91Ó°ÊÓ

One method for determining whether an individual recently fired a gun is to look for traces of antimony in residue collected from the individual's hands. Anodic stripping voltammetry at a mercury film electrode is ideally suited for this analysis. In a typical analysis a sample is collected from a suspect using a cotton-tipped swab wetted with \(5 \%\) \(\mathrm{v} / \mathrm{v} \mathrm{HNO}_{3} .\) After returning to the lab, the swab is placed in a vial that contains \(5.0 \mathrm{~mL}\) of \(4 \mathrm{M}\) HCl that is \(0.02 \mathrm{M}\) in hydrazine sulfate. After soaking the swab, a \(4.0-\mathrm{mL}\) portion of the solution is transferred to an electrochemical cell along with \(100 \mu \mathrm{L}\) of \(0.01 \mathrm{M} \mathrm{HgCl}_{2}\). After depositing the thin film of mercury and the antimony, the stripping step gives a peak current of \(0.38 \mu \mathrm{A}\). After adding a standard addition of \(100 \mu \mathrm{L}\) of \(5.00 \times 10^{2}\) ppb Sb, the peak current increases to \(1.14 \mu\) A. How many nanograms of Sb were collected from the suspect's hand?

Step by step solution

01

Define Variables and Known Values

Let \( C_i \) be the initial concentration of Sb in the solution, \( V_i \) the initial volume of the solution (\(4.0 \) mL), \( C_s \) the concentration of the standard addition (\(5.00 \times 10^2\) ppb), and \( V_s \) the volume of the standard addition (\(100 \mu\)L or \(0.1 \) mL). The initial peak current is \(0.38 \mu A\) and the final peak current is \(1.14 \mu A\) after standard addition.

02

Calculate Initial Concentration from Peak Current Ratio

Using the relationship between concentration and peak current, we can set up a proportion: \( \frac{I_{initial}}{I_{final}} = \frac{C_i}{C_i + C_s \times \frac{V_s}{V_i + V_s}} \). Plug in the given values: \( \frac{0.38}{1.14} = \frac{C_i}{C_i + (5.00 \times 10^2 \ times \frac{0.1}{4.1})} \). Solve for \( C_i \).

03

Solve for Initial Concentration \( C_i \)

\( \frac{0.38}{1.14} = \frac{C_i}{C_i + (50 \times \frac{10^2 \times 0.1}{4.1})} \). Calculate \( C_i \): solve the equation \( 0.3833 \times (C_i + 12.1951) = C_i \). Rearranging gives \( C_i (1 - 0.3833) = 0.3833 \times 12.1951 \). Simplifying gives \( C_i \approx 7.59 \) ppb.

04

Calculate Mass of Sb Collected

Convert \( C_i \), which is in ppb (ng/mL), to mass using the initial volume of the solution. \( Mass = C_i \times V_i = 7.59 \times 4.0 \) ng/mL \( = 30.36 \) ng. This is the total mass of Sb collected from the suspect's hand.

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Key Concepts

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

Anodic Stripping Voltammetry

Anodic Stripping Voltammetry (ASV) is a key technique in analytical chemistry used to detect and quantify trace metals. It is especially valuable due to its sensitivity, often reaching down to parts-per-billion (ppb) levels. Here's how it generally works: a metal ion is first deposited onto an electrode surface by reducing the ion to a metal film, usually using a mercury electrode, for a set period. This is the **deposition step**.

After this, the deposited metal is gradually oxidized (stripped away) by reversing the process, and during this **stripping step**, the current is measured. The current, which correlates to the amount of the metal gathered, produces a peak that corresponds to the concentration of the analyte in the solution. This is because the current is directly proportional to the analyte's concentration in the sample.

To enhance performance:

• Ensure the electrode is clean to improve film formation.
• Use a controlled environment to reduce interference.
• Properly calibrate to match expected concentration ranges.

This technique is especially well-suited for forensic analysis, such as determining if an individual recently fired a gun through residue detection.

Electrochemical Analysis

Electrochemical analysis is a broad field within analytical chemistry that focuses on the use and study of electrochemical cells. Here, we're concerned with reactions at the interface of an electrode immersed in a solution. The principles behind these chemical processes help us measure the amount of matter transformed by an electric current.

In the specific context of the exercise, a mercury film electrode is utilized for its efficacy in forming amalgams with metals like antimony. This particular setup allows for sensitive detection of trace elements.

Two crucial electrochemical techniques are typically used:

• **Potentiometry** - Measures the voltage of an electrochemical cell.
• **Voltammetry** - Measures the current due to the application of a potential.

For trace detection, voltammetry, as employed in the stated anodic stripping voltammetry, is preferred due to its high sensitivity and specific selectivity. Proper understanding and application of electrochemical methods can lead to precise and accurate measurements of trace amounts of chemicals in various matrices.

Trace Element Detection

Detecting trace elements is critical in various fields, including environmental monitoring, clinical diagnostics, and forensic investigations. Trace elements like antimony often exist in very low concentrations, making detection challenging but necessary, particularly in forensic applications like gunshot residue analysis.

Anodic stripping voltammetry stands out as a potent method due to several reasons:

• **Sensitivity**: Achieves detection down to ppb levels, ideal for low-concentration samples.
• **Selectivity**: Can often differentiate between multiple elements in a complex matrix.
• **Efficiency**: Rapid analysis is possible, which is crucial in time-sensitive contexts.

Understanding the interplay of current peaks and concentration enables precise quantification of elements like antimony. The method is reliable for determining trace elements in a variety of samples, making it invaluable for both quantitative and qualitative insights.

To enhance capabilities, ensuring sample purity, careful calibration, and appropriate choice of standards can drastically improve detection accuracy. This enables scientists and investigators to make informed decisions based on the evidence collected in laboratory setups.