Equation Sheet and Reference Data

Potentially Useful Equations

This section provides essential equations and constants commonly used in introductory General Chemistry.

• Density: The density (d) of a substance is defined as its mass (m) per unit volume (V).

• Atomic Mass: The average atomic mass of an element is calculated using the weighted average of its isotopes.

• Avogadro's Number: The number of particles (atoms, molecules, ions) in one mole of a substance.

particles = 1 mole

Periodic Table of the Elements

The periodic table organizes all known chemical elements by increasing atomic number, electron configuration, and recurring chemical properties. It is essential for identifying element groups, periods, and predicting chemical behavior.

Chapter 1: Matter, Measurement, and Scientific Approach

Understanding the Scientific Approach

The scientific approach involves systematic observation, hypothesis formation, experimentation, and the development of theories and laws.

• Theory: A well-substantiated explanation of some aspect of the natural world.

• Law: A statement based on repeated experimental observations that describes some aspect of the world.

• Hypothesis: A tentative explanation that can be tested by experiments.

States of Matter and Classification

Matter can be classified by its physical state and composition.

• States of Matter: Solid, liquid, gas.

• Pure Substances: Elements and compounds with fixed composition.

• Mixtures: Homogeneous (uniform composition) and heterogeneous (non-uniform composition).

Physical and Chemical Properties and Changes

• Physical Properties: Can be observed without changing the substance (e.g., melting point, density).

• Chemical Properties: Describe a substance's ability to undergo chemical changes (e.g., flammability).

• Physical Change: Does not alter the chemical composition (e.g., melting, boiling).

• Chemical Change: Alters the chemical composition (e.g., rusting, combustion).

Energy: Law of Conservation and Types

• Law of Conservation of Energy: Energy cannot be created or destroyed, only transformed.

• Kinetic Energy: Energy of motion.

• Potential Energy: Energy due to position or composition.

Units of Measurement and SI Prefixes

• SI Units: Standard units for scientific measurement (meter, kilogram, second, mole, etc.).

• SI Prefixes: Used to express multiples or fractions of units (e.g., kilo-, milli-, centi-).

• Density: Commonly measured in g/mL or g/cm3.

Significant Figures and Calculations

• Significant Figures: Digits in a measurement that are known with certainty plus one estimated digit.

• Rules: Nonzero digits are always significant; zeros between nonzero digits are significant; leading zeros are not significant; trailing zeros are significant if there is a decimal point.

• Maintaining Significant Figures: When performing calculations, the result should have the same number of significant figures as the measurement with the fewest significant figures.

Precision and Accuracy

• Precision: How close repeated measurements are to each other.

• Accuracy: How close a measurement is to the true value.

Dimensional Analysis

• Dimensional Analysis: A method to convert one unit to another using conversion factors.

• Example: Converting grams to moles using molar mass.

Chapter 2: Atoms and Elements

Atomic Theory and Structure

• Dalton's Atomic Theory: All matter is composed of atoms; atoms of the same element are identical; atoms combine in simple ratios to form compounds.

• Nuclear Theory: Atoms have a dense nucleus containing protons and neutrons; electrons occupy the surrounding space.

Subatomic Particles

• Proton: Positively charged particle in the nucleus.

• Neutron: Neutral particle in the nucleus.

• Electron: Negatively charged particle outside the nucleus.

• Atomic Number (Z): Number of protons in the nucleus.

• Mass Number (A): Sum of protons and neutrons.

Isotopes and Atomic Mass

• Isotopes: Atoms of the same element with different numbers of neutrons.

• Average Atomic Mass: Weighted average of all isotopes' masses.

Ions

• Cation: Atom that has lost electrons (positive charge).

• Anion: Atom that has gained electrons (negative charge).

Periodic Table Organization

• Groups: Vertical columns with similar chemical properties.

• Periods: Horizontal rows.

• Metals, Nonmetals, Metalloids: Classified by physical and chemical properties.

• Main Group and Transition Elements: Main group (s and p blocks), transition (d block).

Atomic Mass Calculations

• Use the relative abundance and mass of each isotope to calculate the average atomic mass.

• Example: If isotope X-45 (32.88%, 44.8776 amu) and X-47 (67.12%, 46.9643 amu):

Mole Concept and Avogadro's Number

• Mole: The amount of substance containing Avogadro's number of particles.

• Converting between mass, moles, and number of particles using molar mass and Avogadro's number.

Sample Table: Subatomic Particles in Atoms and Ions

Additional info: Table entries inferred for illustration.

Chapter 3: Molecules and Compounds

Types of Chemical Bonds

• Ionic Bonds: Formed between metals and nonmetals via electron transfer.

• Covalent Bonds: Formed between nonmetals via electron sharing.

• Metallic Bonds: Involve delocalized electrons among metal atoms.

Chemical Formulas

• Empirical Formula: Simplest whole-number ratio of elements in a compound.

• Molecular Formula: Actual number of atoms of each element in a molecule.

• Structural Formula: Shows the arrangement of atoms.

Naming Compounds

• Ionic Compounds: Name the cation first, then the anion (e.g., NaCl: sodium chloride).

• Covalent Compounds: Use prefixes to indicate the number of each atom (e.g., CO2: carbon dioxide).

• Acids: Named based on the anion (e.g., HCl: hydrochloric acid; HNO3: nitric acid).

• Polyatomic Ions: Familiarity with common ions (e.g., NO3-: nitrate, SO42-: sulfate).

Calculating Molar Mass and Conversions

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

• Conversions between grams, moles, and number of particles using molar mass and Avogadro's number.

• Example: To find the number of moles in 12.01 g of carbon (molar mass = 12.01 g/mol):

Empirical and Molecular Formula Determination

• Empirical formula is determined from percent composition by mass.

• Molecular formula is a whole-number multiple of the empirical formula.

Sample Table: Common Polyatomic Ions

Additional info: Table entries inferred for illustration.

Practice and Review

Sample Calculation: Atomic Mass

• Given isotopic masses and abundances, calculate the average atomic mass.

• Example: For element X with isotopes X-45 (44.8776 amu, 32.88%) and X-47 (46.9643 amu, 67.12%):

Sample Calculation: Moles and Mass

• To find the number of atoms in a given mass, use molar mass and Avogadro's number.

• Example: Number of phosphorus atoms in 0.158 g of P (molar mass = 30.97 g/mol):

mol atoms

Sample Calculation: Empirical Formula

• Given percent composition, determine the empirical formula.

• Example: 66.6% C, 11.2% H, 22.2% O by mass.

Steps:

1. Assume 100 g sample: 66.6 g C, 11.2 g H, 22.2 g O.

2. Convert to moles: C: , H: , O:

3. Divide by smallest number of moles to get ratio.

Key Terms and Concepts

• Significant Figures

• Isotope

• Mole

• Empirical Formula

• Molecular Formula

• Ion

• Polyatomic Ion

• Atomic Number

• Mass Number

• Avogadro's Number

• Molar Mass

Additional info: This study guide is based on a practice exam and review topics for a General Chemistry course, covering foundational concepts, calculations, and nomenclature.