highly versatile tool. For vitamins, whose molecular structures absorb UV/visible light at various unique wavelengths, this characteristic is particularly important. It enables the distinction of similar compounds based on their absorbance patterns or UV spectra. The measured signals from the diode array UV/Vis detector correspond to the concentration of vitamins in the sample. By comparing these signals against those from a set of standards, it becomes possible to determine both the qualitative identity and quantitative concentration of vitamins in complex samples like multivitamin tablets.

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Most popular questions from this chapter

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.

Janusa and coworkers describe the determination of chloride by CZE. \(^{29}\) Analysis of a series of external standards gives the following calibration curve. $$ \text { area }=-883+5590 \times \text { ppm } \mathrm{Cl}^{-} $$ A standard sample of \(57.22 \% \mathrm{w} / \mathrm{w} \mathrm{Cl}^{-}\) is analyzed by placing \(0.1011-\mathrm{g}\) portions in separate \(100-\mathrm{mL}\) volumetric flasks and diluting to volume. Three unknowns are prepared by pipeting \(0.250 \mathrm{~mL}, 0.500 \mathrm{~mL},\) and \(0.750 \mathrm{~mL}\) of the bulk unknown in separate \(50-\mathrm{mL}\) volumetric flasks and diluting to volume. Analysis of the three unknowns gives areas of \(15310,31546,\) and \(47582,\) respectively. Evaluate the accuracy of this analysis.

A series of polyvinylpyridine standards of different molecular weight was analyzed by size-exclusion chromatography, yielding the following results. \begin{tabular}{cc} formula weight & retention volume (mL) \\ \hline 600000 & 6.42 \\ 100000 & 7.98 \\ 20000 & 9.30 \\ 3000 & 10.94 \end{tabular} When a preparation of polyvinylpyridine of unknown formula weight is analyzed, the retention volume is \(8.45 \mathrm{~mL}\). Report the average formula weight for the preparation.

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.

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.
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