General Chemistry I: Comprehensive Study Notes (Practice Exam Review)

Chemical Tools: Experimentation & Measurement

Significant Figures and Measurement

Accurate measurement and proper use of significant figures are foundational in chemistry. Significant figures reflect the precision of a measured value.

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

• Reading Instruments: Always record all certain digits and one uncertain digit.

• Example: If a ruler shows a metal bar at 10.22 cm, the measurement should be recorded as 10.22 cm (4 significant figures).

Density and Units

Density is a physical property defined as mass per unit volume.

• Formula: $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$

• Units: Commonly expressed in g/cm3 or g/mL.

• Example: A piece of silver with a mass of 52.0 g and a density of 10.5 g/cm3 occupies $\frac{52.0\ \text{g}}{10.5\ \text{g/cm}^3} = 4.95\ \text{cm}^3$.

Accuracy and Precision

Understanding the difference between accuracy and precision is essential for evaluating experimental results.

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

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

Atoms, Molecules & Ions

Atomic Structure and Isotopes

Atoms consist of protons, neutrons, and electrons. Isotopes are atoms of the same element with different numbers of neutrons.

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

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

• Isotopes: Atoms with the same Z but different A.

• Example: $^{39}_{19}\text{K}$ has 19 protons, 20 neutrons, and 19 electrons.

Average Atomic Mass

The average atomic mass of an element is calculated using the masses and abundances of its isotopes.

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

• Example Table:

Isotope	Mass (amu)	Abundance (%)
Al-26	25.986	18.7
Al-27	26.982	81.3

• Calculation: $\text{Avg. mass} = (25.986 \times 0.187) + (26.982 \times 0.813)$

Ions and Ionic Compounds

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

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

• Example: $\text{Na}^+$, $\text{Cl}^-$

Mass Relationships in Chemical Reactions

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions using balanced equations.

• Mole Concept: 1 mole = $6.022 \times 10^{23}$ entities.

• Molar Mass: Mass of 1 mole of a substance (g/mol).

• Limiting Reactant: The reactant that is completely consumed first, limiting the amount of product formed.

• Example: $2\text{Al} + 3\text{Cl}_2 \rightarrow 2\text{AlCl}_3$

Percent Composition and Empirical Formulas

• Percent Composition: $\%\ \text{element} = \frac{\text{mass of element in 1 mol}}{\text{molar mass}} \times 100$

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

Reactions in Aqueous Solution

Types of Chemical Reactions

• Precipitation Reactions: Formation of an insoluble product (precipitate).

• Acid-Base Reactions: Transfer of protons (H+).

• Redox Reactions: Transfer of electrons.

Net Ionic Equations

• Show only the species that actually change during the reaction.

• Example: $\text{AgNO}_3(aq) + \text{NaCl}(aq) \rightarrow \text{AgCl}(s) + \text{NaNO}_3(aq)$

• Net Ionic: $\text{Ag}^+(aq) + \text{Cl}^-(aq) \rightarrow \text{AgCl}(s)$

Periodicity & Electronic Structure of Atoms

Quantum Numbers and Orbitals

• Principal Quantum Number (n): Energy level (n = 1, 2, 3, ...).

• Angular Momentum Quantum Number (l): Shape of orbital (s, p, d, f).

• Magnetic Quantum Number (ml): Orientation of orbital.

• Spin Quantum Number (ms): +1/2 or -1/2.

Electron Configurations

• Describes the arrangement of electrons in an atom.

• Example: $\text{Na}: 1s^2 2s^2 2p^6 3s^1$

• Hund's Rule: Electrons fill degenerate orbitals singly before pairing.

Periodic Trends

• Atomic Radius: Increases down a group, decreases across a period.

• Ionization Energy: Energy required to remove an electron; increases across a period, decreases down a group.

• Electronegativity: Tendency to attract electrons; increases across a period, decreases down a group.

Ionic and Covalent Bonding

Ionic Compounds

• Formed from the transfer of electrons from metals to nonmetals.

• Example: $\text{Na}^+ + \text{Cl}^- \rightarrow \text{NaCl}$

Covalent Compounds

• Formed by sharing electrons between nonmetals.

• Lewis Structures: Show bonding and lone pairs of electrons.

• Resonance: Some molecules can be represented by two or more valid Lewis structures.

Bond Polarity and Molecular Geometry

• Bond Polarity: Difference in electronegativity leads to polar bonds.

• VSEPR Theory: Predicts molecular shapes based on electron pair repulsion.

• Example: $\text{CO}_2$ is linear; $\text{H}_2\text{O}$ is bent.

Thermochemistry: Chemical Energy

Enthalpy and Calorimetry

• Enthalpy (H): Heat content of a system at constant pressure.

• Calorimetry: Measurement of heat flow.

• Formula: $q = m c \Delta T$

• Example: If 100 g of water is heated from 25°C to 35°C, $q = 100\ \text{g} \times 4.18\ \text{J/g}^\circ\text{C} \times 10^\circ\text{C} = 4180\ \text{J}$

Hess's Law

• The enthalpy change for a reaction is the same, regardless of the pathway taken.

• Application: Used to calculate $\Delta H$ for reactions by combining known equations.

Standard Enthalpy of Formation

• Definition: Enthalpy change when 1 mole of a compound forms from its elements in their standard states.

• Notation: $\Delta H_f^\circ$

Gases: Their Properties & Behavior

Gas Laws

• Boyle's Law: $P_1V_1 = P_2V_2$ (at constant T and n)

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

• Ideal Gas Law: $PV = nRT$

• Standard Temperature and Pressure (STP): 0°C (273.15 K) and 1 atm; 1 mol gas = 22.4 L at STP.

Gas Stoichiometry

• Relates volumes of gases in chemical reactions using the ideal gas law.

• Example: How many liters of $\text{O}_2$ are needed to react with 5.0 g of $\text{H}_2$ at STP?

Solutions & Their Properties

Concentration Units

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

• Example: To make 250 mL of 0.133 M $\text{KNO}_3$, need $0.250\ \text{L} \times 0.133\ \text{mol/L} = 0.0333\ \text{mol}$

Additional info:

• These notes are based on a comprehensive set of practice exam questions covering the core topics of a General Chemistry I course, including atomic structure, periodicity, chemical bonding, stoichiometry, thermochemistry, and gas laws.

• Tables and diagrams referenced in the questions (e.g., threshold frequencies, isotopic abundances) are summarized or recreated above for clarity.