Chapter 4 Gen Chem NOTES

• Electron Shielding and Effective Nuclear Charge ($Z_{\text{eff}}$):

  • Electron Shielding: Inner-shell electrons shield outer valence electrons from the full attractive charge of the nucleus.

  • Effective Nuclear Charge ($Z_{\text{eff}}$): The net positive charge experienced by an electron in a multi-electron atom, approximately calculated as:     $Z_{\text{eff}} = \text{number of protons} - \text{number of inner electrons}$

  • Comparison of Lithium and Beryllium:

  • Lithium ($\text{Li}$, atomic number 3, configuration $1s^2 2s^1$): Nucleus has a $3+$ charge; 2 inner core electrons ($1s^2$).       $Z_{\text{eff}} = 3 - 2 = 1+$

  • Beryllium ($\text{Be}$, atomic number 4, configuration $1s^2 2s^2$): Nucleus has a $4+$ charge; 2 inner core electrons ($1s^2$).       $Z_{\text{eff}} = 4 - 2 = 2+$

  • Because Beryllium has a higher effective nuclear charge ($Z_{\text{eff}} = 2+$), its valence electrons are pulled more tightly toward the nucleus, making Beryllium smaller and less reactive than Lithium.

  • Periodic Trend Across Rows: As atomic number increases across a period from left to right, $Z_{\text{eff}}$ increases progressively from $1+$ to $8+$. Consequently, elements on the right side of the periodic table hold their valence electrons much more tightly.

• Atomic Radii Definitions and Trends:

  • Nonbonding Radius (van der Waals Radius): Half the distance between the nuclei of two non-bonded atoms in a tightly-packed solid.

  • Bonding Radius (Covalent Radius): Half the distance between the nuclei of two covalently bonded identical atoms.

  • Periodic Trends in Atomic Radius:

  • Across a Period (Left to Right): Atomic radius decreases due to increasing $Z_{\text{eff}}$, which pulls the electron shell closer to the nucleus.

  • Down a Group (Top to Bottom): Atomic radius increases because additional electron shells (principal energy levels $n$) are added.

  • Specific Atomic Radii Values (in picometers, $pm$):

  • Period 1: $\text{H} = 32\,pm$, $\text{He} = 37\,pm$

  • Period 2: $\text{Li} = 130\,pm$, $\text{Be} = 99\,pm$, $\text{B} = 84\,pm$, $\text{C} = 75\,pm$, $\text{N} = 71\,pm$, $\text{O} = 64\,pm$, $\text{F} = 60\,pm$, $\text{Ne} = 62\,pm$

  • Period 3: $\text{Na} = 160\,pm$, $\text{Mg} = 140\,pm$, $\text{Al} = 124\,pm$, $\text{Si} = 114\,pm$, $\text{P} = 109\,pm$, $\text{S} = 104\,pm$, $\text{Cl} = 100\,pm$, $\text{Ar} = 101\,pm$

  • Period 4: $\text{K} = 200\,pm$, $\text{Ca} = 174\,pm$, $\text{Ga} = 123\,pm$, $\text{Ge} = 120\,pm$, $\text{As} = 120\,pm$, $\text{Se} = 118\,pm$, $\text{Br} = 117\,pm$, $\text{Kr} = 116\,pm$

  • Period 5: $\text{Rb} = 215\,pm$, $\text{Sr} = 190\,pm$, $\text{In} = 142\,pm$, $\text{Sn} = 140\,pm$, $\text{Sb} = 140\,pm$, $\text{Te} = 137\,pm$, $\text{I} = 136\,pm$, $\text{Xe} = 136\,pm$

  • Period 6: $\text{Cs} = 238\,pm$, $\text{Ba} = 206\,pm$, $\text{Tl} = 144\,pm$, $\text{Pb} = 145\,pm$, $\text{Bi} = 150\,pm$, $\text{Po} = 142\,pm$, $\text{At} = 148\,pm$, $\text{Rn} = 146\,pm$

• Ionic Radii Comparisons:

  • Cations: Loss of electrons reduces electron-electron repulsion and often removes an entire outer shell, resulting in a cation smaller than its neutral parent atom.

  • $\text{Na}\ (\text{atomic radius } 160\,pm) \rightarrow \text{Na}^+\ (\text{ionic radius } 102\,pm)$

  • $\text{K}\ (\text{atomic radius } 200\,pm) \rightarrow \text{K}^+\ (\text{ionic radius } 138\,pm)$

  • Anions: Gain of electrons increases electron-electron repulsion, causing the electron cloud to expand, resulting in an anion larger than its neutral parent atom.

  • $\text{Cl}\ (\text{atomic radius } 100\,pm) \rightarrow \text{Cl}^-\ (\text{ionic radius } 181\,pm)$

  • $\text{Br}\ (\text{atomic radius } 117\,pm) \rightarrow \text{Br}^-\ (\text{ionic radius } 196\,pm)$

• Ionization Energy ($\text{IE}$):

  • Definition: The amount of energy required to remove an electron from a gas-phase atom or ion.

  • Representative Ionization Equations:

  • $\text{Li}(g) \rightarrow \text{Li}^+(g) + e^-, \quad \text{IE} = 520\,kJ\,mol^{-1}$

  • $\text{Al}(g) \rightarrow \text{Al}^+(g) + e^-, \quad \text{IE}_1 = 578\,kJ\,mol^{-1}$

  • $\text{Al}^+(g) \rightarrow \text{Al}^{2+}(g) + e^-, \quad \text{IE}_2 = 1817\,kJ\,mol^{-1}$

  • $\text{Al}^{2+}(g) \rightarrow \text{Al}^{3+}(g) + e^-, \quad \text{IE}_3 = 2745\,kJ\,mol^{-1}$

  • Sublevel Stability and Anomalies:

  • Atoms are extra stabilized by completely filled or half-filled energy sublevels.

  • Drop from Group 2A to Group 3A (e.g., $\text{Be}$ to $\text{B}$): The $p$ sublevel electron in Group 3A is higher in energy and shielded by full $s$ orbital electrons, making it easier to remove.

  • Drop from Group 5A to Group 6A (e.g., $\text{N}$ to $\text{O}$): Nitrogen has a stable, half-filled $2p^3$ configuration. Oxygen ($2p^4$) experiences electron pairing repulsion in one $p$ orbital, lowering the energy needed for ionization.

  • Successive Ionization Energies and Octet Rule Validation:

  • Removing core electrons (after valence electrons are exhausted) requires a massive jump in energy because core electrons experience a higher $Z_{\text{eff}}$ and reside in a shell closer to the nucleus.

  • Sodium ($\text{Na}$: $[\text{Ne}]3s^1$): $\text{IE}_1 = 496\,kJ\,mol^{-1}$; $\text{IE}_2 = 4562\,kJ\,mol^{-1}$ (Huge jump after losing 1 valence electron).

  • Magnesium ($\text{Mg}$: $[\text{Ne}]3s^2$): $\text{IE}_1 = 738\,kJ\,mol^{-1}$; $\text{IE}_2 = 1451\,kJ\,mol^{-1}$; $\text{IE}_3 = 7733\,kJ\,mol^{-1}$ (Huge jump after losing 2 valence electrons).

  • Aluminum ($\text{Al}$: $[\text{Ne}]3s^2 3p^1$): $\text{IE}_1 = 578\,kJ\,mol^{-1}$; $\text{IE}_2 = 1817\,kJ\,mol^{-1}$; $\text{IE}_3 = 2745\,kJ\,mol^{-1}$; $\text{IE}_4 = 11577\,kJ\,mol^{-1}$ (Huge jump after losing 3 valence electrons).

  • Silicon ($\text{Si}$: $[\text{Ne}]3s^2 3p^2$): $\text{IE}_1 = 787\,kJ\,mol^{-1}$; $\text{IE}_2 = 1577\,kJ\,mol^{-1}$; $\text{IE}_3 = 3232\,kJ\,mol^{-1}$; $\text{IE}_4 = 4356\,kJ\,mol^{-1}$; $\text{IE}_5 = 16091\,kJ\,mol^{-1}$ (Huge jump after losing 4 valence electrons).

• Metallic Character:

  • Definition: The measure of how readily an element loses valence electrons.

  • Periodic Trend: Metallic character increases moving down and to the left on the periodic table.

  • Key Factors: Metals have a loose hold on valence electrons due to smaller $Z_{\text{eff}}$ and larger atomic radius (electrons located farther from the nucleus).

• Periodic Trends Overview:

• Atomic Radius: Increases down a group, increases to the left across a period.

• Ionization Energy: Increases up a group, increases to the right across a period.

• Electron Affinity (more exothermic): Increases up a group, increases to the right across a period.

• Metallic Character: Increases down a group, increases to the left across a period.

Chemical Ions and Nomenclature

• Lewis Dot Symbols and Valence Electrons:

  • Definition: A notation using dots arranged around a chemical symbol to represent an atom's valence electrons.

  • Main Group Correlation: For main group elements (1A to 8A), the group number indicates the total number of valence electrons:

  • Group 1A: 1 valence electron (e.g., $\text{H}\cdot$, $\text{Li}\cdot$, $\text{Na}\cdot$)

  • Group 2A: 2 valence electrons (e.g., $\cdot\text{Be}\cdot$, $\cdot\text{Mg}\cdot$)

  • Group 3A: 3 valence electrons (e.g., $\cdot\text{B}\cdot$, $\cdot\text{Al}\cdot$)

  • Group 4A: 4 valence electrons (e.g., $\cdot\dot{\text{C}}\cdot$, $\cdot\dot{\text{Si}}\cdot$)

  • Group 5A: 5 valence electrons (e.g., $\cdot\ddot{\text{N}}\cdot$, $\cdot\ddot{\text{P}}\cdot$)

  • Group 6A: 6 valence electrons (e.g., $\cdot\ddot{\text{O}}\mathbf{:}$, $\cdot\ddot{\text{S}}\mathbf{:}$)

  • Group 7A: 7 valence electrons (e.g., $\mathbf{:}\ddot{\text{F}}\mathbf{:}$, $\mathbf{:}\ddot{\text{Cl}}\mathbf{:}$)

  • Group 8A: 8 valence electrons (e.g., $\mathbf{:}\ddot{\text{Ne}}\mathbf{:}$, $\mathbf{:}\ddot{\text{Ar}}\mathbf{:}$) [Exception: Helium $\text{He}\mathbf{:}$ has 2 valence electrons].

• Isoelectronic Ions:

  • Ions that share the same total number of electrons and identical electron configurations as a noble gas.

  • Example: Neon configuration ($10\ e^-$): $\text{N}^{3-}$, $\text{O}^{2-}$, $\text{F}^-$, $\text{Na}^+$, $\text{Mg}^{2+}$, and $\text{Al}^{3+}$ are all isoelectronic with Neon ($\text{Ne}$).

• Monatomic Cation Nomenclature:

  • Fixed Charge Cations: Metal cations with single stable oxidation states retain the neutral element name followed by "ion".

  • $\text{Na}^+$: sodium

  • $\text{Mg}^{2+}$: magnesium

  • $\text{Al}^{3+}$: aluminum

  • Variable Charge Cations: Metals (predominantly transition metals and lower main group metals) that form multiple stable ions require Roman numerals indicating charge in the modern Stock System:

  • Iron ($\text{Fe}$):

    • $\text{Fe}^{2+}$: iron(II) [Older name: ferrous]

    • $\text{Fe}^{3+}$: iron(III) [Older name: ferric]

  • Copper ($\text{Cu}$):

    • $\text{Cu}^+$: copper(I) [Older name: cuprous]

    • $\text{Cu}^{2+}$: copper(II) [Older name: cupric]

  • Lead ($\text{Pb}$): $\text{Pb}^{2+}$ (lead(II)), $\text{Pb}^{4+}$ (lead(IV))

  • Tin ($\text{Sn}$): $\text{Sn}^{2+}$ (tin(II)), $\text{Sn}^{4+}$ (tin(IV))

  • Chromium ($\text{Cr}$): $\text{Cr}^{2+}$ (chromium(II)), $\text{Cr}^{3+}$ (chromium(III))

  • Manganese ($\text{Mn}$): $\text{Mn}^{2+}$ (manganese(II)), $\text{Mn}^{3+}$ (manganese(III))

  • Cobalt ($\text{Co}$): $\text{Co}^{2+}$ (cobalt(II)), $\text{Co}^{3+}$ (cobalt(III))

  • Nickel ($\text{Ni}$): $\text{Ni}^+$ (nickel(I)), $\text{Ni}^{2+}$ (nickel(II))

  • Fixed Charge Transition Metals to Memorize: $\text{Zn}^{2+}$ (zinc), $\text{Ag}^+$ (silver), $\text{Cd}^{2+}$ (cadmium).

• Monatomic Anion Nomenclature:

  • Nonmetals gain electrons to form negatively charged anions with noble gas configurations.

  • Named by replacing the element's suffix with "-ide":

  • Chlorine ($\text{Cl}$) $\rightarrow \text{Cl}^-$: chloride

  • Oxygen ($\text{O}$) $\rightarrow \text{O}^{2-}$: oxide

  • Sulfur ($\text{S}$) $\rightarrow \text{S}^{2-}$: sulfide

  • Nitrogen ($\text{N}$) $\rightarrow \text{N}^{3-}$: nitride

  • Fluorine ($\text{F}$) $\rightarrow \text{F}^-$: fluoride

  • Bromine ($\text{Br}$) $\rightarrow \text{Br}^-$: bromide

  • Iodine ($\text{I}$) $\rightarrow \text{I}^-$: iodide

  • Phosphorus ($\text{P}$) $\rightarrow \text{P}^{3-}$: phosphide

• Polyatomic Ions:

  • Definition: A covalent collection of two or more covalently bonded atoms carrying a net overall electrical charge.

  • Polyatomic Ion Reference Table:

  • Cation:

    • $\text{NH}_4^+$: Ammonium

  • Anions:

    • $\text{NO}_3^-$: Nitrate

    • $\text{NO}_2^-$: Nitrite

    • $\text{SO}_4^{2-}$: Sulfate

    • $\text{SO}_3^{2-}$: Sulfite

    • $\text{HSO}_4^-$: Bisulfate (or hydrogen sulfate)

    • $\text{CO}_3^{2-}$: Carbonate

    • $\text{HCO}_3^-$: Bicarbonate (or hydrogen carbonate)

    • $\text{PO}_4^{3-}$: Phosphate

    • $\text{HPO}_4^{2-}$: Hydrogen phosphate

    • $\text{H}_2\text{PO}_4^-$: Dihydrogen phosphate

    • $\text{ClO}_4^-$: Perchlorate

    • $\text{ClO}_3^-$: Chlorate

    • $\text{ClO}_2^-$: Chlorite

    • $\text{ClO}^-$: Hypochlorite

    • $\text{C}_2\text{H}_3\text{O}_2^-$: Acetate

    • $\text{OH}^-$: Hydroxide

    • $\text{CN}^-$: Cyanide

    • $\text{O}_2^{2-}$: Peroxide

    • $\text{CrO}_4^{2-}$: Chromate

    • $\text{Cr}_2\text{O}_7^{2-}$: Dichromate

    • $\text{MnO}_4^-$: Permanganate

• Oxyanion Nomenclature Rules:

  • Oxyanion Definition: A polyatomic anion containing oxygen bound to another central element.

  • Base Form: Standard oxyanion takes the root name + "-ate" (e.g., $\text{CO}_3^{2-}$ carbonate, $\text{PO}_4^{3-}$ phosphate).

  • Two Oxyanions Series:

  • Higher oxygen count: "-ate" (e.g., $\text{NO}_3^-$ nitrate)

  • Lower oxygen count: "-ite" (e.g., $\text{NO}_2^-$ nitrite)

  • Four Oxyanions Series (Chlorine, Bromine, Iodine series):

  • Most oxygen (4 O atoms): "per- … -ate" (e.g., $\text{ClO}_4^-$ perchlorate)

  • Base oxygen (3 O atoms): "-ate" (e.g., $\text{ClO}_3^-$ chlorate)

  • Fewer oxygen (2 O atoms): "-ite" (e.g., $\text{ClO}_2^-$ chlorite)

  • Least oxygen (1 O atom): "hypo- … -ite" (e.g., $\text{ClO}^-$ hypochlorite)

Ionic Bonding, Lattices, and Compounds

• Electrostatic Forces and Coulomb's Law:

  • Coulomb's Law Equation:

    $F_e = k_e \frac{|q_1 q_2|}{r^2}$ - $F_e$: Electrostatic force of attraction between oppositely charged ions. - $q_1, q_2$: Magnitudes of electrical charges on the two ions. - $r$: Inter-ionic distance between centers of nuclei. - $k_e$: Coulombic constant.

• Key Proportionalities:

  • $F_e \propto |q_1 q_2|$: Larger ionic charges produce significantly stronger attractive forces.

  • $F_e \propto \frac{1}{r^2}$: Smaller ionic radii place ions closer together, resulting in greater electrostatic force.

  • Ionic Compounds and Lattices:

• Ionic Bond: Electrostatic force of attraction holding oppositely charged cations and anions together.

• Ionic Compound: Neutral chemical compound composed of cations and anions.

• Ionic Lattice:

- Solid-state ionic compounds do not form isolated molecules; instead, they exist in a continuous 3D crystalline array (lattice) where each cation is surrounded by anions and vice versa.

• Formula Units and Empirical Formulas:

  • Empirical Formula: Chemical formula representing the lowest whole-number ratio of elements in a compound.

  • Formula Unit: The smallest neutral repeating collection of ions forming an ionic compound (e.g., $\text{NaCl}$).

• Predicting Ionic Formulas (Charge Neutrality):

  • In every neutral ionic compound, total positive charges must equal total negative charges.

  • Example 1: Potassium and Sulfide

  • Ions: $\text{K}^+$ ($+1$ charge) and $\text{S}^{2-}$ ($-2$ charge)

  • Charge balance: $2(\text{K}^+) + 1(\text{S}^{2-}) = 2(+1) + 1(-2) = 0$

  • Empirical Formula: $\text{K}_2\text{S}$

  • Example 2: Calcium and Nitrate

  • Ions: $\text{Ca}^{2+}$ ($+2$ charge) and $\text{NO}_3^-$ ($-1$ charge)

  • Charge balance: $1(\text{Ca}^{2+}) + 2(\text{NO}_3^-) = 1(+2) + 2(-1) = 0$

  • Empirical Formula: $\text{Ca}(\text{NO}_3)_2$

  • Example 3: Aluminum and Sulfate

  • Ions: $\text{Al}^{3+}$ ($+3$ charge) and $\text{SO}_4^{2-}$ ($-2$ charge)

  • Charge balance: $2(\text{Al}^{3+}) + 3(\text{SO}_4^{2-}) = 2(+3) + 3(-2) = 6+ + 6- = 0$

  • Empirical Formula: $\text{Al}_2(\text{SO}_4)_3$

• Ionic Compound Nomenclature Rules:

  • Name cation first, followed by anion.

  • Binary Examples:

  • $\text{NaCl}$: sodium chloride

  • $\text{MgCl}_2$: magnesium chloride

  • Variable Charge Metal Examples:

  • $\text{CuCl}$: copper(I) chloride

  • $\text{CuCl}_2$: copper(II) chloride

  • $\text{Fe}(\text{NO}_2)_2$: iron(II) nitrite

  • Polyatomic Examples:

  • $\text{MgSO}_4$: magnesium sulfate

  • $(\text{NH}_4)_2\text{S}$: ammonium sulfide

• Hydrates:

  • Definition: An ionic solid compound containing a fixed stoichiometric ratio of water molecules bound within its crystalline lattice.

• Nomenclature: Ionic name + Greek prefix + "hydrate".

• Examples:

  • $\text{NiCl}_2 \cdot 6\text{H}_2\text{O}$: nickel(II) chloride hexahydrate

  • $\text{CuSO}_4 \cdot 5\text{H}_2\text{O}$: copper(II) sulfate pentahydrate

  • $\text{FeCl}_2 \cdot 4\text{H}_2\text{O}$: iron(II) chloride tetrahydrate

Covalent Bonding and Molecular Compounds

• Covalent Bonding Fundamentals:

  • Covalent Bond: Chemical bond formed when two nonmetal atoms share one or more pairs of valence electrons to achieve stable full valence shells.

  • Example: Two Hydrogen atoms ($\text{H}\cdot + \cdot\text{H}$) share two electrons to form a single covalent bond in $\text{H}_2$ ($\text{H}-\text{H}$).

• Diatomic Elements ("The Magnificent Seven"):

• Seven elemental nonmetals exist naturally as homonuclear diatomic molecules:

  • Hydrogen: $\text{H}_2$

  • Nitrogen: $\text{N}_2$

  • Oxygen: $\text{O}_2$

  • Fluorine: $\text{F}_2$

  • Chlorine: $\text{Cl}_2$

  • Bromine: $\text{Br}_2$

  • Iodine: $\text{I}_2$

  • Bond Multiplicity in Lewis Structures:

• Single Bond: Sharing 1 pair of electrons (2 total electrons), e.g., $\mathbf{:}\ddot{\text{F}}-\ddot{\text{F}}\mathbf{:}$.

• Double Bond: Sharing 2 pairs of electrons (4 total electrons), e.g., $\mathbf{:}\text{O}=\text{O}\mathbf{:}$.

• Triple Bond: Sharing 3 pairs of electrons (6 total electrons), e.g., $\mathbf{:}\text{N}\equiv\text{N}\mathbf{:}$.

  • Molecular Formula vs. Empirical Formula:

• Molecular Formula: Reflects the exact actual number of atoms of each element present in a discrete covalent molecule.

• Empirical Formula: Reflects the simplified lowest whole-number ratio of atoms.

• Example: Hydrazine:

  • Empirical Formula: $\text{NH}_2$

  • Molecular Formula: $\text{N}_2\text{H}_4$

• Example: Phosphorus Oxides structural diversity:

  • Phosphorus monoxide: $\text{PO}$

  • Diphosphorus trioxide: $\text{P}_2\text{O}_3$

  • Diphosphorus tetroxide: $\text{P}_2\text{O}_4$

  • Tetraphosphorus decoxide: $\text{P}_4\text{O}_{10}$

  • Naming Binary Covalent Compounds:

• Order of Elements: Element positioned further to the left on the periodic table is named first. If both are in the same group, the element lower down is named first. The second element is named as an anion ending in "-ide".

• Numerical Prefixes:

  • 1: mono- (omit on first element)

  • 2: di-

  • 3: tri-

  • 4: tetra-

  • 5: penta-

  • 6: hexa-

  • 7: hepta-

  • 8: octa-

  • 9: nona-

  • 10: deca-

• Vowel Drop Rule: Drop final "a" or "o" from prefix when paired with an oxide anion (e.g., "tetroxide" instead of "tetraoxide", "pentoxide" instead of "pentaoxide").

• Examples:

  • $\text{PCl}_3$: phosphorus trichloride

  • $\text{PCl}_5$: phosphorus pentachloride

  • $\text{NO}_2$: nitrogen dioxide

  • $\text{N}_2\text{O}_4$: dinitrogen tetroxide

Distinguishing Ionic and Covalent Compounds

• Comparative Overview:

  • Covalent Compounds:

  • Formed strictly between nonmetal atoms.

  • Electrons are shared.

  • Form discrete neutral molecules.

  • Defined by molecular formulas.

  • Ionic Compounds:

  • Formed between metal cations and nonmetal anions (or polyatomic ions).

  • Electrons are transferred to form oppositely charged ions.

  • Do not form isolated molecules; exist in continuous 3D crystalline lattices.

  • Defined by formula units / empirical formulas.

• Identification Practice Examples:

  • $\text{MgBr}_2$: Metal + Nonmetal $\rightarrow$ Ionic $\rightarrow$ Magnesium bromide

  • $\text{SF}_6$: Nonmetal + Nonmetal $\rightarrow$ Covalent $\rightarrow$ Sulfur hexafluoride

  • $\text{FeCl}_3$: Variable charge metal + Nonmetal $\rightarrow$ Ionic $\rightarrow$ Iron(III) chloride

  • $\text{AgNO}_3$: Metal + Polyatomic anion $\rightarrow$ Ionic $\rightarrow$ Silver nitrate

Aqueous Solutions, Electrolytes, and Acids

• Electrolyte Solutions and Conductivity:

• Electrolyte Solution: An aqueous solution containing dissolved free-moving ions capable of conducting electricity.

• Pure Water: Does not contain dissolved ions; light bulb remains unlit (non-conducting).

• Sugar Water: Molecular covalent compound dissolves as neutral molecules without generating ions; light bulb remains unlit (non-conducting).

• Salt Water ($\text{NaCl}(aq)$): Soluble ionic lattice dissociates completely into free mobile ions ($\text{Na}^+$ and $\text{Cl}^-$); completes the circuit and light bulb glows brightly (electrolyte).

  • Dissociation Process:

• The process in which solid ionic crystalline structures separate into individual solvated cations and anions when dissolved in water.

  • Acid Nomenclature and Classification:

• Acid Definition: Molecular covalent compounds that ionize in aqueous solution to produce hydrogen ions ($\text{H}^+$).

• Binary Acids (Hydrogen + Nonmetal): Named as "hydro-" + root element name + "-ic acid".

  • $\text{HF}(aq)$: hydrofluoric acid

  • $\text{HCl}(aq)$: hydrochloric acid

  • $\text{HBr}(aq)$: hydrobromic acid

  • $\text{HI}(aq)$: hydroiodic acid

• Oxyacids (Hydrogen + Oxyanion):

  • If oxyanion ends in "-ate" $\rightarrow$ convert to "-ic acid":

    • $\text{NO}_3^-$ (nitrate) $\rightarrow \text{HNO}_3$: nitric acid

    • $\text{CO}_3^{2-}$ (carbonate) $\rightarrow \text{H}_2\text{CO}_3$: carbonic acid

    • $\text{SO}_4^{2-}$ (sulfate) $\rightarrow \text{H}_2\text{SO}_4$: sulfuric acid

    • $\text{PO}_4^{3-}$ (phosphate) $\rightarrow \text{H}_3\text{PO}_4$: phosphoric acid

    • $\text{ClO}_4^-$ (perchlorate) $\rightarrow \text{HClO}_4$: perchloric acid

    • $\text{CrO}_4^{2-}$ (chromate) $\rightarrow \text{H}_2\text{CrO}_4$: chromic acid

  • If oxyanion ends in "-ite" $\rightarrow$ convert to "-ous acid":

    • $\text{NO}_2^-$ (nitrite) $\rightarrow \text{HNO}_2$: nitrous acid

    • $\text{ClO}_2^-$ (chlorite) $\rightarrow \text{HClO}_2$: chlorous acid

  • Electrolyte Summary:

• Substances that act as electrolytes in aqueous solution comprise:

  1. Soluble ionic compounds

  2. Acids (covalent compounds that ionize to release $\text{H}^+$)

Quantitative Chemical Formula Determination

• Determination of Empirical Formula from Combustion Analysis:

  • Problem Statement: Combustion of a hydrocarbon sample containing carbon and hydrogen only produces $14.12\,g$ of $\text{CO}_2$ and $5.78\,g$ of $\text{H}_2\text{O}$. Determine the moles of C and H present and the empirical formula.

  • Step 1: Calculate moles of Carbon from $\text{CO}_2$ ($\text{Molar mass} = 44.01\,g\,mol^{-1}$):     $14.12\,g\,\text{CO}_2 \times \frac{1\,mol\,\text{CO}_2}{44.01\,g\,\text{CO}_2} \times \frac{1\,mol\,\text{C}}{1\,mol\,\text{CO}_2} = 0.3208\,mol\,\text{C}$

  • Step 2: Calculate moles of Hydrogen from $\text{H}_2\text{O}$ ($\text{Molar mass} = 18.02\,g\,mol^{-1}$):     $5.78\,g\,\text{H}_2\text{O} \times \frac{1\,mol\,\text{H}_2\text{O}}{18.02\,g\,\text{H}_2\text{O}} \times \frac{2\,mol\,\text{H}}{1\,mol\,\text{H}_2\text{O}} = 0.642\,mol\,\text{H}$

  • Step 3: Determine lowest whole-number molar ratio:

  • Divide by smallest mole value ($0.3208$):

    • Carbon: $\frac{0.3208}{0.3208} = 1.00\,mol\,\text{C}$

    • Hydrogen: $\frac{0.642}{0.3208} = 2.00\,mol\,\text{H}$

  • Empirical Formula: $\text{CH}_2$

• Determination of Empirical Formula from Percent Composition:

  • Problem Statement 1: A compound contains $71.61\%$ C, $7.51\%$ H, and $20.88\%$ N by mass. Find the empirical formula.

  • Assume a $100\,g$ sample:

    • $\text{Mass C} = 71.61\,g$, $\text{Mass H} = 7.51\,g$, $\text{Mass N} = 20.88\,g$

  • Convert masses to moles:

    • $\text{Moles C} = 71.61\,g \times \frac{1\,mol\,\text{C}}{12.01\,g\,\text{C}} = 5.9625\,mol\,\text{C}$

    • $\text{Moles H} = 7.51\,g \times \frac{1\,mol\,\text{H}}{1.01\,g\,\text{H}} = 7.436\,mol\,\text{H}$

    • $\text{Moles N} = 20.88\,g \times \frac{1\,mol\,\text{N}}{14.01\,g\,\text{N}} = 1.4904\,mol\,\text{N}$

  • Divide by smallest mole value ($1.4904$):

    • C ratio: $\frac{5.9625}{1.4904} \approx 4.0$

    • H ratio: $\frac{7.436}{1.4904} \approx 5.0$

    • N ratio: $\frac{1.4904}{1.4904} = 1.0$

  • Empirical Formula: $\text{C}_4\text{H}_5\text{N}$

  • Problem Statement 2 (Ibuprofen): Ibuprofen is analyzed as $75.69\%$ C, $8.80\%$ H, and $15.51\%$ O by mass. Determine its empirical formula.

  • Assume a $100\,g$ sample:

    • $\text{Moles C} = 75.69\,g \times \frac{1\,mol\,\text{C}}{12.01\,g\,\text{C}} = 6.3022\,mol\,\text{C}$

    • $\text{Moles H} = 8.80\,g \times \frac{1\,mol\,\text{H}}{1.01\,g\,\text{H}} = 8.713\,mol\,\text{H}$

    • $\text{Moles O} = 15.51\,g \times \frac{1\,mol\,\text{O}}{16.00\,g\,\text{O}} = 0.96938\,mol\,\text{O}$

  • Divide by smallest mole value ($0.96938$):

    • C ratio: $\frac{6.3022}{0.96938} = 6.501$

    • H ratio: $\frac{8.713}{0.96938} = 8.988 \approx 9.0$

    • O ratio: $\frac{0.96938}{0.96938} = 1.0$

  • Apply non-integer multiplier rule ($6.501$ ends near $0.50$, so multiply all ratios by 2):

    • $\text{C} = 6.501 \times 2 = 13.002 \approx 13$

    • $\text{H} = 8.988 \times 2 = 17.976 \approx 18$

    • $\text{O} = 1.0 \times 2 = 2$

  • Empirical Formula: $\text{C}_{13}\text{H}_{18}\text{O}_2$

• Fractional Multiplier and Rounding Guidelines:

  • If mole ratios end in specific non-integer decimals, multiply all ratios by the corresponding integer:

  • Decimal near $0.50 \rightarrow \times 2$

  • Decimal near $0.33$ or $0.67 \rightarrow \times 3$

  • Decimal near $0.25$ or $0.75 \rightarrow \times 4$

  • Decimal within $0.05$ of a whole number $\rightarrow$ Round directly to nearest whole number.

• Molecular Formula Determination from Empirical Formula:

  • Problem Statement: Elemental analysis gives an empirical formula of $\text{CH}_2\text{F}$. Mass spectrometry reveals a molecular mass of $66.0\,u$. Find the molecular formula.

  • Step 1: Calculate mass of empirical formula unit (\text{CH}_2\text{F}):     $\text{Empirical Mass} = 12.01\,u + 2(1.01\,u) + 19.00\,u = 33.0\,u$

  • Step 2: Determine integral multiplier ($n$):     $n = \frac{\text{Molecular Mass}}{\text{Empirical Mass}} = \frac{66.0\,u}{33.0\,u} = 2$

  • Step 3: Multiply empirical formula subscripts by $n$ ($2$):     $\text{Molecular Formula} = 2 \times (\text{CH}_2\text{F}) = \text{C}_2\text{H}_4\text{F}_2$