Inorganic Qualitative and Quantitative Chemistry Exam Review

Periodic Table Trends and Atomic Identity

• Electronegativity and the Phonics Scale: According to the transcript's discussion of the phonics scale (referring to the Pauling scale), elements such as nitrogen, chlorine, and oxygen exhibit high electronegativity values.

• Atomic Radius Trends:

  • Moving from left to right across a period, the atomic radius decreases.

  • The atomic radius increases as you move down a group.

• Ionization Energy Trends:

  • Ionization energy decreases from top to bottom within a group.

  • Ionization energy increases from left to right across a period.

• Identity of an Element: The identity of an element is defined strictly by the number of protons.

  • Isotopes: Variations in the number of neutrons, which do not change the element's identity.

  • Mass Number: Defined as the sum of of protons and neutrons ($\text{Mass Number} = p^+ + n^0$).

The Lanthanide Contraction and Relativistic Effects

• Lanthanide Contraction in Period 5 and 6:

  • Zirconium ($Zr$) in Period 5 and Hafnium ($Hf$) in Period 6 have nearly identical atomic radii, approximately $159\,pm$.

  • This phenomenon is caused by the filling of the $4f$ subshell in the lanthanide series. The poor shielding of these electrons causes the $6s$ electrons to be pulled closer to the nucleus, offsetting the expected increase in size that usually accompanies the addition of new electron shells.

• Relativistic Effects in Heavy Elements:

  • Gold ($Au$): In very heavy elements like gold, $s$ electrons move at a significant fraction of the speed of light. This increases their mass and causes the orbital to contract. This stabilizes the $6s^2$ pair and increases ionization energy, making gold noble and resistant to oxidation compared to silver.

  • Mercury ($Hg$): Mercury is liquid at room temperature because the relativistic contraction of the $6s^2$ orbital is so strong that these electrons do not participate effectively in metallic bonding. This results in very weak interatomic forces, behaving almost like a pseudo-noble gas.

Group 14 and the Inert Pair Effect

• Oxidation State Stability: In Group 14, the stability of the $+2$ oxidation state increases relative to the $+4$ state as one moves down the group.

  • Carbon and Silicon: Stable at the $+4$ state.

  • Lead ($Pb$) and Tin ($Sn$): Lead is much more stable in the $+2$ oxidation state than the $+4$ state. This is attributed to the Inert Pair Effect, where the $6s^2$ electrons become increasingly difficult to involve in bonding due to relativistic effects and poor shielding from the $d$ and $f$ orbitals.

Transition Metal Properties and Strength

• Oxidation States: Manganese ($Mn$) is capable of forming a stable oxoanion, permanganate ($MnO_4^-$), in the $+7$ oxidation state.

• Metallic Lattice and Bonding Strength:

  • The strength of metallic bonds in transition metals depends on the number of unpaired $d$ electrons available for delocalization.

  • Tungsten ($W$) vs. Copper ($Cu$): Tungsten ($5d^4 6s^2$) has more unpaired electrons than Copper ($3d^{10} 4s^1$). Consequently, Tungsten is significantly harder and has a much higher melting point.

  • Copper's structure is Face-Centered Cubic ($FCC$), while Tungsten is Body-Centered Cubic ($BCC$), but the electron count is the dominant factor in bond strength.

Electron Affinity and Solubility

• Chlorine vs. Fluorine: Chlorine exhibits a greater electron affinity than Fluorine. Although Fluorine is more electronegative, its $2p$ subshell is so small that electron-electron repulsion slightly offsets the nuclear attraction. Chlorine's $3p$ subshell has more room, facilitating easier electron addition.

• Hume-Rothery Rules: In the context of solid solutions, a large electronegativity difference between a solvent and a solute is avoided. A high difference may lead to the formation of stable, brittle, ionic-like intermetallics, which reduces the solubility range.

Chemical Equilibrium and Stoichiometry

• Normality of Oxidizing Agents: For a $0.1\,M$ solution of Potassium Dichromate ($K_2Cr_2O_7$) used in acidic medium where it is reduced to $Cr^{3+}$:

  • The half-reaction is: $Cr_2O_7^{2-} + 14H^+ + 6e^- \rightarrow 2Cr^{3+} + 7H_2O$.

  • The number of electrons ($n$) transferred is $6$.

  • The transcript notes the normality for a specific context as $0.3\,N$.

• Equilibrium Constants ($K$):

  • The value of the equilibrium constant is only affected by temperature; it is not affected by the addition of a catalyst.

  • Catalysts: Increase the rate at which equilibrium is reached but do not shift the equilibrium position or change the constant.

• Le Chatelier's Principle:

  • Inert Gas: Adding an inert gas at constant volume increases total pressure but does not change the partial pressures of the reactants, therefore it has no effect on the equilibrium position.

  • Pressure: Increasing pressure shifts the reaction toward the side with fewer moles of gas.

  • Solids: Adding more solid reactants (e.g., $CaCO_3$) that are already at equilibrium has no effect on the equilibrium pressures of the gaseous components (e.g., $CO_2$) because the activity of a solid is defined as $1$.

Analytical Chemistry and Calculations

• pH and pOH Calculations: For a solution with a $pH$ of $3$:

  • $pH + pOH = 14$

  • $pOH = 14 - 3 = 11$

  • Concentration of $OH^-$: $[OH^-] = 10^{-pOH} = 10^{-11}\,M$.

• Molarity and Mass: To find the molarity of solution with $4\,g$ of $NaOH$ (molecular weight $= 40\,g/mol$) in a $500\,ml$ ($0.5\,L$) solution:

  • $\text{moles of NaOH} = \frac{4\,g}{40\,g/mol} = 0.1\,mol$

  • $\text{Molarity} = \frac{0.1\,mol}{0.5\,L} = 0.2\,M$.

• Back Titration Example: Purity calculation for a sample of $CaCO_3$:

  • Sample mass: $0.5\,g$.

  • Added $HCl$: $50\,ml$ of $0.1\,M$ ($0.005\,moles$).

  • Excess acid titrated with $NaOH$: $10\,ml$ of $0.1\,M$ ($0.001\,moles$).

  • Moles of $HCl$ reacted with sample: $0.005 - 0.001 = 0.004\,moles$ .

  • Stoichiometry is $1:2$ ($1\,CaCO_3 : 2\,HCl$), so moles of $CaCO_3 = 0.002\,moles$.

  • Mass of $CaCO_3 = 0.002\,mol \times 100\,g/mol = 0.2\,g$.

  • Purity: $\frac{0.2}{0.5} \times 100 = 40\%$.

• Primary Standards: Potassium Hydrogen Phthalate ($KHP$) is cited as an example of a primary standard in acid-base titrations.

• Gravimetric Analysis Errors:

  • Peptization: The process where a precipitate returns to a colloidal state during washing.

  • Systematic Error: Using an uncalibrated pipette that consistently delivers the wrong volume (e.g., $0.1\,ml$ off every time).

Coordination Chemistry and Material Science

• Jahn-Teller Effect: Seen in Copper ($II$) complexes ($Cu^{2+}$). It involves the geometric distortion (elongation or compression of axial bonds) of an octahedral field to remove electronic degeneracy and lower the system's total energy.

• Conductivity of Carbon Allotropes:

  • Graphite: An electrical conductor because it has delocalized $\pi\,electrons$ that allow for electron mobility.

  • Diamond: An insulator because electrons are locked in localized $\sigma\,bonds$.

• Passivation: Aluminum shows passivation by forming a coherent, non-porous oxide layer ($Al_2O_3$) that prevents further oxidation of the underlying metal. Iron does not form such a protective layer.

• Work Function: Platinum ($Pt$) exhibits a very high work function (the minimum energy to remove an electron from a solid surface) due to its high effective nuclear charge ($Z_{eff}$), making it one of the hardest surfaces from which to extract electrons.

Metallurgy and Fire Assay

• Litharge ($PbO$): In fire assaying, the primary function of litharge is to provide metallic lead, which collects precious metals like gold and silver for analysis.

• Haff-Reaction Softness: Silver ($Ag^+$) and sulfide ($S^{2-}$) are classified as "soft" acids and bases with high polarizability. Soft acids prefer soft bases, which is why silver is often found as sulfide minerals rather than oxides.