Problem 13 - Analytical Chemistry

Question

Lozano-Calero and colleagues developed a method for the quantitative analysis of phosphorous in cola beverages based on the formation of the blue-colored phosphomolybdate complex, \(\left(\mathrm{NH}_{4}\right)_{3}\left[\mathrm{PO}_{4}\left(\mathrm{MoO}_{3}\right)_{12}\right] .^{21}\) The complex is formed by adding \(\left(\mathrm{NH}_{4}\right)_{6} \mathrm{Mo}_{7} \mathrm{O}_{24}\) to the sample in the presence of a reducing agent, such as ascorbic acid. The concentration of the complex is determined spectrophotometrically at a wavelength of \(830 \mathrm{nm}\), using an external standards calibration curve. In a typical analysis, a set of standard solutions that contain known amounts of phosphorous is prepared by placing appropriate volumes of a 4.00 ppm solution of \(\mathrm{P}_{2} \mathrm{O}_{5}\) in a \(5-\mathrm{mL}\) volumetric flask, adding \(2 \mathrm{~mL}\) of an ascorbic acid reducing solution, and diluting to volume with distilled water. Cola beverages are prepared for analysis by pouring a sample into a beaker and allowing it to stand for \(24 \mathrm{~h}\) to expel the dissolved \(\mathrm{CO}_{2}\). A \(2.50-\mathrm{mL}\) sample of the degassed sample is transferred to a 50 -mL volumetric flask and diluted to volume. A \(250-\mu \mathrm{L}\) aliquot of the diluted sample is then transferred to a \(5-\mathrm{mL}\) volumetric flask, treated with \(2 \mathrm{~mL}\) of the ascorbic acid reducing solution, and diluted to volume with distilled water. (a) The authors note that this method can be applied only to noncolored cola beverages. Explain why this is true. (b) How might you modify this method so that you can apply it to any cola beverage? (c) Why is it necessary to remove the dissolved gases? (d) Suggest an appropriate blank for this method? (e) The author's report a calibration curve of $$ A=-0.02+\left(0.72 \mathrm{ppm}^{-1}\right) \times C_{\mathrm{P}_{2} \mathrm{O}_{5}} $$ A sample of Crystal Pepsi, analyzed as described above, yields an absorbance of \(0.565 .\) What is the concentration of phosphorous, reported as ppm \(\mathrm{P}\), in the original sample of Crystal Pepsi?

Step-by-Step Solution

Answer

The method is limited to noncolored colas due to color interference in measurement. Remove gases to avoid reaction interference. Use a blank with no beverage. Phosphorus concentration is about 71.08 ppm in the original cola sample.

Step 1: Understand why the method is limited to noncolored beverages

The method relies on spectrophotometric measurement at 830 nm to quantify the complex. Colored beverages can absorb light at this wavelength, causing interference with the measurement of the phosphomolybdate complex, thereby affecting accuracy.

Step 2: Modify the method for colored beverages

One way to apply this method to colored beverages is by including additional spectral analysis to subtract the absorbance due to the beverage's color. Alternatively, use a different wavelength where the beverage color has less interference, if possible.

Step 3: Understand why expelling dissolved gases is necessary

CO₂ dissolves in cola beverages, forming carbonic acid. Carbonate species can interfere with the reaction that forms the phosphomolybdate complex. Expelling CO₂ reduces this interference, ensuring that the reaction and subsequent spectrophotometric analysis are accurate.

Step 4: Suggest an appropriate blank

An appropriate blank for this experiment would be a solution prepared in the same way as the sample, but without the cola beverage. This includes the ascorbic acid solution and distilled water, ensuring any absorbance is due to the reagents.

Step 5: Solve for concentration of phosphorus in Crystal Pepsi

Given the equation for the calibration curve, \( A = -0.02 + (0.72 \, \text{ppm}^{-1}) \times C_{\mathrm{P}_{2} \mathrm{O}_{5}} \), set \( A = 0.565 \) and solve for \( C_{\mathrm{P}_{2} \mathrm{O}_{5}} \).\[ \begin{align*} 0.565 &= -0.02 + 0.72 \times C_{\mathrm{P}_{2} \mathrm{O}_{5}} \ 0.585 &= 0.72 \times C_{\mathrm{P}_{2} \mathrm{O}_{5}} \ C_{\mathrm{P}_{2} \mathrm{O}_{5}} &= \frac{0.585}{0.72} \ C_{\mathrm{P}_{2} \mathrm{O}_{5}} &\approx 0.8125 \, \text{ppm} \end{align*} \] The concentration of phosphorous as P can be determined by converting this P₂O₅ concentration using the molecular weight ratio: \( \text{ppm P} = \frac{31}{141.94} \times 0.8125 \approx 0.1777 \, \text{ppm} \).

Step 6: Apply dilution factors to find concentration in original sample

The phosphorus concentration found corresponds to the final diluted sample measurement. To find the concentration in the original Crystal Pepsi, use the cumulative dilution factor. The first dilution is 2.50 mL in 50 mL, the second is 250 µL in 5 mL. Apply the dilution factors:\[ \begin{align*} \text{Dilution factor from 2.50 mL to 50 mL} &= \frac{50}{2.50} = 20 \ \text{Dilution factor from 250 µL to 5 mL} &= \frac{5}{0.250} = 20 \ \text{Total dilution factor} &= 20 \times 20 = 400 \ \text{Concentration in original sample} &= 0.1777 \, \text{ppm} \times 400 = 71.08 \, \text{ppm} \end{align*} \] The concentration of phosphorus in the original Crystal Pepsi is approximately 71.08 ppm.

Key Concepts

Phosphomolybdate Complex

In chemical analysis, the formation of specific complexes can be an easy way to measure concentrations of particular components. The phosphomolybdate complex is one such compound, formed during the analysis to determine phosphorus content. This process involves combining ammonium molybdate with a phosphorus source. In the presence of a reducing agent like ascorbic acid, a blue-colored complex is created.

This complex is highly important because its bright blue color at a wavelength of 830 nm allows for its concentration to be measured accurately using spectrophotometric methods. Various factors such as temperature, pH, and the presence of other ions can affect the formation of the phosphomolybdate complex. Thus, it's crucial to maintain consistent conditions to get reliable results.

Spectrophotometry

Spectrophotometry is a technique used to measure the amount of light absorbed by a sample. It works based on the principle that different compounds absorb light at different wavelengths.

During a spectrophotometric analysis, light is passed through a sample, and the amount of light absorbed is measured. For the phosphomolybdate complex, the wavelength used is 830 nm, which corresponds to the blue color of the complex. By measuring the absorbance at this specific wavelength, the concentration of phosphorus in the sample can be indirectly determined.

Some advantages of spectrophotometry include its non-destructive nature and the possibility to analyze very small amounts of samples quickly. However, its limitation is that it requires a standard calibration curve for quantitative analysis and is susceptible to interference from other substances that absorb light at the same wavelength.

Standard Calibration Curve

A calibration curve is a must-have in quantitative spectrophotometry for determining unknown concentrations. It's created by preparing a series of standard solutions with known concentrations and measuring their absorbance. These data points are then plotted with concentration on one axis and absorbance on the other.

The relationship is typically linear, and the equation of the line gives the correlation between concentration and absorbance. Once the curve is established, unknown sample concentrations can be determined by measuring their absorbance and locating it on the graph. This method relies on the idea that absorbance is directly proportional to concentration, thanks to the Beer's Law principle.

Having a precise calibration curve is essential as it directly impacts the accuracy of the concentrations determined from unknown samples. It often involves regression analysis to derive the best fit line that accounts for experimental variability and matrix effects.

Dilution Factors

Dilution is a common technique in the lab to adjust the concentration of a solution to a desired lower value. When performing serial dilutions, it's crucial to account for each factor in the calculation of the final concentration.

In the case of phosphorus analysis in cola beverages, multiple dilution steps are often necessary. For instance, a standard initial dilution might involve transferring a specific volume of the original sample into a larger volumetric flask to achieve the first diluted sample. Another dilution may follow by using a small aliquot of this diluted sample.

To compute the new concentration after these dilutions, use the dilution factor formula, which is the ratio of the final volume to the initial volume. Multiply the concentration from each stage by its respective dilution factor to gain the cumulative dilution effect. This multi-step dilution process helps adjust concentrations into ranges that are more manageable for accurate spectrophotometric readings and calculations.