science notes

1. States of Matter and Kinetic Molecular Theory

• Fundamental States of Matter

  • Solid

  • Definite shape and fixed volume.

  • Particles are closely packed in an orderly, rigid lattice structure.

  • Particles vibrate about fixed positions; intermolecular forces are very strong.

  • Possesses the lowest kinetic energy among the three states.

  • Liquid

  • Indefinite shape (assumes the shape of its container) and fixed volume.

  • Particles remain closely associated but lack long-range order.

  • Particles slide and flow past one another; moderate intermolecular forces.

  • Possesses intermediate kinetic energy.

  • Gas

  • Indefinite shape and indefinite volume (expands uniformly to fill any container).

  • Particles are widely separated with negligible intermolecular attraction.

  • Particles move rapidly, continuously, and randomly in straight-line trajectories.

  • Possesses the highest kinetic energy.

• Phase Changes and Thermal Energy

  • Melting: Solid to liquid at a fixed melting point ($\text{endothermic}$, absorbs heat).

  • Freezing (Solidification): Liquid to solid at a fixed freezing point ($\text{exothermic}$, releases heat).

  • Vaporisation: Liquid to gas ($\text{endothermic}$, absorbs heat).

  • Boiling: Bulk process occurring throughout the liquid at a defined boiling point (e.g., $100\,^\circ\text{C}$ for pure water at $1\,\text{atm}$).

  • Evaporation: Surface process occurring at any temperature below the boiling point.

  • Condensation: Gas to liquid ($\text{exothermic}$, releases heat).

  • Sublimation: Direct change from solid to gas without entering the liquid state (e.g., solid $CO_2$; $\text{endothermic}$).

  • Deposition: Direct change from gas to solid without entering the liquid state ($\text{exothermic}$).

2. Properties and Classification of Matter

• Physical vs. Chemical Properties

  • Physical Properties: Characteristics observed or measured without altering the chemical identity of the substance.

  • Intensive Properties: Independent of the amount of substance present (e.g., density, melting point, boiling point, electrical conductivity).

  • Extensive Properties: Proportional to the size or mass of the sample (e.g., total mass, volume, length).

  • Chemical Properties: Characteristics describing the ability of a substance to form new chemical substances via chemical reactions (e.g., flammability, toxicity, heat of combustion, oxidation potential).

• Density and Calculations

  • Density ($\rho$) is an intensive physical property defined as mass per unit volume:     $\rho = \frac{m}{V}$

  • Rearranged to solve for mass ($m$):     $m = \rho \times V$

  • Rearranged to solve for volume ($V$):     $V = \frac{m}{\rho}$

  • Standard chemistry units:

  • Solids and liquids: $g\,cm^{-3}$

  • Gases: $g\,dm^{-3}$

• Classification of Matter

  • Pure Substances

  • Elements: Consist of only one type of atom; cannot be chemically decomposed into simpler substances (e.g., $Fe$, $O_2$, $Cu$).

  • Compounds: Consist of two or more distinct elements chemically combined in fixed, definite stoichiometric proportions (e.g., $H_2O$, $NaCl$, $CO_2$).

  • Mixtures

  • Homogeneous Mixtures (Solutions): Uniform composition and uniform physical properties throughout a single phase (e.g., dissolved sodium chloride in water, clean air).

  • Heterogeneous Mixtures: Non-uniform composition with physically distinct phases and boundaries (e.g., sand and iron filings, oil and water suspension).

3. Atomic Structure, Subatomic Particles, and Isotopes

• The Subatomic Particles

  • Proton ($p^+$)

  • Position: Inside the dense central nucleus.

  • Relative charge: $+1$

  • Relative mass: approximately $1\,\text{u}$

  • Rest mass: $1.673 \times 10^{-27}\,\text{kg}$

  • Neutron ($n^0$)

  • Position: Inside the dense central nucleus.

  • Relative charge: $0$ (neutral)

  • Relative mass: approximately $1\,\text{u}$

  • Rest mass: $1.675 \times 10^{-27}\,\text{kg}$

  • Electron ($e^-$)

  • Position: Electron shells (orbitals) surrounding the nucleus.

  • Relative charge: $-1$

  • Relative mass: $\frac{1}{1836}\,\text{u}$

  • Rest mass: $9.109 \times 10^{-31}\,\text{kg}$

• Nuclide Notation and Atomic Numbers

  • Atomic Number ($Z$): The number of protons residing in the nucleus. Identifies the chemical element.

  • Mass Number ($A$): The sum of protons and neutrons in the nucleus:     $A = Z + N$

  • Neutron Number ($N$): Calculated by subtracting atomic number from mass number:     $N = A - Z$

  • For any neutral atom:     $\text{Number of protons} = \text{Number of electrons}$

  • Standard nuclide format: $_{Z}^{A}\text{X}$

• Isotopes and Relative Atomic Mass ($A_r$)

  • Isotopes are atoms belonging to the same element that have the same atomic number ($Z$) but different mass numbers ($A$) due to a differing quantity of neutrons ($N$).

  • Isotopes have identical chemical reactivity because their valence electron configuration is identical.

  • Relative atomic mass formula using percentage abundance:     $A_r = \frac{\sum (\text{Isotopic Mass} \times \text{Percentage Abundance})}{100}$

  • Relative atomic mass formula using fractional (decimal) abundance:     $A_r = \sum (\text{Isotopic Mass} \times \text{Fractional Abundance})$

• Electron Configuration and Valence Shells

  • Electron shell maximum capacity rule:     $\text{Maximum Capacity} = 2n^2$

  • First shell ($n = 1$): up to $2$ electrons.

  • Second shell ($n = 2$): up to $8$ electrons.

  • Third shell ($n = 3$): accommodates $8$ electrons for stable main-group configuration.

  • Cation Formation: Neutral atom loses valence electrons to form a positively charged ion (e.g., $Na \rightarrow Na^+ + e^-$).

  • Anion Formation: Neutral atom gains valence electrons to form a negatively charged ion (e.g., $Cl + e^- \rightarrow Cl^-$).

4. Scientific Notation and Significant Figures

• Scientific Notation

  • Written in the standard exponential form:     $N \times 10^n$     where $1 \le |N| < 10$ and $n$ is an integer.

  • Positive exponents indicate numbers greater than or equal to $10$ (decimal shift to the left).

  • Negative exponents indicate numbers strictly between $0$ and $1$ (decimal shift to the right).

  • Multiplication in scientific notation:     $(a \times 10^x) \times (b \times 10^y) = (a \times b) \times 10^{x+y}$

  • Division in scientific notation:     $\frac{a \times 10^x}{b \times 10^y} = \left(\frac{a}{b}\right) \times 10^{x-y}$

• Rules for Counting Significant Figures

  • All non-zero digits are significant (e.g., $54.2\,\text{g}$ has $3$ significant figures).

  • Captive zeros (zeros placed between two non-zero digits) are always significant (e.g., $7003\,\text{m}$ has $4$ significant figures).

  • Leading zeros (zeros preceding the first non-zero digit) are never significant; they serve only as placeholders (e.g., $0.0048\,\text{g}$ has $2$ significant figures).

  • Trailing zeros (zeros at the end of a number):

  • Significant if and only if a decimal point is explicitly shown (e.g., $85.00\,\text{cm}^3$ has $4$ significant figures).

  • Ambiguous or non-significant if no decimal point is shown (e.g., $8500\,\text{cm}^3$ typically indicates $2$ significant figures, best clarified via scientific notation as $8.500 \times 10^3\,\text{cm}^3$ for $4$ significant figures).

  • Exact numbers (counted quantities or defined unit conversions) have an infinite number of significant figures.

• Rules for Calculations with Significant Figures

  • Multiplication and Division: The final calculated value must be rounded to contain the same number of significant figures as the measurement with the fewest significant figures.

  • Addition and Subtraction: The final calculated value must be rounded to match the measurement having the fewest decimal places (least precise place value).

5. Essential Formula Summary

• Density Formula:   $\rho = \frac{m}{V}$

• Mass Rearrangement:   $m = \rho \times V$

• Volume Rearrangement:   $V = \frac{m}{\rho}$

• Mass Number:   $A = Z + N$

• Neutron Count:   $N = A - Z$

• Relative Atomic Mass:   $A_r = \frac{\sum (\text{Mass} \times \text{Abundance}\,\%)}{100}$

• Shell Capacity:   $\text{Capacity} = 2n^2$

• Net Charge of an Ion:   $$\