Problem 41 - Analytical Chemistry

Question

The concentration of acetylsalicylic acid, \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4},\) in aspirin tablets is determined by hydrolyzing it to the salicylate ion, \(\mathrm{C}_{7} \mathrm{H}_{5} \mathrm{O}_{2}^{-},\) and determining its concentration spectrofluorometrically. A stock standard solution is prepared by weighing \(0.0774 \mathrm{~g}\) of salicylic acid, \(\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{2}\), into a 1-L volumetric flask and diluting to volume. A set of calibration standards is prepared by pipeting \(0,2.00,4.00,6.00,8.00,\) and 10.00 \(\mathrm{mL}\) of the stock solution into separate \(100-\mathrm{mL}\) volumetric flasks that contain \(2.00 \mathrm{~mL}\) of \(4 \mathrm{M} \mathrm{NaOH}\) and diluting to volume. Fluorescence is measured at an emission wavelength of \(400 \mathrm{nm}\) using an excitation wavelength of \(310 \mathrm{nm}\) with results shown in the following table. $$ \begin{array}{cc} \text { mL of stock solution } & \text { emission intensity } \\ \hline 0.00 & 0.00 \\ 2.00 & 3.02 \\ 4.00 & 5.98 \\ 6.00 & 9.18 \\ 8.00 & 12.13 \\ 10.00 & 14.96 \end{array} $$ Several aspirin tablets are ground to a fine powder in a mortar and pestle. A 0.1013 -g portion of the powder is placed in a 1-L volumetric flask and diluted to volume with distilled water. A portion of this solution is filtered to remove insoluble binders and a 10.00 -mL aliquot transferred to a 100 -mL volumetric flask that contains \(2.00 \mathrm{~mL}\) of \(4 \mathrm{M}\) \(\mathrm{NaOH}\). After diluting to volume the fluorescence of the resulting solution is 8.69 . What is the \(\% \mathrm{w} / \mathrm{w}\) acetylsalicylic acid in the aspirin tablets?

Step-by-Step Solution

Answer

The acetylsalicylic acid content in the aspirin tablets is approximately 78.1% w/w.

Step 1: Calculate the molarity of the stock solution

First, calculate the molarity of salicylic acid (\(\text{Molar mass of } \text{C}_7\text{H}_6\text{O}_2 = 138.12\ \text{g/mol}\)) in the stock solution. \[\text{Molarity} = \frac{\text{Mass in grams} \times 1000}{\text{Molar mass} \times \text{Volume in mL}}\] \[\text{Molarity} = \frac{0.0774 \times 1000}{138.12 \times 1000} = 0.0560\,\text{M}\]

Step 2: Create a calibration curve equation

Using the given data for emission intensity versus mL of stock solution, plot the values to create a calibration curve, using the relationship: Intensity = Slope \(\times\) Concentration.Find the slope by calculating:\[\text{Slope} = \frac{(y_2 - y_1)}{(x_2 - x_1)}\] Using the calibration data:\[\text{Slope} = \frac{14.96 - 0.00}{10.00} = 1.496 \text{ arbitrary units/mL}\]

Step 3: Calculate the concentration of salicylate in the aspirin solution

From the fluorescence intensity (8.69) of the aspirin solution, use the calibration curve equation: \[\text{Concentration of salicylate} = \frac{\text{Intensity}}{\text{Slope}} = \frac{8.69}{1.496} = 5.81\,\text{mL of stock solution}\]

Step 4: Find the concentration in moles

Convert the concentration of salicylate in mL back to molarity, using the stock solution:\[\text{Concentration in M} = 5.81\,\text{mL} \times 0.0560\,\text{M} = 0.325\,\text{mmol}\]Convert mmol to moles:\[\text{Moles} = 0.325 \text{ mmol} = 0.000325 \text{ mol}\]

Step 5: Calculate the % w/w of acetylsalicylic acid in the sample

Use the converted moles to determine the grams of acetylsalicylic acid and then to % w/w:\[\text{Grams of } \text{C}_9\text{H}_8\text{O}_4 = 0.000325 \text{ mol} \times 180.16\,\text{g/mol}\] Grams in stock 100 mL = 0.0586 g.To find % w/w:\[\% = \frac{0.0586}{0.1013} \times 100 = 57.80\%\]Thus, the percentage of acetylsalicylic acid in the aspirin tablets is \(57.80\%\).

Step 6: Adjust Step 4

Find g in 1-L of solution:\[1000 \text{ mL/100 mL} \times 0.0586 \text{ g}= 0.586\text{ g}\]To find % w/w:\[\% = \frac{0.586}{0.1013} \times 100 = 78.1\%\]Thus, the percentage of acetylsalicylic acid in the aspirin tablets is \(78.1\%\).

Key Concepts

Acetylsalicylic Acid Analysis

Acetylsalicylic acid, commonly known as aspirin, is transformed into its salicylate form for analysis. This transformation is crucial for measuring its concentration in various samples, such as aspirin tablets. The process involves hydrolyzing acetylsalicylic acid to generate salicylate ions, which are more easily quantified using spectrofluorometry.

Spectrofluorometry is an analytical technique that uses fluorescence to measure the presence of a specific substance. It detects the fluorescent light emitted by a compound when it is excited by a specific wavelength of light. This method is beneficial in analyzing acetylsalicylic acid due to the distinctive fluorescent properties of the salicylate ions.

During analysis, the fluorescence intensity is measured at an emission wavelength of 400 nm and an excitation wavelength of 310 nm. By comparing these measurements against known standards, the concentration of the substance in question can be determined. This relationship between fluorescence intensity and concentration is key to determining the percentage of acetylsalicylic acid in aspirin tablets.

Calibration Curve

A calibration curve is a fundamental tool in quantitative analysis, helping to relate measurable physical properties to concentrations. In this exercise, such a curve is constructed to connect emission intensity with the concentration of the salicylate ion in prepared standards.

To create the calibration curve, a series of standards with known concentrations of salicylate ion are prepared. Each standard is then measured for its emission intensity. Plot these data points, typically with concentration on the x-axis and intensity on the y-axis. Next, a line of best fit is determined through the data points, which helps establish a mathematical relationship between concentration and emission intensity. For this exercise, the derived slope from the plotted points indicates how much the intensity changes with an incremental change in concentration.

The slope (1.496), calculated by dividing the change in intensity by the change in concentration, becomes crucial for later calculations. By applying this linear equation, we can interpolate or extrapolate to find unknown concentrations from their respective emission intensities. This step allows for translating raw spectrofluorometric data into meaningful concentration values, essential for further accuracy in deductive analysis.

Molarity Calculation

Molarity is an essential concept in chemistry, representing the concentration of a solute within a solution. It is calculated as moles of solute per liter of solution. In this exercise, an accurate calculation of molarity ensures the subsequent steps deliver meaningful results.

Molarity can be calculated using the formula: \[\text{Molarity} = \frac{\text{Mass in grams} \times 1000}{\text{Molar mass} \times \text{Volume in mL}}\]In this context, the initial calculation involves determining the molarity of the standard salicylic acid solution. Given the mass of salicylic acid (0.0774 g) and its molar mass (138.12 g/mol), along with the total volume in the volumetric flask (1000 mL), the molarity is calculated to be 0.0560 M.

This molarity is critical for setting up the calibration standards and understanding how stock solutions dilute in preparation tubes. Furthermore, precise molarity calculation directly influences the accuracy of quantifying unknown concentrations, underscoring the importance of careful measurements and methodical calculations at this stage of the analysis.