Untitled Notes

Chapter 17: Fundamentals of Spectrophotometry

Wavelength (λ):
- Definition: The distance between wave peaks, measured in meters (m).
Frequency (ν):
- Definition: The number of oscillations in a second, measured in Hertz (Hz).
Key Relationship:
- The speed of light (c) is expressed as:
  c = λν
- Where:
- c: Speed of light (constant, approximately 3 imes 10^8 m/s)
- λ: Wavelength
- ν: Frequency
Photon Energy (E):
- Formula:
  E = hν
- Where:
- E: Energy per photon
- h: Planck's constant, approximately 6.626 imes 10^{-34} J·s
- ν: Frequency
Wavenumber (v):
- Definition: The number of waves per unit distance, given by the formula:
  v = rac{1}{λ}
Speed (c):
- Constant, independent of the frequency and wavelength.

Energy Levels: Energy associated with different wavelengths expressed in kJ/mol.
- Y-rays: 1.2 imes 10^7 kJ/mol
- X-rays: 12,000 kJ/mol
- Ultraviolet: 310 kJ/mol
- Electronic excitation: 150 kJ/mol
- Bond breaking and ionization: 0.080 - 150 kJ/mol
Frequency Levels in Hz:
- Ranges from:
- 10^{20} Hz (Y-rays) to 10^{8} Hz (Microwave)
Visible Spectrum:
- Wavelength (m):
- 10^{-7} ext{ m} to 10^{-6} ext{ m}
- Represented in nanometers (nm):
- 400 nm (violet) to 800 nm (red)

Absorbance (A):
- Formula:
  A = ext{ln} rac{P_0}{P} = - ext{ln} T
- Where:
- P₀: Incident light intensity
- P: Transmitted light intensity
- T: Transmittance
Components of Beer’s Law:
- A = εbc
- Where:
- ε: Molar absorptivity (extinction coefficient)
- b: Path length (cm)
- c: Concentration (Molarity)

Example 1: Quantifying a component in a mixture.
- A 250.0 mL solution contains 25.8 mg benzene (C₆H₆, FM: 78.11) in hexane with:
  - Absorption peak at 256 nm.
  - Absorbance: 0.266 in a 1.000 cm cell.
- Calculation Required: Find the molar absorptivity of benzene.
Example 2: Hexane contaminated with benzene.
- Absorbance: 0.070 at 256 nm in a 5.000 cm cell.
- Calculation Required: Find the concentration of benzene (mg/L).
- Key Advantage: Non-destructive evaluation of samples.
Example 3: Potassium permanganate (KMnO₄).
- Given:
  - Concentration: 7.25 imes 10^{-5} ext{ M}
  - Transmittance: 44.1% in a 2.10 cm cell at wavelength 525 nm.
- Calculation Required: Find the absorbance of this solution and the molar absorptivity of KMnO₄.

Total Absorbance Formula: A{ ext{total}} = A1 + A2 + … + An
- Where:
- A: Absorbance at a single wavelength.
- No interaction between species affecting absorbance.

Purpose: Monitoring absorbance during a titration to determine the equivalence point.
Advantage: Corrects for physical dilution of solutions without altering the dissolved material concentration.

Given:
- Observed absorbance after adding 75 µL of ferric nitrilotriacetate to 1.500 mL of apotransferrin is 0.222.
- Final volume: 1.5 mL + 0.075 mL = 1.575 mL
- Corrected Absorbance Formula:
  ext{Corrected Absorbance} = rac{1.575 ext{ mL}}{1.500 ext{ mL}} imes 0.222 = 0.233

Processes Involved:
- Electronic excitation transitioning the molecule from ground state to excited states.
- States:
- Ground state
- Excited states
- Energy levels from n = 1 to n = ext{∞}
Basic Vibrational Excitation Modes:
- Modes such as scissoring, rocking, wagging, in-plane bending, and twisting.

Definitions:
- Singlet State: All electrons are paired.
- Triplet State: Two unpaired electrons, resulting in different spins.
Electronic Excitation: Each state may contain energy levels leading to diverse molecular behaviors.

Number of Modes:
- Formula: 3n - 6 where n = number of atoms in the molecule.
- Example Calculation for formaldehyde (4 atoms):
  3(4) - 6 = 6 modes.
Wavenumber (cm⁻¹):
- Stretching modes have higher frequencies than bending modes.

States Involved:
- S_0: Ground electronic state
- S_1: Lowest excited singlet state
- T_1: Lowest excited triplet state
Processes:
- Absorption, fluorescence, and phosphorescence processes identifiable in time scales.
- Fluorescence: Typically on the order of 10^{-8} to 10^{-4} seconds.
- Phosphorescence: Can last from 10^{-4} seconds to hours.

Characteristics:
- Intensity: Phosphorescence is less intense, often around 10 times lower than fluorescence.
- Duration: Phosphorescence persists significantly longer than fluorescence.
- Energy Levels: Phosphorescence generally occurs at lower energies with longer wavelengths compared to fluorescence.

Absorption and Emission Spectra:
- Typically mirror images of each other but can vary based on energy transitions and molecular geometry.
- Example: Absorption (black line) vs. Emission (colored line) of bis(benzylimido)-perylene in dichloromethane solution.

Observed Patterns:
- Absorption and emission spectra are correlated but show differences due to relaxation of geometrical configurations in ground and excited states after transitions.

Setup and Measurement:
- Instruments used include light source and monochromators to separate emitted light based on wavelength.

Emission Spectrum:
- Distribution of light emitted versus wavelength.
Excitation Spectrum:
- Emission intensity versus different excitation wavelengths.

Expression for Intensity: I = kP_o c
- Where:
- c: Concentration
- P_o: Irradiance
Fluorescence Intensity Chart:
- Demonstrates intensity changes with concentration.

Examples:
- Fluorescein, Calcein, reactive groups selective for specific ionic species (e.g., Ca²+).
- Fluorescein structure and its related functionalities in luminescence.