Models of the Particulate Nature of Matter, Atomic Structure, and Emission Spectra

Particulate Nature of Matter: Elements, Compounds, and Mixtures

Elements
- All substances are composed of one or more elements.
- Elements cannot be broken down by any chemical process.
- There are 118 known elements.
- The smallest part of an element is an atom.
Compounds
- Made of more than one element chemically combined in a fixed ratio.
- Can be broken down chemically into their constituent elements.
- Possess chemical and physical properties distinct from their component elements.
- Example: $H_2O$ (consisting of 2 hydrogen atoms and 1 oxygen atom).
Mixtures
- Components are not chemically bonded and are not present in a fixed ratio.
- Components retain their individual properties.
- Can be separated by physical means.
- Types of Mixtures:
  - Homogeneous: Components are in the same phase (e.g., Air).
  - Heterogeneous: Components are in different phases (e.g., Oil and water).

Separation Techniques for Homogeneous and Heterogeneous Mixtures

Criteria for Choosing a Method
- Solubility in water or other solvents.
- Melting and boiling points of components.
- Whether the mixture is homogeneous or heterogeneous.
1. Filtration
- Purpose: Separate an insoluble solid from a liquid.
- Procedure:
  1. Fold filter paper into a cone and place it in a funnel.
  2. Wet the filter paper with a small amount of solvent.
  3. Pour the mixture slowly into the funnel.
  4. The filtrate (liquid) passes into the flask below.
  5. The residue (solid) is trapped on the filter paper.
  6. Wash the residue with cold solvent and dry.
- Types of Filtration:
  - Normal Filtration: Uses a filter funnel and filter paper; driven by gravity; used for larger solid particles.
  - Vacuum Filtration: Uses a Buchner funnel and Buchner flask; a vacuum pump creates reduced pressure to pull liquid through faster; used for very small solid particles.
2. Evaporation & Recrystallization
- Purpose: Separate and purify a soluble solid from a solution.
- Procedure:
  1. Warm the mixture with a solvent (e.g., water, ethanol, hexane) to dissolve the soluble component.
  2. Filter the hot solution to remove insoluble impurities.
  3. Evaporate the solvent to leave the solid behind.
  4. Purification: Dissolve the solid in a minimum amount of hot solvent.
  5. Cool slowly so pure crystals form (impurities remain dissolved).
  6. Filter to collect crystals.
  7. Wash with a small amount of cold solvent to avoid re-dissolving crystals.
  8. Dry the crystals.
3. Separatory Funnel
- Purpose: Separate two immiscible liquids (liquids that do not mix).
- Procedure:
  1. Pour the mixture into the funnel and replace the stopper.
  2. Shake to mix, then allow it to stand until two layers form.
  3. The more dense liquid sinks to the bottom.
  4. Remove the stopper and open the tap to run off the lower (denser) layer into a container.
  5. Collect the less dense upper layer separately from the top.
4. Distillation and Reflux
- Distillation Purpose: Obtain a pure solvent from a mixture or separate liquids with different boiling points.
- Distillation Procedure:
  1. Heat the mixture in a flask (e.g., using a water bath).
  2. The component with the lower boiling point evaporates first.
  3. The vapour travels into the condenser (water flows in at the bottom, out at the top).
  4. The condenser cools the vapour back into a liquid.
  5. The distillate is collected in a separate flask.
  6. A thermometer monitors the boiling point to confirm the substance identity.
- Reflux:
  - Uses the same apparatus but the purpose is to allow volatile compounds to react together when heated for extended periods.
  - Vapour is continuously condensed and returned to the flask, preventing loss of compounds via evaporation.
5. Melting Point Determination
- Purpose: Check the purity of a solid substance.
- Procedure:
  1. Place solid sample in a small melting point tube.
  2. Place tube in an oil bath with a thermometer and heat gradually.
  3. Record the temperature at melting.
  4. Compare with literature values.
- Interpreting Results:
  - Sharp melting point matching literature value = Pure substance.
  - Lower than literature value = Impure substance.
  - Melts over a wide temperature range = Impure substance.

Chromatography: Principles and Applications

General Concepts
- Used for separating mixtures with very small amounts of components.
- Used to determine purity and identify substances.
- Two Phases:
  - Stationary Phase: Fixed phase.
  - Mobile Phase: Moving phase.
- Separation is based on the tendency to adsorb onto a surface or dissolve in a solvent.
Paper Chromatography
- Stationary Phase: Water absorbed in cellulose paper.
- Mobile Phase: Organic solvent (e.g., ethanol, propanone, or ethanoic acid).
- Process: Mixture is spotted $\approx 1\,cm$ from the base and placed in a closed container with solvent. Separation occurs based on relative solubility in each phase.
- Visualization: Naked eye, staining (e.g., iodine), or UV light.
- Retardation Factor ( $R_f$ ): Specific to each solute for a given eluent, used for identification.
- $R_f = \frac{\text{distance moved by solute (x)}}{\text{distance moved by solvent eluent (y)}}$
Thin-Layer Chromatography (TLC)
- Uses a thin layer of alumina ( $Al_2O_3$ ) or silica ( $SiO_2$ ) on glass or another inert support.
- Mechanism: Adsorption; silica/alumina have a high affinity for water, so separation is by partition with water as the stationary phase.
- Advantage: Components can be recovered pure by scraping the section off the glass, dissolving in solvent, and evaporating.
- Two-Way Chromatography: Used to separate substances with similar $R_f$ (like amino acids) by rotating the paper $90°$ and running a different solvent.

Kinetic Molecular Theory and Physical States

Kinetic Molecular Theory (KMT)
- Matter consists of particles in constant motion.
- Particle energy depends on absolute temperature.
- Change of state occurs when particle energy changes.
- Average empty space increases from solid $\rightarrow$ liquid $\rightarrow$ gas.
- Intermolecular forces strengthen as particles move closer together.
States of Matter
- Solid (s): Fixed shape and volume; particles held by intermolecular forces; vibrate but have no translational velocity.
- Liquid (l): Takes the shape of the container; fixed volume; possesses some translational velocity, allowing for diffusion.
- Gas (g): Completely fills the container; negligible intermolecular forces; rapid, random motion; fast diffusion.
Changes of State
- Melting: Temperature remains constant; heat energy (enthalpy of fusion, $\Delta H_{fus}$ ) overcomes lattice forces.
- Boiling: Temperature remains constant; energy (enthalpy of vaporization, $\Delta H_{vap}$ ) overcomes intermolecular forces.
- Once the state change is complete (e.g., all liquid to gas), temperature rises as particles move faster.
Cooling Curves
- Shows the reverse process of heating.
- Flat sections represent changes of state at constant temperature.
- Stages:
  - A $\rightarrow$ B: Gas cooling.
  - B $\rightarrow$ C: Condensing (gas + liquid).
  - C $\rightarrow$ D: Liquid cooling.
  - D $\rightarrow$ E: Freezing (liquid + solid).
  - E $\rightarrow$ F: Solid cooling.

Maxwell–Boltzmann Distribution and Thermal Properties

Distribution of Molecular Velocities
- Particles in a gas or liquid travel at varying velocities.
- Maxwell–Boltzmann Curve: Graph showing the distribution of kinetic energies.
- Temperature Effects (T_2 > T_1):
  - Curve becomes broader and flatter.
  - Peak shifts right (indicating higher average kinetic energy).
  - Total area under the curve remains constant (same number of particles).
- Evaporation: The fastest-moving particles escape the surface, decreasing the average kinetic energy of the remaining liquid, which results in cooling.
Temperature Units and Constants
- Absolute temperature is proportional to average kinetic energy ( $\frac{1}{2} \text{mass} \times \text{velocity}^2$ ).
- SI Unit: kelvin (K); $1\,K = 1°C$ difference.
- Absolute Zero: $0\,K = -273°C$ .
- Conversion: $K = °C + 273$ .
- Water Points: Freezes at $273\,K$ , boils at $373\,K$ .
Boiling and Vapour Pressure
- Evaporation: Occurs at any temperature in an open system.
- Vapour Pressure: Increases as temperature increases.
- Boiling Point: Occurs when vapour pressure equals external pressure.
- Standard Boiling Point: Defined at $101\,325\,Pa$ ( $1.01 \times 10^5\,Pa = 1\,atm$ ).
- Pressure Variations: Water boils at $373\,K$ at $1\,atm$ , but at $\approx 344\,K$ ( $71°C$ ) on Mount Everest ( $3.4 \times 10^4\,Pa$ ) due to lower atmospheric pressure.
- Boiling points vary based on the strength of attractive forces between particles; weaker forces lead to lower boiling points.

Atomic Structure and Sub-atomic Particles

Sub-atomic Particles
- Proton:
  - Relative mass: $1$
  - Relative charge: $+1$
  - Location: Nucleus
  - Actual mass: $1.673 \times 10^{24}\,g$
- Neutron:
  - Relative mass: $1$
  - Relative charge: $0$ (neutral)
  - Location: Nucleus
- Electron:
  - Relative mass: $5 \times 10^4$ (negligible)
  - Relative charge: $-1$
  - Location: Energy levels/shells around the nucleus
  - Actual charge: $1.602 \times 10^{19}\,сoulombs$
- Nucleons: Collective term for protons and neutrons.
Structure of the Atom
- All atoms are neutral, with equal numbers of protons and electrons.
- Atom radius: $\approx 10^{10}\,m$ .
- Nucleus radius: $\approx 10^{14}\,m$ .
- Most of the atom is empty space; mass is concentrated in the nucleus.

Shorthand Notation, Isotopes, and Relative Atomic Mass

Notation Symbols
- Mass Number (A): Sum of protons and neutrons.
- Atomic Number (Z): Number of protons (and electrons in neutral atoms); defines the element.
- Charge: Positive ions lose electrons; negative ions gain electrons.
- Calculation: Number of neutrons = $A - Z$ .
Notation Examples
- $_4^9Be$ : $Z=4$ , $A=9$ , $4\,p$ , $5\,n$ , $4\,e$ .
- $_{20}^{40}Ca^{2+}$ : $Z=20$ , $A=40$ , $20\,p$ , $20\,n$ , $18\,e$ (lost $2\,e^-$ ).
- $_{17}^{37}Cl^-$ : $Z=17$ , $A=37$ , $17\,p$ , $20\,n$ , $18\,e$ (gained $1\,e^-$ ).
Isotopes
- Atoms of the same element with the same number of protons but different numbers of neutrons.
- Chemical Properties: Identical due to identical electron counts.
- Physical Properties: Different due to differing masses (affects density, boiling point, etc.).
- Examples:
  - Hydrogen: $^1H$ , $^2H$ (deuterium), $^3H$ (tritium).
  - Carbon: $^{12}C$ , $^{14}C$ .
  - Chlorine: $^{35}Cl$ , $^{37}Cl$ .
Relative Atomic Mass ( $A_r$ )
- Based on $\frac{1}{12}$ of the mass of a Carbon-12 atom.
- It is a weighted average of isotopic masses based on natural abundance.
- Chlorine Example: Exists as $^{35}Cl$ and $^{37}Cl$ in a $3:1$ ratio (75\%:25\%$).\n\n# Mass Spectrometry (AHL)\n\n* **Purpose**: Determine relative atomic masses experimentally.\n* **Process Steps**:\n 1. **Vaporization**: Sample is vaporized and injected.\n 2. **Ionization**: High-energy electrons create 1+ ions.\n 3. **Acceleration**: Ions pass through parallel plates and are accelerated by an electric field.\n 4. **Deflection**: External magnetic field deflects ions. Deflection depends on mass (lighter deflects more) and charge (higher charge deflects more).\n 5. **Detection**: Records mass/charge ratio and relative abundance.\n\n* **Worked Example: Lead (Pb)**\n * Isotopic Mass 204: Abundance 0.2 $($ 2\%\)\n * Isotopic Mass 206: Abundance 2.4 $($ 24\%\)\n * Isotopic Mass 207: Abundance 2.2 $($ 22\%\)\n * Isotopic Mass 208: Abundance 5.2 $($ 52\%\)\n * The relative atomic mass is calculated by the weighted mean of these values.\n\n# Electromagnetic Spectrum and Emission Spectra\n\n* **The Electromagnetic (EM) Spectrum**\n * Relationship: c = \lambda \times f.\n * Energy: Smaller wavelength (\lambda $)$ \rightarrow $higher frequency ($ f $)$ \rightarrow more energy.\n * **Order (Low to High Energy)**: radio waves \rightarrow $microwaves$ \rightarrow $infrared$ \rightarrow $visible light$ \rightarrow $ultraviolet$ \rightarrow $X-rays$ \rightarrow\gamma-radiation.\n * **Visible Light**: Red (low energy) \rightarrow violet (high energy); ROYGBIV.\n\n* **Spectra Types**\n * **Continuous Spectrum**: White light through a prism shows all colors unbroken.\n * **Line Spectrum**: Energy supplied to an element produces emission at specific wavelengths, unique to each element.\n * **Hydrogen Visible Line Spectrum (nm)**: 656 (red), 486 (blue), 434, 410, 397, 389, 365. Lines converge toward the high-energy (violet/UV) end.\n\n* **Explanation of Emission Spectra**\n * Electrons jump to higher levels when energy is supplied.\n * Dropping back down emits a photon with energy equal to the gap between levels.\n * **Lyman Series (UV)**: Electrons fall to n=1 (largest energy changes).\n * **Balmer Series (Visible)**: Electrons fall to n=2.\n * **Paschen Series (Infrared)**: Electrons fall to n=3.\n * **Convergence**: Lines converge because energy levels themselves converge at higher n.\n * **Series Limit**: At n = \infty \rightarrow 2 $, the wavelength is$ 365\,nm.\n\n# Electron Configurations and Orbital Filling Rules\n\n* **Organization of Electrons**\n * Max electrons in level n = 2n^2.\n * **Sublevels**: s, p, d, f.\n * **Orbitals per sublevel**: s=1 $($ 2\,e^- $max),$ p=3 $($ 6\,e^- $max),$ d=5 $($ 10\,e^- $max),$ f=7 $($ 14\,e^- max).\n\n* **Filling Order (Auffbau Principle)**\n * 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 4d < 4f.\n * **Note**: 4s $is lower in energy than$ 3d.\n\n* **Orbital Properties**\n * **Definition**: A 3D region of high probability for an electron (Heisenberg's Uncertainty Principle).\n * **Shapes**:\n * **s Orbitals**: Spherical.\n * **p $Orbitals**: Three dumbbell-shaped orbitals ($ p_x, p_y, p_z $) oriented orthogonally ($ 90°) to each other.\n\n* **Rules for Filling**\n * **Aufbau Principle**: Fill lowest energy first.\n * **Pauli Exclusion Principle**: Max 2 electrons per orbital; must have opposite spins.\n * **Hund's Rule**: Fill orbitals in the same sublevel singly first before pairing.\n\n* **Irregularities and Ions**\n * **Chromium (Cr $)**:$ [Ar] 4s^1 3d^5 $(half-full$ 3d sublevel).\n * **Copper (Cu $)**:$ [Ar] 4s^1 3d^{10} $(full$ 3d sublevel).\n * **Positive Ions**: Electrons are removed from the highest energy level first.\n * **Transition Metal Ion Rule**: The 4s $electrons are removed before$ 3d $electrons (e.g.,$ Fe^{2+} = [Ar] 3d^6).\n\n# Ionization Energies and Evidence for Energy Levels (AHL)\n\n* **First Ionization Energy (IE_1)**\n * **Definition**: Energy required to remove one electron from a mole of gaseous atoms in their ground state.\n * **Equation**: X_{(g)} \rightarrow X^+_{(g)} + e^-\n * **Units**: kJ\,mol^{-1}; always endothermic.\n\n* **Trends in First Ionization Energy**\n * **Highest value**: Helium (only 2 protons and 2 electrons in the lowest level).\n * **Sharp drop at Li and Na**: Marks the beginning of a new, higher energy shell (n=2 $and$ n=3).\n * **General increase across a period**: Due to increased nuclear charge pulling the same shell tighter.\n * **Dip at Boron (B $)**: Evidence of sublevels (moving from$ 2s $to higher-energy$ 2p).\n * **Dip at Oxygen (O $)**: Evidence of Hund's rule/repulsion; at oxygen, electrons must pair up in a$ p orbital, and the repulsion between like charges makes the electron easier to remove.\n\n* **Successive Ionization Energies**\n * Energy increases for each successive electron as the nuclear charge attracts remaining electrons more strongly.\n * **Big Jumps**: Indicate removal of an electron from a lower (inner) energy shell.\n * **Valence Electrons**: The number of electrons removed before the first big jump identify the group number.\n\n* **Ionization Energy Calculation from Hydrogen Spectrum**\n * At the convergence limit (n=1 \rightarrow n=\infty), the electron is removed.\n * For Hydrogen, the limit is in the UV region at \lambda = 91.2\,nm.\n * Energy can be calculated using E = hf $. This value matches the experimentally determined$ IE_1 of Hydrogen.\n\n* **Summary of Evidence**\n * **Periodic Pattern in IE_1**: Distinct main energy levels.\n * **Small Dips (B, O)**: Existence of sublevels (s, p).\n * **Big Jumps**: Electron count per main level (group number).\n * **Convergence Limit**: Direct calculation of ionization energy via E=hf$$.