Problem 19 - Analytical Chemistry

Question

Lead (Pb) concentration in polluted water is determined using solid-phase extraction (SPE), combining preconcentration and the standard addition method (SAM), followed by absorbance measurement of a suitable Pb-complex. Assume only the Pb-complex absorbs light at the wavelength used. For the first step of \(\mathrm{SPE},\) a \(1000-\mathrm{mL}\) volume of either the original sample or spiked sample was preconcentrated (extracted). Then for the second step, a \(5-\mathrm{mL}\) volume of elution solvent was used to remove the preconcentrated Pb-complex from the SPE cartridge for each sample. For the preconcentrated, original polluted water sample the absorbance was 0.32 . Meanwhile, the spiked water sample contained an additional \(5.0 \times 10^{-8}\) mol Pb-complex per \(1000 \mathrm{~mL}\) of original sample. The absorbance of the preconcentrated, spiked solution was \(0.44 .\) The pathlength was \(1 \mathrm{~cm} .\) The molar absorptivity for the \(\mathrm{Pb}\) -complex is \(\varepsilon=\) \(2.0 \times 10^{4} \mathrm{Lmol}^{-1} \mathrm{~cm}^{-1}\) (a) What is the concentration of the Pb-complex in the original polluted water sample (prior to preconcentration)? Either use an equation or graphical approach. (b) What is the theoretical (ideal) preconcentration factor, \(P_{\text {ideal, }}\) for this analysis? (c) What is the experimental preconcentration factor, \(P_{\text {expt, }}\) and how does it quantitatively compare to the theoretical \(P_{\text {ideal, }}\) from part (b)?

Step-by-Step Solution

Answer

(a) Original concentration: \(1.33 \times 10^{-7}\) mol/L. (b) Theoretical factor, \(P_{\text{ideal}}:\) 200. (c) Experimental factor, \(P_{\text{expt}}:\) 120; efficiency: 60\%.

Step 1: Calculate Original Concentration in Eluted Solution

First, we'll calculate the Pb-complex concentration in the eluted solution using the measured absorbances and the molar absorptivity.We use Beer-Lambert Law:\[A = \varepsilon c l \]For the original sample, we have:\[0.32 = \varepsilon \cdot c_{elu} \cdot 1 \]Let's solve for \(c_{elu}\) (concentration in elution solvent):\[ c_{elu} = \frac{0.32}{\varepsilon} = \frac{0.32}{2.0 \times 10^{4}} = 1.6 \times 10^{-5} \text{ mol/L} \]

Step 2: Calculate Spiked Concentration in Elution

Next, we calculate the concentration using the spiked sample's data. The absorbance is:\[0.44 = \varepsilon \cdot (c_{elu} + c_{spk}) \cdot 1 \]Where \(c_{spk}\) is the concentration due to the spike alone. From this equation:\[ c_{elu} + c_{spk} = \frac{0.44}{2.0 \times 10^{4}} = 2.2 \times 10^{-5} \text{ mol/L} \]\(c_{elu}\) from previous calculation is subtracted to isolate the contribution of the spike:\[c_{spk} = 2.2 \times 10^{-5} - 1.6 \times 10^{-5} = 6.0 \times 10^{-6} \text{ mol/L} \]

Step 3: Calculate Original Concentration before Preconcentration

The spiked Pb-complex concentration in the sample is originally \( 5.0 \times 10^{-8} \) mol/L before preconcentration (due to spiking).Given the elution and spiking conditions:The concentration increase due to spiking after elution (from Step 2) of \(6.0 \times 10^{-6} \text{ mol/L} \) corresponds to the spiked concentration of \(5.0 \times 10^{-8} \text{ mol/L} \) before preconcentration.We derive the preconcentration factor as:\[ P_{\text{spike}} = \frac{6.0 \times 10^{-6}}{5.0 \times 10^{-8}} = 120 \]Thus, the concentration of the original Pb-complex in the raw sample is:\[ c_{\text{orig}} = \frac{1.6 \times 10^{-5}}{120} = 1.33 \times 10^{-7} \text{ mol/L} \]

Step 4: Calculate Theoretical Preconcentration Factor

Considering the volumes involved:The original sample volume is 1000 mL, and after preconcentration, it's reduced to an elution volume of 5 mL.The theoretical preconcentration factor \( P_{\text{ideal}} \) is:\[ P_{\text{ideal}} = \frac{1000}{5} = 200 \]

Step 5: Compare Experimental and Theoretical Preconcentration Factors

In the analysis, we derived the experimental preconcentration factor from the spiking experiment as 120 (from Step 3). Compared to the theoretical factor of 200 (from Step 4), the efficiency of preconcentration is:\[\text{Efficiency} = \left(\frac{120}{200}\right) \times 100\% = 60\% \]

Key Concepts

Solid-Phase Extraction (SPE)

Solid-Phase Extraction (SPE) is a valuable technique in analytical chemistry used to isolate and preconcentrate compounds from complex mixtures, such as polluted water. Using SPE, analytes are absorbed onto a solid phase, typically housed in a cartridge. The pollutants, such as lead complexes, are trapped on this solid phase while the rest of the sample passes through.
Once the compounds are captured, an elution solvent releases them from the solid phase into a more concentrated form. This method relies on selective interaction between the analyte and the solid phase, providing a robust technique for separating specific compounds from unwanted materials.
Benefits of SPE include:

• Enhancing the detection limits by increasing the analyte's concentration.
• Improving accuracy and reproducibility in complex sample matrices.
• Reducing matrix effects that might interfere with analysis.

SPE is particularly useful for environmental applications, such as determining metal concentrations in water, due to its efficiency in handling large volumes and its applicability to a wide range of substances.

Standard Addition Method (SAM)

The Standard Addition Method (SAM) is a quantitative technique used to counteract sample matrix effects, which can skew analytical results. It involves spiking a sample with a known quantity of the analyte and measuring the resultant change in signal. This method helps estimate the analyte's concentration in the original matrix by comparing the overall change.
In SAM, two measurements are typically taken: one of the original sample and one of the spiked sample. The comparison of results helps calculate the analyte's concentration accurately. This is particularly important when matrices contain components that can obscure or enhance the analyte's signal.

• SAM is highly effective when matrix effects are present.
• It improves reliability when direct calibration curves are unreliable.
• Works best for consistent samples, like industrial or environmental samples.

SAM ensures more accurate assessments, especially useful in analyzing heavy metals in various matrices, like water.

Beer-Lambert Law

The Beer-Lambert Law provides a fundamental principle in spectrophotometry, establishing a relationship between absorbance, concentration, and path length. It is expressed as: \[A = \varepsilon \cdot c \cdot l\] where:

• \(A\) is the absorbance, a unitless measure of how much light is absorbed.
• \(\varepsilon\) is the molar absorptivity, indicating how well a substance absorbs light at a given wavelength.
• \(c\) represents the concentration of the analyte.
• \(l\) is the path length, typically in centimeters, that the light travels through the sample.

This law assumes a linear relationship, essential for quantifying substances in solution based on their ability to absorb light.
In practical applications, the Beer-Lambert Law allows researchers to determine the concentration of analytes in a sample accurately, assuming that only the analyte absorbs at the measurement wavelength. The law's simplicity makes it a powerful tool in analytical methods, including SPE.

Preconcentration Factor

The preconcentration factor quantifies the efficiency of concentrating an analyte from a large sample to a smaller volume, vital in analytical techniques like SPE. It indicates how much the concentration of the analyte has been increased during the extraction process.
Mathematically, it is expressed as: \[ P = \frac{V_{original}}{V_{elution}} \] where:

• \(V_{original}\) refers to the initial sample volume before preconcentration.
• \(V_{elution}\) is the volume of the elution solvent used to recover the analyte.

A higher preconcentration factor means enhanced sensitivity and lower detection limits.
In the example provided, the theoretical preconcentration factor gives an ideal scenario, while the experimental value may be lower due to losses or inefficiencies during actual sample handling. Comparing theoretical and experimental preconcentration factors helps assess the SPE process's performance, ensuring methods are optimized for successful analyte recovery.

Molar Absorptivity

Molar absorptivity, also known as molar extinction coefficient, gauges how strongly a chemical species absorbs light at a specific wavelength. It is a crucial parameter in the Beer-Lambert Law, represented by \(\varepsilon\), and has units of \(\text{L} \cdot \text{mol}^{-1} \cdot \text{cm}^{-1}\).
A higher molar absorptivity value means that even small concentrations can produce significant absorbance, advantageous for detecting low-level analytes. The molar absorptivity depends on the intrinsic properties of the analyte and the wavelength of light used for measurement.
In practical scenarios, knowing the molar absorptivity allows one to determine the concentration of an analyte in a solution when you know the absorbance and path length. Accurate values are critical for quantitative analysis, particularly in the presence of interfering substances, as it ensures precise absorbance readings directly relate to analyte amounts.
Molar absorptivity is essential to verifying analytical predictions and maintaining reliable, high-quality measurements in laboratory settings where light-based measurements are key.