ACS Final Exam Review: Introductory Chemistry Study Guide

Measurement and Problem Solving

Metric Prefixes and Unit Conversions

Understanding metric prefixes and unit conversions is essential for accurate scientific measurement and communication.

• Metric Prefixes: Prefixes such as kilo- (103), centi- (10-2), milli- (10-3), and nano- (10-9) are used to express different orders of magnitude.

• Unit Conversions: Conversion factors are used to convert between units within the metric system and between English and International (SI) systems.

• Example: To convert 5 kilometers to meters: $5\ \text{km} \times \frac{1000\ \text{m}}{1\ \text{km}} = 5000\ \text{m}$

Significant Figures

Significant figures reflect the precision of a measured value.

• Definition: The digits in a measurement that are known with certainty plus one estimated digit.

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

• Example: 0.00450 has three significant figures.

Density Calculations

Density is a physical property that relates mass and volume.

• Definition: Density ($d$) is mass ($m$) per unit volume ($V$).

• Formula: $d = \frac{m}{V}$

• Applications: Rearranging the formula allows calculation of mass or volume if the other variables are known.

• Example: If $m = 10\ \text{g}$ and $V = 2\ \text{mL}$, then $d = 5\ \text{g/mL}$.

Matter and Energy

Physical and Chemical Changes

Understanding the difference between physical and chemical changes is fundamental in chemistry.

• Physical Change: Alters the form or appearance of matter but does not change its composition (e.g., melting, boiling).

• Chemical Change: Results in the formation of new substances with different properties (e.g., rusting, burning).

• Example: Ice melting is a physical change; iron rusting is a chemical change.

Physical Processes

Phase changes involve energy transfer and are classified as follows:

• Vaporization: Liquid to gas

• Condensation: Gas to liquid

• Freezing: Liquid to solid

• Melting: Solid to liquid

• Sublimation: Solid to gas

• Deposition: Gas to solid

Temperature Conversions

Temperature can be converted between Fahrenheit and Celsius using the following formula:

• Formula: $^\circ\text{C} = \frac{5}{9} ( ^\circ\text{F} - 32 )$

• Example: 98.6°F to °C: $^\circ\text{C} = \frac{5}{9} (98.6 - 32) = 37^\circ\text{C}$

Endothermic and Exothermic Processes

Energy changes accompany physical and chemical processes.

• Endothermic: Absorbs heat from surroundings (ΔH > 0).

• Exothermic: Releases heat to surroundings (ΔH < 0).

• Example: Melting ice is endothermic; combustion is exothermic.

Heat Calculations

The amount of heat absorbed or released can be calculated using:

• Formula: $q = m c \Delta T$

• Where: $q$ = heat (J), $m$ = mass (g), $c$ = specific heat (J/g·°C), $\Delta T$ = temperature change (°C)

• Example: 10 g water, $c = 4.18$ J/g·°C, $\Delta T = 5^\circ$C: $q = 10 \times 4.18 \times 5 = 209$ J

Atoms and Elements

Isotopes and Atomic Mass

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

• Definition: Isotopes have the same number of protons but different numbers of neutrons.

• Average Atomic Mass: Calculated using the relative abundance and mass of each isotope.

• Formula: $\text{Average atomic mass} = \sum (\text{fractional abundance} \times \text{isotope mass})$

• Example: $^{12}$C (98.9%, 12.000 amu), $^{13}$C (1.1%, 13.003 amu): $0.989 \times 12.000 + 0.011 \times 13.003 = 12.011$ amu

Subatomic Particles in Atoms and Ions

Atoms and ions are characterized by their numbers of protons, neutrons, and electrons.

• Neutral Atom: Number of protons = number of electrons.

• Cation: Positively charged ion; fewer electrons than protons.

• Anion: Negatively charged ion; more electrons than protons.

• Neutrons: Number = mass number – atomic number.

• Example: $^{23}$Na: 11 protons, 12 neutrons, 11 electrons; Na+: 11 protons, 12 neutrons, 10 electrons.

Molecules and Compounds

Naming and Writing Chemical Formulas

Chemical nomenclature follows systematic rules for both ionic and molecular compounds.

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

• Molecular Compounds: Use prefixes to indicate the number of atoms (e.g., CO2: carbon dioxide).

• Writing Formulas: Balance charges for ionic compounds; use prefixes for molecular compounds.

Chemical Composition

Mole Conversions and Percent Composition

The mole is a fundamental unit for counting particles in chemistry.

• Mole to Mass: $\text{mass} = \text{moles} \times \text{molar mass}$

• Mass to Moles: $\text{moles} = \frac{\text{mass}}{\text{molar mass}}$

• Mole to Particles: $\text{particles} = \text{moles} \times 6.022 \times 10^{23}$

• Percent by Mass: $\%\ \text{by mass} = \frac{\text{mass of element}}{\text{mass of compound}} \times 100\%$

• Example: In H2O, %H = $\frac{2.02}{18.02} \times 100\% = 11.2\%$

Chemical Reactions

Balancing and Writing Equations

Chemical equations must be balanced to obey the law of conservation of mass.

• Balancing: Adjust coefficients to ensure equal numbers of each atom on both sides.

• Ionic and Net Ionic Equations: Show dissociated ions in aqueous solutions; net ionic equations omit spectator ions.

• Spectator Ions: Ions that do not participate in the actual chemical change.

Oxidation and Reduction

Redox reactions involve the transfer of electrons.

• Oxidation: Loss of electrons; increase in oxidation number.

• Reduction: Gain of electrons; decrease in oxidation number.

• Oxidation Number: Assigned to atoms to track electron transfer.

Quantities in Chemical Reactions

Stoichiometry and Percent Yield

Stoichiometry allows calculation of reactant and product quantities in chemical reactions.

• Mass-Mass Calculations: Use balanced equations and molar masses to relate reactants and products.

• Percent Yield: $\%\ \text{yield} = \frac{\text{actual yield}}{\text{theoretical yield}} \times 100\%$

Electrons in Atoms and the Periodic Table

Electron Configuration

Electron configuration describes the arrangement of electrons in an atom or ion.

• Neutral Atoms: Fill orbitals according to the Aufbau principle, Pauli exclusion principle, and Hund's rule.

• Ions: Remove or add electrons according to charge.

• Example: Na: 1s2 2s2 2p6 3s1; Na+: 1s2 2s2 2p6

Chemical Bonding

Bond Polarity and Molecular Geometry

Chemical bonds and molecular shapes determine the properties of substances.

• Polar Bonds: Occur when there is a difference in electronegativity between bonded atoms.

• Polar Molecules: Have an uneven distribution of charge due to bond polarity and molecular shape.

• Electronegativity Trends: Increase across a period, decrease down a group.

• Octet Rule: Atoms tend to gain, lose, or share electrons to achieve eight valence electrons.

• Molecular Geometry: Determined by VSEPR theory (e.g., linear, bent, trigonal planar, tetrahedral).

Gases

Properties and Gas Laws

Gases have unique properties and follow specific laws.

• Properties: Compressible, expand to fill container, low density.

• Boyle’s Law: $P_1V_1 = P_2V_2$ (at constant T, n)

• Charles’s Law: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ (at constant P, n)

• Ideal Gas Law: $PV = nRT$

• Dalton’s Law: $P_{\text{total}} = \sum P_i$

Liquids, Solids, and Intermolecular Forces

Types of Intermolecular Forces

Intermolecular forces affect the physical properties of substances.

• Dispersion Forces: Present in all molecules; weakest.

• Dipole-Dipole Forces: Between polar molecules.

• Hydrogen Bonding: Strong dipole-dipole interaction involving H bonded to N, O, or F.

Solutions

Concentration and Colligative Properties

Solutions are characterized by concentration and colligative properties.

• Concentration Units: % (mass/volume), % (mass/mass), molarity ($M = \frac{\text{moles solute}}{\text{liters solution}}$)

• Ion Concentration: Calculate using stoichiometry and dissociation equations.

• Colligative Properties: Depend on the number of solute particles (boiling point elevation, freezing point depression, osmotic pressure).

• Isotonic, Hypertonic, Hypotonic Solutions: Relate to osmotic pressure and cell behavior.

Acids and Bases

Definitions, Strength, and pH Calculations

Acids and bases are classified by their properties and strength.

• Acid: Donates H+ ions; Base: Accepts H+ ions.

• Strong Acids: Completely ionize in solution (e.g., HCl, HNO3).

• Conjugate Acid-Base Pairs: Differ by one H+ ion.

• Buffer Solutions: Resist changes in pH; contain weak acid and its conjugate base.

• pH Calculation: $\text{pH} = -\log[\text{H}_3\text{O}^+]$

• Relationship: $[\text{H}_3\text{O}^+][\text{OH}^-] = 1.0 \times 10^{-14}$ at 25°C

• Acidic: pH < 7; Neutral: pH = 7; Basic: pH > 7

Chemical Equilibrium

Equilibrium and Le Chatelier’s Principle

Chemical equilibrium occurs when the rates of forward and reverse reactions are equal.

• Equilibrium Constant: $K = \frac{[\text{products}]}{[\text{reactants}]}$ (concentrations at equilibrium)

• Le Chatelier’s Principle: A system at equilibrium responds to disturbances by shifting to minimize the disturbance.

Radioactivity and Nuclear Chemistry

Types of Decay and Nuclear Reactions

Nuclear chemistry involves changes in the nucleus of atoms.

• Alpha Decay (α): Emission of a helium nucleus ($^4_2\text{He}$)

• Beta Decay (β): Emission of an electron ($^0_{-1}\text{e}$)

• Gamma Decay (γ): Emission of high-energy photons

• Balancing Nuclear Reactions: Sum of mass numbers and atomic numbers must be equal on both sides.

• Half-Life: Time required for half of a radioactive sample to decay.

• Formula: $N = N_0 \left( \frac{1}{2} \right)^{\frac{t}{t_{1/2}}}$

• Fission: Splitting of a heavy nucleus into lighter nuclei.

• Fusion: Combining of light nuclei to form a heavier nucleus.