General Chemistry Foundations: Matter, Atoms, Molecules, and Solutions

Chapter 1: Matter and Measurements

Matter and Its Composition

Matter is anything that occupies space and has mass. It is composed of atoms and molecules, which are the fundamental building blocks of chemistry.

• Atoms: Smallest unit of matter, made up of protons, neutrons, and electrons.

• Molecular element: Two or more of the same type of atom joined by a chemical bond (e.g., H2, O2).

• Compounds: Two or more different atoms joined together by a chemical bond (e.g., CO2, H2O).

Scientific Method of Inquiry

Chemists use the scientific method to learn about the physical world. This involves making observations, forming hypotheses, developing laws, and constructing theories.

• Law of Conservation of Mass: In a chemical reaction, matter is neither created nor destroyed.

• Dalton's Atomic Theory: All matter is composed of small, indestructible particles called atoms.

Scientific Measurements and Notation

Measurements in chemistry require proper formatting and reporting to ensure clarity and reproducibility.

• Scientific notation: Expresses numbers as a decimal and exponent (e.g., 5,283 = 5.283 x 103).

• Reporting data: All digits except the last are certain; the last digit is estimated.

• Significant Figures: Rules for addition/subtraction (smallest decimal place) and multiplication/division (smallest number of significant figures).

• Rounding: If the digit after the last is 0-4, leave unchanged; if 5-9, round up.

Precision and Accuracy

Precision refers to how close a series of measurements are to one another, while accuracy measures how close a value is to the actual value.

• Standard deviation: $\sigma_s = \sqrt{\sum (x_i - \bar{x})^2 / (n-1)}$

• Percent deviation: $\%\text{dev} = \frac{\text{average deviations}}{\text{average}} \times 100$

• Relative standard deviation (RSD): $\text{RSD} = \frac{\sigma_s}{\text{mean}} \times 100$

• Percent error: $\%\text{error} = \frac{\text{experimental value} - \text{actual value}}{\text{actual value}} \times 100$

SI Units and Metric Prefixes

Chemists use SI units based on the metric system for consistency.

• Length: meter (m)

• Mass: kilogram (kg)

• Time: second (s)

• Temperature: Kelvin (K)

• Metric prefixes: Mega (106), Kilo (103), Milli (10-3), Micro (10-6), Nano (10-9), Pico (10-12)

Dimensional Analysis and Density

Dimensional analysis uses conversion factors to convert between units. Density is a key property used in conversions.

• Density: $\text{Density} = \frac{\text{mass}}{\text{volume}}$ (units: g/mL)

Energy Units and Temperature

Energy is measured in joules (J), calories (cal), and kilowatt-hours (kWh). Temperature conversions are essential in chemistry.

• Kelvin: $K = ^\circ C + 273.15$

• Celsius: $^\circ C = \frac{(^\circ F - 32)}{1.8}$ or $^\circ C = (^\circ F - 32) \times \frac{5}{9}$

States of Matter and Types of Substances

Matter exists as solids, liquids, or gases. Substances can be pure (elements or compounds) or mixtures (homogeneous or heterogeneous).

• Solids: Crystalline (ordered) or amorphous (disordered)

• Liquids: Particles close but free to move

• Gases: Particles far apart and move freely

• Mixtures: Homogeneous (well mixed) or heterogeneous (distinct layers/parts)

Physical and Chemical Changes

Physical changes alter state or size without changing composition. Chemical changes result in new substances with different properties.

• Physical separation techniques: Filtration, distillation, chromatography

Chapter 2: Elements, Atoms, and Ions

History and Atomic Theory

The concept of atoms originated with the Greeks and evolved through the work of many scientists. Dalton's Atomic Theory explained mass laws and the nature of atoms.

• Mass Conservation: Atoms cannot be created or destroyed.

• Definite Composition: Compounds have fixed ratios of elements by mass.

• Multiple Proportions: Elements combine in ratios of small whole numbers.

Subatomic Particles

Atoms are composed of protons, neutrons, and electrons, each with distinct properties.

• Proton: Positive charge, mass ≈ 1 amu

• Neutron: Neutral, mass ≈ 1 amu

• Electron: Negative charge, mass ≈ 0.00055 amu

Atomic Structure and Isotopes

Atoms are electrically neutral, with a nucleus containing protons and neutrons, surrounded by electrons. Isotopes are atoms of the same element with different numbers of neutrons.

• Atomic Number (Z): Number of protons

• Mass Number (A): Number of protons + neutrons

• Isotope notation: $^A_ZX$ or X-A

Periodic Table and Element Properties

The periodic table organizes elements by atomic number. Each element is defined by its number of protons, and can have varying numbers of neutrons (isotopes) and electrons (ions).

• Cations: Positive ions (lost electrons)

• Anions: Negative ions (gained electrons)

• Groups: Columns with similar properties (e.g., alkali metals, halogens)

Compounds and Chemical Bonds

Compounds are formed by chemical bonds between atoms. Ionic bonds involve electron transfer; covalent bonds involve electron sharing.

• Ionic compounds: Lattice of alternating ions

• Covalent compounds: Individual molecules

• Chemical formula: Indicates number and type of elements

• Empirical formula: Simplest ratio of elements

• Molecular formula: Actual number of atoms

• Structural formula: Shows bonding arrangement

Naming Compounds

Compounds are named based on their composition and bonding type.

• Type I: Metal + nonmetal, fixed charge

• Type II: Metal + nonmetal, variable charge (use Roman numerals)

• Type III: Two nonmetals (use prefixes for number of atoms)

• Acids: Binary acids (hydro- + anion base + -ic acid), oxyacids (-ous for -ite, -ic for -ate)

• Hydrocarbons: Alkanes (CnH2n+2), named by number of carbons

Formula Mass and Molar Mass

The formula mass (molecular mass, molar mass) is the sum of atomic masses in a compound, expressed in amu or g/mol.

• Molar Mass: $\text{Molar Mass} = \sum [\# \text{atoms} \times \text{atomic mass}]$

Chapter 3: Solutions and Chemical Quantities

The Mole and Avogadro's Number

Counting individual atoms or molecules is impractical, so chemists use the mole as a counting unit. One mole contains 6.022 x 1023 particles (Avogadro's number).

• Mole: Defined as exactly 12 grams of C-12 isotope

• Molar Mass: Mass of one mole of a substance (g/mol)

Converting Between Grams, Moles, and Molecules

To convert between mass, moles, and number of molecules, use the molar mass and Avogadro's number.

• Step 1: Convert grams to moles using molar mass

• Step 2: Convert moles to molecules using Avogadro's number

Empirical and Molecular Formulas

Empirical formulas show the simplest ratio of elements; molecular formulas show the actual number of atoms. The molecular formula is a multiple of the empirical formula.

• Empirical formula calculation: Convert % composition to grams, then to moles, divide by smallest number of moles, adjust to whole numbers.

• Molecular formula: $n = \frac{\text{molar mass}}{\text{empirical formula molar mass}}$

Solution Chemistry and Concentration

Solutions are homogeneous mixtures of two or more substances. The concentration of a solution describes the amount of solute present.

• Solvent: Substance present in largest amount

• Solute: Substance present in smaller amount

• Molarity (M): $M = \frac{\text{moles solute}}{\text{liters solution}}$

• Molality (m): $m = \frac{\text{moles solute}}{\text{kg solvent}}$

• Mole fraction: $\text{mole fraction} = \frac{\text{moles solute}}{\text{total moles}}$

• Mass %: $\text{mass %} = \frac{\text{mass solute}}{\text{mass solution}} \times 100$

• ppm: $\text{ppm} = \frac{\text{mass solute}}{\text{mass solution}} \times 10^6$

• ppb: $\text{ppb} = \frac{\text{mass solute}}{\text{mass solution}} \times 10^9$

Preparation and Dilution of Solutions

Solutions can be prepared by dissolving a known amount of solute in solvent. Dilutions are made using the equation $M_1V_1 = M_2V_2$.

Interactions in Solutions

In aqueous solutions, interactions occur between solvent molecules, solute molecules, and between solvent and solute.

Concentration of Ions in Solution

The concentration of ions in solution can be calculated using the molarity of the compound and the mole ratio of ions.

• Example: 6.00 M K2SO4 yields 12.00 M K+ and 6.00 M SO42-

Appendix: Subatomic Particle Properties

Particle	Mass (kg)	Mass (amu)	Charge (relative)	Charge (C)
Proton	1.67262 × 10-27	1.00727	1+	+1.60218 × 10-19
Neutron	1.67493 × 10-27	1.00866	0	0
Electron	0.00091 × 10-27	0.00055	1–	–1.60218 × 10-19