Unit 13: Other Analytical Techniques
Exploring specialized methods for elemental analysis, crystal structure determination, and classical quantitative analysis.
13.22 Atomic Absorption Spectroscopy (AAS)
Atomic Absorption Spectroscopy (AAS) is a highly sensitive technique used for the quantitative analysis of individual elements in a sample. It is particularly good for measuring the concentration of trace metals.
The principle is based on the same concept as UV-Vis spectroscopy, but applied to individual atoms instead of molecules. The process involves:
- Atomization: The sample (usually a liquid) is sprayed into a very hot flame (e.g., acetylene-air, ~2300 °C). The high temperature evaporates the solvent and breaks all chemical bonds, converting the sample into a cloud of free, ground-state atoms.
- Absorption: A special lamp, called a hollow-cathode lamp, which contains the specific element being analyzed, emits light at the exact wavelengths that the target element's atoms can absorb. This light is passed through the flame.
- Detection: The atoms of the target element in the flame absorb some of this light, promoting their electrons to higher energy levels. A detector measures how much of the specific wavelength of light has been absorbed.
According to the Beer-Lambert Law, the amount of light absorbed is directly proportional to the concentration of the target element in the original sample. This makes AAS an excellent tool for measuring very low concentrations of metals.
Solved Examples:
- What is the primary purpose of Atomic Absorption
Spectroscopy?
Solution: To determine the concentration of a specific element (usually a metal) in a sample. It is a quantitative technique. - Why is a very hot flame used in AAS?
Solution: To provide enough energy to break down the sample into a cloud of free, neutral atoms in their ground state. This process is called atomization. - Why is a special hollow-cathode lamp needed for each
element?
Solution: Because atoms absorb light at very specific, narrow wavelengths. The lamp must emit the exact wavelength that the target element can absorb to ensure the measurement is highly specific. - An environmental chemist wants to measure the concentration of lead in a
river water sample. Which technique would be most
suitable?
Solution: Atomic Absorption Spectroscopy (AAS) would be ideal because it is extremely sensitive for detecting trace amounts of metals like lead. - What is atomization?
Solution: It is the process of converting a sample into its individual, gaseous atoms. - Does AAS analyze molecules or atoms?
Solution: It analyzes individual atoms. - How is the concentration of an unknown sample determined using
AAS?
Solution: By creating a calibration curve. The absorbances of several standard solutions of known concentrations are measured, and a graph of absorbance vs. concentration is plotted. The absorbance of the unknown sample is then measured, and its concentration is found from the graph. - What is the main difference between AAS and UV-Vis
spectroscopy?
Solution: AAS measures the absorption of light by individual atoms to determine elemental concentration, while UV-Vis measures the absorption by molecules to study electronic transitions and determine molecular concentration. - Why is AAS so sensitive?
Solution: Because the absorption lines for atoms are extremely narrow, and the use of a specific hollow-cathode lamp makes the measurement highly selective, allowing for the detection of very low concentrations without interference. - Name an application for AAS in the food
industry.
Solution: To test for the presence and quantity of heavy metal contaminants (like lead, cadmium, or mercury) in food products.
13.23 X-ray Diffraction (XRD)
X-ray Diffraction (XRD) is a powerful non-destructive technique used to determine the atomic and molecular structure of a crystal. It works by irradiating a crystalline sample with X-rays.
The wavelength of X-rays is similar to the distance between atoms in a crystal lattice. When the X-ray beam strikes the crystal, the atoms scatter the X-rays. The scattered waves interfere with each other. In specific directions, the waves will interfere constructively, producing an intense beam. This phenomenon is called diffraction.
The relationship between the angle of the diffracted beam, the wavelength of the X-rays, and the spacing between the atomic planes in the crystal is described by Bragg's Law: $$ n\lambda = 2d \sin\theta $$ Where 'n' is an integer, 'λ' is the wavelength of the X-rays, 'd' is the spacing between the crystal planes, and 'θ' is the angle of diffraction.
By measuring the angles and intensities of the diffracted beams, scientists can work backwards to calculate the 'd' spacings and ultimately build a complete 3D model of the electron density, revealing the precise arrangement of atoms in the crystal.
Solved Examples:
- What is the primary use of X-ray
Diffraction?
Solution: To determine the three-dimensional arrangement of atoms within a crystalline solid. - Why are X-rays used in this technique instead of visible
light?
Solution: The wavelength of X-rays is on the same order of magnitude as the spacing between atoms in a crystal, which is a requirement for diffraction to occur. The wavelength of visible light is far too long. - What does the term "diffraction"
mean?
Solution: It is the bending and spreading of waves as they pass by an obstacle or through an aperture whose size is comparable to the wavelength of the waves. - What is Bragg's Law used for?
Solution: It relates the angles at which X-rays are diffracted to the spacing between the planes of atoms in a crystal, allowing this spacing ('d') to be calculated. - Can XRD be used to analyze a gas or a
liquid?
Solution: No. XRD requires the sample to be a crystalline solid, where the atoms are arranged in a regular, repeating lattice. - What was one of the most famous discoveries made using X-ray
Diffraction?
Solution: The determination of the double helix structure of DNA by Rosalind Franklin, James Watson, and Francis Crick. - What is "constructive interference"?
Solution: It is when scattered waves are in phase with each other, causing their amplitudes to add up and produce a more intense, detectable beam. - In Bragg's Law ($n\lambda = 2d \sin\theta$), what does 'd'
represent?
Solution: It represents the distance between adjacent planes of atoms in the crystal lattice. - How is XRD used in the pharmaceutical
industry?
Solution: To study the crystal structure of drugs. Different crystalline forms (polymorphs) of the same drug can have different properties, such as solubility and effectiveness. - Is XRD a qualitative or quantitative
technique?
Solution: It is primarily a qualitative technique for structure determination, but it can also be used quantitatively to determine the proportions of different crystalline phases in a mixture.
13.24 Review of Quantitative Titrations (Acid-Base, Redox)
Titration is a classical method of quantitative analysis used to determine the concentration of an unknown solution (the analyte) by reacting it with a solution of known concentration (the standard solution or titrant).
The titrant is added slowly from a burette to a known volume of the analyte in a flask until the reaction is just complete. This point, called the equivalence point, is visualized by a color change from an indicator or by an instrumental measurement.
Acid-Base Titrations
Used to determine the concentration of an unknown acid or base by neutralizing it with a standard base or acid. The equivalence point is detected using a pH indicator like phenolphthalein or methyl orange. The key calculation is based on the mole ratio from the balanced equation.
Redox Titrations
Used to determine the concentration of an oxidizing or reducing agent. The reaction involves the transfer of electrons. Often, one of the reactants acts as its own indicator. For example, in a titration with potassium permanganate ($KMnO_4$), the solution turns from colorless to a permanent faint pink at the endpoint as the purple $MnO_4^-$ ion is no longer being consumed.
Solved Examples:
- What is the purpose of a titration?
Solution: To accurately determine the concentration of an unknown solution. - What is the equivalence point in a
titration?
Solution: The point at which the moles of titrant added are stoichiometrically equal to the moles of analyte in the flask. - What is a standard solution?
Solution: A solution whose concentration is known precisely. - What piece of glassware is used to dispense the
titrant?
Solution: A burette. - What piece of glassware is used to accurately measure the volume of the
analyte?
Solution: A pipette. - In the titration of HCl with NaOH, what is the role of
phenolphthalein?
Solution: It is a pH indicator that changes color (from colorless to pink) at the equivalence point, allowing the end of the titration to be visualized. - A student titrates 25.0 cm³ of NaOH with 0.100 M HCl. The average titre is
22.5 cm³. What is the concentration of the
NaOH?
Solution: The reaction is 1:1. Moles HCl = $0.100 \times (22.5/1000) = 0.00225$ mol. Moles NaOH = 0.00225 mol. Concentration NaOH = $0.00225 / (25.0/1000) = 0.090$ M. - What is a common self-indicating titrant in redox
titrations?
Solution: Potassium permanganate ($KMnO_4$), which is intensely purple and turns colorless upon reaction. - What is the difference between an acid-base titration and a redox
titration?
Solution: An acid-base titration involves a neutralization reaction (proton transfer), while a redox titration involves an oxidation-reduction reaction (electron transfer). - Why is it important to know the balanced chemical equation for a
titration?
Solution: To determine the stoichiometric mole ratio between the titrant and the analyte, which is essential for the calculation.