General Chemistry 1 Comprehensive Study Notes

General Chemistry 1: Matter, Atomic Structure, Nomenclature, and Stoichiometry

Matter and Its Properties

Definition and Role of Energy

• Matter is defined as anything that possesses mass (the measure of the amount of matter present) and occupies volume (the three-dimensional space taken up by an object).

• Matter is dynamic and constantly capable of transformation. The driving force behind physical and chemical transformations in matter is energy.

• When energy is introduced to a substance in the form of heat, it increases the kinetic energy of its constituent particles. This kinetic energy increase corresponds to a rise in temperature and induces phase changes:

  • Heating a solid increases particle motion until it reaches its melting point, transitioning into a liquid.

  • Continued addition of thermal energy causes liquid particles to overcome intermolecular attractive forces entirely, transitioning into a gas.

Classifications of Matter

Matter is categorized systematically using three main frameworks:

1. Source or Origin

• Organic Matter: Originates from or comprises carbon-based living or once-living organisms.

• Inorganic Matter: Consists of non-living mineral matter and non-carbon-based chemical compounds.

2. State or Phase

• Solid: Characterized by tightly packed, fixed particle arrangements with high density. Particles vibrate in place and cannot move freely.

• Liquid: Characterized by particles that are not rigidly fixed; they can fluidly slide past one another and move relatively freely, adopting the shape of their container while maintaining a fixed volume.

• Gas: Particles are widely scattered with no fixed arrangement or volume. Exhibits low density, high kinetic energy, and high compressibility.

• Plasma: Considered the fourth state of matter. Consists of a highly energized, gas-like state where atoms lose electrons, forming an electrically charged mixture of free ions and electrons. Kinetic energy in plasma is significantly higher than in neutral gases.

• Bose-Einstein Condensate (BEC): The fifth state of matter, formed when subatomic particles called bosons are cooled to temperatures approaching absolute zero ($0\,K$ or $-273.15^\circ C$). At this state, individual quantum wavefunctions overlap, causing particles to condense into a single macroscopic quantum state.

Phase Changes and Enthalpy

Phase changes represent physical transitions between states driven by enthalpy ($\Delta H$) changes:

• ENDOthermic Processes: Processes where thermal energy is absorbed by the system from its surroundings ($\Delta H > 0$):

  • Fusion (Melting): Solid to Liquid.

  • Vaporization: Liquid to Gas.

  • Sublimation: Solid directly to Gas.

• EXOthermic Processes: Processes where thermal energy is released by the system into its surroundings ($\Delta H < 0$):

  • Freezing: Liquid to Solid. As molecules adopt a structured, lower-energy lattice, system entropy decreases and heat is given off.

  • Condensation: Gas to Liquid.

  • Deposition: Gas directly to Solid.

3. Composition

• Pure Substance: Matter with a constant chemical composition and uniform properties throughout.

  • Element: The simplest form of matter that cannot be broken down into simpler substances by chemical means; contains only one kind of atom.

  • Compound: A substance composed of two or more different elements chemically combined in fixed, definite proportions.

• Mixture: A physical combination of two or more substances in variable ratios where each retains its individual chemical identity.

  • Heterogeneous Mixture: Features a non-uniform composition with visually distinguishable components or phases.

  • Homogeneous Mixture: Features a uniform composition throughout, appearing single-phase (also referred to as a solution).

Changes in Matter

• Physical Change: A change that alters the physical form or state of a substance without altering its chemical identity or composition. No new substance is created.

• Chemical Change: A transformation that alters the atomic rearrangement and identity of a substance, resulting in the formation of one or more new chemical substances.

• Key Evidences of a Chemical Change:

  1. Appearance of a unexpected color change.

  2. Emission or absorption of energy in the form of heat, light, or sound.

  3. Formation of gas bubbles or evolution of a distinct new odor.

  4. Formation of an insoluble solid precipitate within a liquid solution.

  5. Irreversibility under normal physical conditions.

Properties of Matter

• Physical Properties: Characteristics observed or measured without altering the chemical composition of the material. Examples include color, odor, melting point, boiling point, mass, volume, and density.

  • Density ($d$): A physical property representing the mass contained per unit volume of a substance.         $\text{Density } (d) = \frac{\text{Mass } (m)}{\text{Volume } (V)}$         Standard SI derived units: $\text{g/cm}^3$ or $\text{kg/m}^3$

  • Extensive Properties: Depend explicitly on the amount of matter being measured (e.g., mass, volume, length, enthalpy).

  • Intensive Properties: Independent of the amount of matter present; depend solely on the identity and nature of the substance (e.g., density, temperature, melting point, boiling point).

• Chemical Properties: Characteristics describing a substance's capacity to undergo chemical reactions and change into different substances:

  • Combustibility: Quantitative measure of a material's capability to ignite and sustain combustion in the presence of oxygen.

  • Chemical Stability: Resistance to decomposition or reaction under specific environmental conditions.

  • Relative Reactivity: Rate and capacity to react with other chemical reagents.

  • Response to Test Reactions: Specific behavior when exposed to standard reagents (e.g., acid-base indicators).

  • Ionization: Tendency to gain or lose electrons to form ionic species.

Atoms, Ions, and Molecules

Atomic Theory and Subatomic Particles

An atom is the fundamental structural unit of matter.

• John Dalton's Atomic Theory: Lauded as the foundation of modern quantitative chemistry, built on five central postulates:

  1. All matter is composed of indivisible particles called atoms.

  2. Atoms of a given element are identical in mass and chemical properties.

  3. Compounds are formed when atoms of different elements combine in small whole-number ratios.

  4. Atoms cannot be created, subdivided, or destroyed in chemical processes.

  5. In chemical reactions, atoms are combined, separated, or rearranged.

Discovery of Subatomic Particles

1. Electron ($e^-$): Discovered by J.J. Thomson (1898) using the Cathode Ray Tube Experiment. By applying electric and magnetic fields, he demonstrated that cathode rays were composed of negatively charged particles deflected by magnetic charges.

2. Proton ($p^+$): Discovered by Ernest Rutherford (1911) using the Gold Foil Experiment. By directing alpha particles ($\text{He}^{2+}$) at a thin gold sheet, he observed deflections at large angles, proving the existence of a dense, positively charged center termed the nucleus.

3. Neutron ($n^0$): Discovered by James Chadwick (1932) using the Beryllium Bombardment Experiment. It accounted for missing atomic mass (such as helium possessing four times the mass of hydrogen despite having only two protons) by identifying an uncharged particle with a mass nearly equal to that of a proton.

Summary of Fundamental Atomic Notation

• Isotopes: Atoms of the same element that have identical atomic numbers ($Z$) but different mass numbers ($A$) due to varying numbers of neutrons. Average atomic masses listed on the periodic table are non-integers because they represent weighted averages of all naturally occurring stable isotopes.

Ions: Cations and Anions

An ion is an atom or group of atoms possessing a net electrical charge resulting from the loss or gain of electrons:

• Cation: A positively charged ion formed when a neutral atom loses one or more electrons. Typically formed by metal elements.

• Anion: A negatively charged ion formed when a neutral atom gains one or more electrons. Typically formed by non-metal elements (such as halogens).

Molecular and Empirical Formulas

• Molecular Formula: Represents the actual, exact number and types of atoms present in a single discrete molecule of a compound.

• Empirical Formula: Represents the simplest, lowest whole-number ratio of atoms present in a chemical compound.

Examples of Molecular and Empirical Formulas

• Note: Multiple molecular formulas can correspond to the exact same empirical formula. An empirical formula cannot be mathematically converted into a molecular formula without knowing the molar mass of the compound.

Chemical Nomenclature

Naming Monatomic Ions

1. Metal Cations: Retain the parent element's name followed by the word "ion".

   • $\text{Na}^+$ = Sodium ion

   • $\text{Mg}^{2+}$ = Magnesium ion

2. Non-metal Anions: Formed by replacing the original elemental name suffix with "-ide" followed by the word "ion".

   • $\text{F}^-$ = Fluoride ion

   • $\text{O}^{2-}$ = Oxide ion

   • $\text{N}^{3-}$ = Nitride ion

Ionic Compounds

Formed via electrostatic attraction following electron transfer between a Metal (cation) and a Non-Metal (anion).

Polyatomic Ions

Polyatomic ions are charged species composed of two or more covalently bonded atoms that behave as a single discrete unit during reactions.

• The "-ate" / "-ite" Oxyanion Rule:

  • "-ate": Standard threshold form containing the higher number of oxygen atoms (typically 3 or 4 oxygens).

    • $\text{NO}_3^-$ = Nitrate

    • $\text{SO}_4^{2-}$ = Sulfate

  • "-ite": Form containing one fewer oxygen atom than the "-ate" anion.

    • $\text{NO}_2^-$ = Nitrite

    • $\text{SO}_3^{2-}$ = Sulfite

Variable Charge Metals (Classical vs. IUPAC Naming)

Transition metals can form cations with distinct oxidation states. The IUPAC method uses Roman numerals in parentheses to denote charge, while the classical system uses the Latin root with "-ous" for lower charge and "-ic" for higher charge:

Ionic Charge Trends on the Periodic Table

• Group 1: $\text{+1}$

• Group 2: $\text{+2}$

• Group 13: $\text{+3}$ (e.g., $\text{Al}^{3+}$)

• Group 15: $\text{-3}$ (e.g., $\text{N}^{3-}$)

• Group 16: $\text{-2}$ (e.g., $\text{O}^{2-}$)

• Group 17: $\text{-1}$ (e.g., $\text{Cl}^-$)

• Group 18: $\text{0}$ (Noble gases)

• Fixed-charge transition elements: $\text{Ag}^+$ (Silver), $\text{Zn}^{2+}$ (Zinc), $\text{Cd}^{2+}$ (Cadmium).

Writing Ionic Formulas (Criss-Cross Method)

To write neutral formulas, cross the numerical magnitude of the cation's charge to become the subscript of the anion, and vice-versa:

1. Magnesium iodide: $\text{Mg}^{2+}$ and $\text{I}^- \rightarrow \text{MgI}_2$

2. Strontium nitrate: $\text{Sr}^{2+}$ and $\text{NO}_3^- \rightarrow \text{Sr(NO}_3\text{)}_2$

3. Iron (III) oxide: $\text{Fe}^{3+}$ and $\text{O}^{2-} \rightarrow \text{Fe}_2\text{O}_3$

Practice: Naming Ionic Compounds

• $\text{AlF}_3$: Aluminum fluoride

• $\text{BaSe}$: Barium selenide

• $\text{Cs}_2\text{S}$: Cesium sulfide

• $\text{NH}_4\text{NO}_2$: Ammonium nitrite

• $\text{Ba(MnO}_4\text{)}_2$: Barium permanganate

• $\text{Sr(C}_2\text{H}_3\text{O}_2\text{)}_2$: Strontium acetate

• $\text{Cu}_2\text{S}$: Copper(I) sulfide

• $\text{FeS}$: Iron(II) sulfide

• $\text{Mn}_2\text{O}_3$: Manganese(III) oxide

Practice: Writing Formulas for Ionic Compounds

• Rubidium bromide: $\text{RbBr}$

• Barium nitride: $\text{Ba}_3\text{N}_2$

• Cesium selenide: $\text{Cs}_2\text{Se}$

• Strontium chromate: $\text{SrCrO}_4$

• Lithium phosphate: $\text{Li}_3\text{PO}_4$

• Calcium perchlorate: $\text{Ca(ClO}_4\text{)}_2$

• Manganese (IV) oxide: $\text{MnO}_2$

• Chromium (III) sulfide: $\text{Cr}_2\text{S}_3$

• Copper (I) chloride: $\text{CuCl}$

Covalent Compounds

Covalent compounds are formed by the sharing of electrons between non-metal atoms.

Binary Covalent Prefixes

Naming Rules for Binary Covalent Compounds

1. Name the first non-metal element using its full element name with its corresponding multiplier prefix.

2. Rule Exception: If the first element has only one atom, omit the prefix "mono-".

3. Name the second non-metal element, modified with the prefix matching its subscript and changing its ending to "-ide".

4. Phonetic Rule: Drop the vowels 'a' or 'o' at the end of a prefix when combined with oxide (e.g., $\text{CO}$ is named Carbon monoxide, NOT Monocarbon monooxide).

Practice: Binary Covalent Names and Formulas

1. $\text{Si}_2\text{Br}_6$: Disilicon hexabromide

2. $\text{P}_4\text{S}_3$: Tetraphosphorus trisulfide

3. $\text{Cl}_2\text{O}_7$: Dichlorine heptoxide

4. $\text{As}_2\text{O}_5$: Diarsenic pentoxide

5. $\text{N}_2\text{F}_4$: Dinitrogen tetrafluoride

6. Dinitrogen tetroxide: $\text{N}_2\text{O}_4$

7. Tetraphosphorus decasulfide: $\text{P}_4\text{S}_{10}$

8. Diboron trioxide: $\text{B}_2\text{O}_3$

9. Sulfur hexafluoride: $\text{SF}_6$

Stoichiometric Quantities and the Mole Concept

Atomic Mass and Average Atomic Mass

• Atomic Mass: The total mass of an individual atom, measured in atomic mass units ($\text{amu}$). It is numerically equivalent to the mass number ($A$).

• Average Atomic Mass: The weighted average mass of all naturally occurring stable isotopes of an element:     $\text{Average Atomic Mass} = \sum_{i=1}^{n} (a_i \times m_i) = (a_1 \cdot m_1) + (a_2 \cdot m_2) + \dots + (a_n \cdot m_n)$     Where $a_i$ represents the fractional abundance ($\frac{\%\text{ abundance}}{100}$) and $m_i$ represents the mass of isotope $i$.

  • Conceptual Note: The isotope whose percent abundance is closest to $100\%$ dictates the value of the average atomic mass.

The Mole and Avogadro's Number

• Mole ($\text{mol}$): The base SI unit for measuring the amount of substance. Analogous to counting units (e.g., 1 dozen = 12 units).

• Avogadro's Number ($N_A$): A constant defined as exactly $6.022 \times 10^{23}$ particles per mole.     $1\,\text{mole of any particle} = 6.022 \times 10^{23}\,\text{particles (atoms, molecules, or formula units)}$

Molecular Mass vs. Molar Mass

• Molecular Mass: Sum of atomic masses of all atoms present in a single isolated molecule (expressed in $\text{amu}$).

• Molar Mass: Mass of exactly one mole ($6.022 \times 10^{23}$ units) of a substance (expressed in $\text{g/mol}$ or $\text{g}\,\text{mol}^{-1}$).

Worked Example: Comparison of Molecular Mass and Molar Mass

Calculate the molecular mass and molar mass of Rutherfordium dioxide ($\text{RfO}_2$):

• $\text{Rf} = 265 \times 1 = 265$

• $\text{O}_2 = 16.00 \times 2 = 32.00$

• $\text{Sum} = 297.00$

$\text{Molecular Mass of RfO}_2 = 297.00\,\text{amu}$ $\text{Molar Mass of RfO}_2 = 297.00\,\text{g}\,\text{mol}^{-1}$

Conversions via Dimensional Analysis

Conversions use dimensional analysis to cancel unwanted units: $\text{Mass (g)} \xrightleftharpoons[\text{Molar Mass}]{\text{Multiply / Divide}} \text{Moles (mol)} \xrightleftharpoons[N_A]{\text{Multiply / Divide}} \text{Particles}$

• Mass to Moles Calculation: Divide given mass by molar mass.

• Moles to Mass Calculation: Multiply given moles by molar mass.

Problem 1: Mass to Moles Conversion

Calculate how many moles of Helium ($\text{He}$) atoms are contained in $6.46\,\text{g}$ of $\text{He}$ (Molar Mass of $\text{He} = 4.003\,\text{g}\,\text{mol}^{-1}$).

$\text{Moles of He} = 6.46\,\text{g He} \times \left( \frac{1\,\text{mol He}}{4.003\,\text{g He}} \right) = 1.61\,\text{mol He}$

Problem 2: Moles to Mass Conversion

Calculate how many grams of Lead ($\text{Pb}$) are present in $0.356\,\text{mol}$ of $\text{Pb}$ (Molar Mass of $\text{Pb} = 207.2\,\text{g}\,\text{mol}^{-1}$).

$\text{Mass of Pb} = 0.356\,\text{mol Pb} \times \left( \frac{207.2\,\text{g Pb}}{1\,\text{mol Pb}} \right) = 73.76\,\text{g Pb}$

Problem 3: Particles to Mass Conversion

Calculate how many grams of $\text{P}_4\text{S}_3$ are contained in $5.045 \times 10^{23}$ molecules of $\text{P}_4\text{S}_3$ (Given Molar Mass = $220.09\,\text{g}\,\text{mol}^{-1}$).

$\text{Mass of P}_4\text{S}_3 = 5.045 \times 10^{23}\,\text{molecules} \times \left( \frac{1\,\text{mol}}{6.022 \times 10^{23}\,\text{molecules}} \right) \times \left( \frac{220.09\,\text{g}}{1\,\text{mol}} \right)$ $\text{Mass of P}_4\text{S}_3 = 0.83776\,\text{mol} \times 220.09\,\text{g}\,\text{mol}^{-1} = 184.38\,\text{g of P}_4\text{S}_3$

Balancing Chemical Equations and Percent Composition

Law of Conservation of Mass

• Law of Conservation of Mass: Mass is neither created nor destroyed in chemical reactions. The rearrangement of atoms requires that the total mass of the reactants must equal the total mass of the products.

• Example Reaction:     $\text{Na}_2\text{CO}_3(s) + 2\text{HCl}(aq) \rightarrow 2\text{NaCl}(aq) + \text{H}_2\text{O}(l) + \text{CO}_2(g)$

Systematic Steps for Balancing Chemical Equations

1. Determine the initial atom count for every element present on both sides of the reaction arrow.

2. Identify an element that is unbalanced between reactants and products.

3. Place a whole-number coefficient in front of the chemical formula containing that element to equalize atom counts. Never change chemical subscripts.

4. Re-count all atoms and adjust remaining coefficients until all elements satisfy conservation of mass.

Worked Example: Balancing $\text{H}_2 + \text{O}_2 \rightarrow \text{H}_2\text{O}$

• Step 1 (Initial Counts):

  • Reactants: $\text{H} = 2, \text{O} = 2$

  • Products: $\text{H} = 2, \text{O} = 1$

• Step 2 & 3 (Adjust Oxygen):

  • Add coefficient 2 to $\text{H}_2\text{O}$: $\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$

  • Updated Counts: Reactants ($\text{H} = 2, \text{O} = 2$) vs. Products ($\text{H} = 4, \text{O} = 2$)

• Step 4 (Adjust Hydrogen):

  • Add coefficient 2 to $\text{H}_2$: $2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$

  • Final Counts: Reactants ($\text{H} = 4, \text{O} = 2$) vs. Products ($\text{H} = 4, \text{O} = 2$). Equation is balanced!

Percent Composition

Percent composition defines the mass percentage contributed by each individual element to the total mass of a compound:

$\text{Percent Composition of Element} = \left( \frac{\text{Total Mass of Element in 1 mole of Compound}}{\text{Molar Mass of Compound}} \right) \times 100\%$

Steps for Calculating Percent Composition

1. Find the molar mass contribution of each individual element present in the formula.

2. Sum the individual atomic masses to determine the total molar mass of the compound.

3. Divide each element's total mass contribution by the overall molar mass of the compound.

4. Multiply the resulting decimal fraction by 100 to convert to a percentage.

Worked Example: Percent Composition of Silicon Dioxide ($\text{SiO}_2$)

1. Determine Mass Contributions:

   • $\text{Si} = 28.09 \times 1 = 28.09\,\text{g}\,\text{mol}^{-1}$

   • $\text{O} = 16.00 \times 2 = 32.00\,\text{g}\,\text{mol}^{-1}$

2. Determine Total Molar Mass:

   • $\text{Total Molar Mass} = 28.09 + 32.00 = 60.09\,\text{g}\,\text{mol}^{-1}$

3. Calculate Percentages:     $\%\,\text{Si} = \left( \frac{28.09\,\text{g}\,\text{mol}^{-1}}{60.09\,\text{g}\,\text{mol}^{-1}} \right) \times 100\% = 0.47646 \times 100\% = 46.75\%$     $\%\,\text{O} = \left( \frac{32.00\,\text{g}\,\text{mol}^{-1}}{60.09\,\text{g}\,\text{mol}^{-1}} \right) \times 100\% = 0.53253 \times 100\% = 53.25\%$

Practice Problems

1. Balancing Reaction 1

Balance the equation: $\underline{\quad}\text{Fe}_2\text{O}_3 + \underline{\quad}\text{CO} \rightarrow \underline{\quad}\text{Fe} + \underline{\quad}\text{CO}_2$

• Solution: Correct coefficients are 1, 3, 2, 3     $\text{Fe}_2\text{O}_3 + 3\text{CO} \rightarrow 2\text{Fe} + 3\text{CO}_2$

  • Reactant counts: $\text{Fe} = 2, \text{C} = 3, \text{O} = 6$

  • Product counts: $\text{Fe} = 2, \text{C} = 3, \text{O} = 6$

2. Balancing Reaction 2

Balance the equation: $\underline{\quad}\text{C}_3\text{H}_8 + \underline{\quad}\text{O}_2 \rightarrow \underline{\quad}\text{CO}_2 + \underline{\quad}\text{H}_2\text{O}$

• Solution: Correct coefficients are 1, 5, 3, 4     $\text{C}_3\text{H}_8 + 5\text{O}_2 \rightarrow 3\text{CO}_2 + 4\text{H}_2\text{O}$

  • Reactant counts: $\text{C} = 3, \text{H} = 8, \text{O} = 10$

  • Product counts: $\text{C} = 3, \text{H} = 8, \text{O} = 10$

3. Percent Composition of Barium Nitrate

Calculate the percent composition by molar mass of each element in Barium nitrate ($\text{Ba(NO}_3\text{)}_2$):

• Molar Mass Calculation:

  • $\text{Ba} = 137.33 \times 1 = 137.33\,\text{g}\,\text{mol}^{-1}$

  • $\text{N} = 14.01 \times 2 = 28.02\,\text{g}\,\text{mol}^{-1}$

  • $\text{O} = 16.00 \times 6 = 96.00\,\text{g}\,\text{mol}^{-1}$

  • $\text{Total Molar Mass} = 137.33 + 28.02 + 96.00 = 261.35\,\text{g}\,\text{mol}^{-1}$

• Percent Compositions:     $\%\,\text{Ba} = \left( \frac{137.33}{261.35} \right) \times 100\% = 52.55\%$     $\%\,\text{N} = \left( \frac{28.02}{261.35} \right) \times 100\% = 10.72\%$     $\%\,\text{O} = \left( \frac{96.00}{261.35} \right) \times 100\% = 36.73\%$