Foundations of Atomic Theory, Laws of Chemical Combination, Isotopes, Ions, and the Mole Concept

Classification of Matter

Pure Substances and Mixtures

Matter can be classified based on its composition as either a pure substance or a mixture. Pure substances include elements and compounds, while mixtures can be homogeneous or heterogeneous.

• Pure Substance: Contains only one type of particle (element or compound).

• Mixture: Contains two or more different particles physically combined.

• Homogeneous Mixture: Uniform composition throughout (solution).

• Heterogeneous Mixture: Non-uniform composition; different parts are visibly distinct.

Example: Table salt (NaCl) is a pure compound; air is a homogeneous mixture; sand and iron filings form a heterogeneous mixture.

Scientific Laws and Theories

Law of Conservation of Mass

The Law of Conservation of Mass states that matter is neither created nor destroyed in a chemical reaction.

• Equation: $\text{Total mass before reaction} = \text{Total mass after reaction}$

• Application: Balancing chemical equations relies on this law.

Law of Definite Proportions

The Law of Definite Proportions states that a given compound always contains the same elements in the same proportion by mass, regardless of sample size.

• Example: Water (H2O) always contains hydrogen and oxygen in a mass ratio of 1:8.

• Equation: $\text{Mass ratio} = \frac{\text{Mass of element 1}}{\text{Mass of element 2}}$

Law of Multiple Proportions

When two elements form more than one compound, the masses of one element that combine with a fixed mass of the other are in ratios of small whole numbers.

• Example Table:

Compound	Mass of C (g)	Mass of O (g)	Ratio of O in CO2 to CO
CO	12.01	16.00	1
CO2	12.01	32.00	2

• Equation: $\text{Ratio} = \frac{\text{Mass ratio in compound 2}}{\text{Mass ratio in compound 1}}$

Dalton's Atomic Theory

Postulates of Dalton's Atomic Theory

• Elements are made of tiny particles called atoms.

• All atoms of a given element are identical.

• Atoms of different elements are different.

• Atoms combine in simple whole-number ratios to form compounds.

• Atoms are not created or destroyed in chemical reactions.

Example: In water, two hydrogen atoms combine with one oxygen atom (H2O).

Subatomic Particles and Experiments

Millikan Oil-Drop Experiment

The Millikan oil-drop experiment measured the charge of a single electron by balancing gravitational and electrical forces on tiny charged oil droplets.

• Key Principle: The force on a charge in an electric field is $F = qE$.

• Millikan determined the elementary charge $e = 1.602 \times 10^{-19}$ C.

Isotopes and Ions

Isotopes

Isotopes are atoms of the same element with different numbers of neutrons and thus different mass numbers.

• Notation: $^{A}_{Z}\text{X}$, where $A$ is the mass number, $Z$ is the atomic number, and X is the element symbol.

• Example Table:

Isotope	Protons	Neutrons	Symbol
Carbon-12	6	6	$^{12}_{6}\text{C}$
Carbon-13	6	7	$^{13}_{6}\text{C}$
Carbon-14	6	8	$^{14}_{6}\text{C}$

Ions

An ion is an atom or molecule with a net electrical charge due to the loss or gain of electrons.

• Cation: Positively charged ion (loss of electrons).

• Anion: Negatively charged ion (gain of electrons).

• Example: Na atom ($11p^+, 11e^-$) loses one electron to become Na+ ($11p^+, 10e^-$).

Atomic Mass and Mass Spectrometry

Atomic Mass

The atomic mass of an element is the weighted average of the masses of its naturally occurring isotopes.

• Equation: $\text{Atomic mass} = \sum (\text{isotope mass} \times \text{fractional abundance})$

Mass Spectrometry

Mass spectrometry is an analytical technique used to determine the masses and relative abundances of isotopes in a sample.

• Sample is ionized, accelerated, and separated by mass-to-charge ratio ($m/z$).

• The resulting mass spectrum shows peaks corresponding to different isotopes.

• Base peak: The most intense peak, set to 100% relative abundance.

Example Table:

Isotope	Mass (amu)	Abundance (%)
Ga-69	68.9256	60.11
Ga-71	70.9247	39.89

The Mole Concept

Definition and Calculations

The mole is the SI unit for amount of substance, defined as containing $6.022 \times 10^{23}$ entities (Avogadro's number).

• Key Equations:

• Number of moles: $n = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}$

• Number of particles: $N = n \times N_A$

• Volume of gas at STP: $V = n \times 22.4$ L

Example: How many atoms are in 2.00 mol of carbon? $2.00 \times 6.022 \times 10^{23} = 1.204 \times 10^{24}$ atoms.

Summary Table: Laws of Chemical Combination

Law	Description	Example
Conservation of Mass	Mass is neither created nor destroyed	Mass of reactants = mass of products
Definite Proportions	Compounds have fixed mass ratios	NaCl: 39.34% Na, 60.66% Cl
Multiple Proportions	Elements combine in small whole-number ratios	CO and CO2: O mass ratio 2:1

Additional info:

• Some diagrams and tables were inferred and summarized for clarity.

• Sample calculations and classification exercises were referenced but not fully reproduced due to space; students should practice with provided worksheet problems for mastery.