Problem 20 - Analytical Chemistry

Question

Jones and Thatcher developed a spectrophotometric method for analyzing analgesic tablets that contain aspirin, phenacetin, and caffeine. \(^{24}\) The sample is dissolved in \(\mathrm{CHCl}_{3}\) and extracted with an aqueous solution of \(\mathrm{NaHCO}_{3}\) to remove the aspirin. After the extraction is complete, the chloroform is transferred to a \(250-\mathrm{mL}\) volumetric flask and diluted to volume with \(\mathrm{CHCl}_{3} .\) A \(2.00-\mathrm{mL}\) portion of this solution is then diluted to volume in a \(200-\mathrm{mL}\) volumetric flask with \(\mathrm{CHCl}_{3}\). The absorbance of the final solution is measured at wavelengths of \(250 \mathrm{nm}\) and \(275 \mathrm{nm}\), at which the absorptivities, in \(\mathrm{ppm}^{-1} \mathrm{~cm}^{-1},\) for caffeine and phenacetin are $$ \begin{array}{lcc} & \mathrm{a}_{250} & \mathrm{a}_{275} \\ \hline \text { caffeine } & 0.0131 & 0.0485 \\ \text { phenacetin } & 0.0702 & 0.0159 \end{array} $$ Aspirin is determined by neutralizing the \(\mathrm{NaHCO}_{3}\) in the aqueous solution and extracting the aspirin into \(\mathrm{CHCl}_{3}\). The combined extracts are diluted to \(500 \mathrm{~mL}\) in a volumetric flask. A 20.00 -mL portion of the solution is placed in a 100 -mL volumetric flask and diluted to volume with \(\mathrm{CHCl}_{3}\). The absorbance of this solution is measured at \(277 \mathrm{nm}\), where the absorptivity of aspirin is \(0.00682 \mathrm{ppm}^{-1} \mathrm{~cm}^{-1}\). An analgesic tablet treated by this procedure is found to have absorbances of 0.466 at \(250 \mathrm{nm}, 0.164\) at \(275 \mathrm{nm}\), and 0.600 at \(277 \mathrm{nm}\) when using a cell with a \(1.00 \mathrm{~cm}\) pathlength. Report the milligrams of aspirin, caffeine, and phenacetin in the analgesic tablet.

Step-by-Step Solution

Answer

The tablet contains approximately 10.9975 mg of aspirin, 10.84 mg of caffeine, and 6.54 mg of phenacetin.

Step 1: Determine Aspirin Concentration

The absorbance for aspirin at 277 nm is given as 0.600. Use Beer's Law, \(A = \varepsilon c l\), where \(\varepsilon\) (absorptivity) is 0.00682 ppm\(^{-1}\) cm\(^{-1}\), \(A\) is 0.600, and \(l\) is 1.00 cm. Solving for concentration \(c\), we find: \[ c = \frac{A}{\varepsilon \times l} = \frac{0.600}{0.00682 \times 1.00} = 87.98 \text{ ppm} \] This concentration is for the final diluted solution.

Step 2: Calculate Aspirin in Milligrams

The aspirin solution was initially diluted by a factor of 5 (from 20 mL to 100 mL) and then by a further factor of 25 (from 500 mL to 20 mL initially taken). Hence, the total dilution factor is 125. Therefore, the concentration in the original solution is \[ 87.98 \times 125 = 10997.5 \text{ ppm} \] This is equivalent to 10.9975 mg of aspirin in the original sample.

Step 3: Determine Caffeine and Phenacetin Concentrations

For caffeine and phenacetin, set up two equations using their measured absorbances and given absorptivities at 250 nm and 275 nm:- \(A_{250} = 0.466 = 0.0131c_{1} + 0.0702c_{2}\)- \(A_{275} = 0.164 = 0.0485c_{1} + 0.0159c_{2}\) Where \(c_1\) and \(c_2\) are the concentrations of caffeine and phenacetin, respectively.

Step 4: Solve Simultaneous Equations for Caffeine and Phenacetin

Use substitution or elimination to solve the simultaneous equations:1. From \(0.466 = 0.0131c_{1} + 0.0702c_{2}\): \[ c_{1} = \frac{0.466 - 0.0702c_{2}}{0.0131} \]2. Insert \(c_1\) into \(0.164 = 0.0485c_{1} + 0.0159c_{2}\) and solve for \(c_2\).3. Substitute \(c_2\) back into the equation for \(c_1\) to find its value.Through solving, we find \[ c_1 = 8.67\text{ ppm}, \quad c_2 = 5.23\text{ ppm} \] for the final diluted solution.

Step 5: Calculate Caffeine and Phenacetin in Milligrams

Each was diluted through a factor of 100 (2 mL to 200 mL) and 1250 (the initial 250 mL to 2 mL). Thus, the dilution factor is 1250, and so,\[ \text{Caffeine: } 8.67 \times 1250 = 10837.5 \text{ ppm} \approx 10.84 \text{ mg} \]\[ \text{Phenacetin: } 5.23 \times 1250 = 6537.5 \text{ ppm} \approx 6.54 \text{ mg} \]

Key Concepts

Analgesic Tablets

Analgesic tablets are medications that are widely used to relieve pain. Common components include aspirin, caffeine, and phenacetin. Each of these compounds plays a specific role in pain relief.

• Aspirin is famous for its anti-inflammatory properties. It helps to reduce fever and inflammation, making it effective for headaches, muscle pain, and arthritis.
• Caffeine is often included due to its stimulating effects. It can enhance the pain-relieving effect of aspirin and phenacetin, making the overall medication more effective.
• Phenacetin, although less common today, was originally popular for its pain-relieving properties. It's known to alleviate mild to moderate pain.

Analgesic tablets often combine these ingredients to offer a comprehensive approach to pain relief.
In some regions, newer formulations might not contain phenacetin due to safety concerns, highlighting the importance of understanding the components present in any medication you use.

Beer's Law

Beer's Law, crucial for spectrophotometric analysis, describes the relationship between the absorbance of light by a solution and the concentration of solute present. It is mathematically expressed as:\[ A = \varepsilon cl \]where:

• \(A\) represents absorbance (no unit due to its logarithmic nature)
• \(\varepsilon\) is the molar absorptivity or absorptivity coefficient, indicating how well a substance absorbs light at a particular wavelength
• \(c\) is the concentration of the solution in ppm or mol/L
• \(l\) is the path length of the container holding the liquid, usually expressed in centimeters

When applying Beer's Law in experiments, one needs to measure absorbance accurately. This measurement, together with the known absorptivity and path length, helps determine the concentration of a substance within a solution.
A common challenge in employing Beer's Law is ensuring linearity, which means the law holds true only under conditions where the relationship between absorbance and concentration remains linear. This necessitates careful calibration and testing.

Caffeine and Phenacetin Concentration

Determining the concentration of caffeine and phenacetin in a tablet involves a strategic understanding of their unique absorption characteristics at different wavelengths.Steps to Measure Concentrations Using Spectroscopy:

• Each compound absorbs light at specific wavelengths; for caffeine and phenacetin, 250 nm and 275 nm are used.
• Using the measured absorbances at these wavelengths, set up simultaneous equations relating absorbance to concentration for both compounds using their respective absorptivities.
• The equations are:
  • At 250 nm: \(A_{250} = \varepsilon_{250, \, ext{caffeine}} \times c_{ ext{caffeine}} + \varepsilon_{250, \, ext{phenacetin}} \times c_{ ext{phenacetin}}\)
  • At 275 nm: \(A_{275} = \varepsilon_{275, \, ext{caffeine}} \times c_{ ext{caffeine}} + \varepsilon_{275, \, ext{phenacetin}} \times c_{ ext{phenacetin}}\)

This forms a system of linear equations, which can be solved to find the unknown concentrations for caffeine and phenacetin.
The spectrophotometric method allows precise calculation of concentrations when carefully calibrating instruments and considering any potential interferences.