Chemistry Syllabus

State the Pauli exclusion principle.

No two electrons in the same atom can have all four quantum numbers identical. Consequently an orbital holds at most two electrons, and they must have opposite spins ($+\tfrac12$ and $-\tfrac12$).

State Hund's rule of maximum multiplicity.

For degenerate (equal-energy) orbitals, electrons occupy them singly with parallel spins before pairing begins. This maximizes total spin and minimizes electron-electron repulsion.

Write the ground-state electronic configurations of $\ce{Cr}$ (Z=24) and $\ce{Cu}$ (Z=29), and explain the anomaly.

$\ce{Cr}$: $[\ce{Ar}]\,3d^{5}4s^{1}$; $\ce{Cu}$: $[\ce{Ar}]\,3d^{10}4s^{1}$. Half-filled ($d^5$) and fully filled ($d^{10}$) subshells give extra stability (exchange energy and symmetry).

What did the photoelectric effect demonstrate about the nature of light?

It showed light behaves as discrete packets (photons) of energy $E=h\nu$. Electron emission depends on frequency, not intensity, supporting the particle (quantum) nature of light.

State Einstein's photoelectric equation and define each term.

$$h\nu = \phi + \tfrac{1}{2}mv_{\max}^{2}$$ where $h\nu$ is photon energy, $\phi = h\nu_0$ is the work function (minimum energy to eject an electron), and $\tfrac{1}{2}mv_{\max}^{2}$ is the maximum kinetic energy of the emitted electron.

In the photoelectric effect, what are threshold frequency and work function?

Threshold frequency $\nu_0$ is the minimum light frequency that can eject electrons from a metal. Work function $\phi = h\nu_0$ is the corresponding minimum energy needed. Below $\nu_0$ no electrons are emitted regardless of intensity.

In the photoelectric effect, how do light intensity and frequency affect the emitted photoelectrons?

Increasing intensity (above $\nu_0$) increases the number of photoelectrons (current) but not their kinetic energy. Increasing frequency increases the maximum kinetic energy of each photoelectron but not their number.

State the Modern Periodic Law.

The physical and chemical properties of elements are periodic functions of their atomic numbers. (Mendeleev's earlier law was based on atomic mass.)

How are periods and groups defined in the modern periodic table in terms of electronic configuration?

Period number = the principal quantum number ($n$) of the outermost shell being filled. Group number is governed by the number of valence (outermost) electrons. There are 7 periods and 18 groups.

Name the four blocks of the periodic table and the subshell being filled in each.

s-block (filling $ns$), p-block (filling $np$), d-block/transition (filling $(n-1)d$), and f-block/inner transition (filling $(n-2)f$).

How does atomic radius vary across a period and down a group, and why?

It decreases across a period (left to right) due to increasing nuclear charge pulling electrons of the same shell inward. It increases down a group because new shells are added, increasing size despite higher charge.

Compare the size of a cation and an anion with their parent atom.

A cation is smaller than its parent atom (loses electron(s), often a whole shell, and has greater effective nuclear charge per electron). An anion is larger (gains electrons, increasing repulsion and reducing effective nuclear charge per electron).

Arrange the isoelectronic species $\ce{O^{2-}}$, $\ce{F^-}$, $\ce{Na^+}$, $\ce{Mg^{2+}}$ in order of increasing ionic radius and explain.

$\ce{Mg^{2+}} < \ce{Na^+} < \ce{F^-} < \ce{O^{2-}}$. All have 10 electrons; the species with the highest nuclear charge ($\ce{Mg^{2+}}$, $Z=12$) holds them most tightly, so it is smallest.

Define ionization energy (ionization enthalpy).

The minimum energy required to remove the most loosely bound electron from an isolated gaseous atom in its ground state: $$\ce{X(g) -> X^+(g) + e^-},\quad \Delta H = \text{IE}_1 > 0$$

Why is the second ionization energy always greater than the first ($\text{IE}_2 > \text{IE}_1$)?

After removing one electron, the resulting cation has a greater effective nuclear charge per remaining electron and a smaller radius, so the next electron is held more tightly and needs more energy to remove.

How does first ionization energy generally vary across a period and down a group?

It generally increases across a period (greater nuclear charge, smaller size) and decreases down a group (larger size and increased shielding make outer electrons easier to remove).

Why does boron have a lower first ionization energy than beryllium, and oxygen lower than nitrogen?

$\ce{B}$ ($2s^{2}2p^{1}$): the $2p$ electron is higher in energy and easier to remove than $\ce{Be}$'s stable filled $2s^{2}$. $\ce{O}$ ($2p^{4}$): removing one electron relieves $p$-orbital pair repulsion, unlike $\ce{N}$'s stable half-filled $2p^{3}$.

Define electron gain enthalpy (electron affinity) and state its general periodic trend.

The enthalpy change when an electron is added to a neutral gaseous atom: $\ce{X(g) + e^- -> X^-(g)}$. It generally becomes more negative across a period and less negative down a group. Halogens have the most negative values.

Why is the electron gain enthalpy of chlorine more negative than that of fluorine?

Fluorine's small size causes high electron-electron repulsion in its compact $2p$ subshell when an electron is added, making its electron gain enthalpy less negative than chlorine's, despite fluorine being more electronegative.

Define electronegativity and name two common scales used to measure it.

Electronegativity is the tendency of an atom to attract the shared (bonding) pair of electrons toward itself in a covalent bond. Common scales: Pauling scale and Mulliken scale.

How does electronegativity vary across a period and down a group, and which element is the most electronegative?

It increases across a period and decreases down a group. Fluorine is the most electronegative element (Pauling value $\approx 4.0$).

State the conditions for and characteristics of an ionic (electrovalent) bond.

Formed by complete transfer of electron(s) from a metal (low IE) to a non-metal (high electron affinity), producing oppositely charged ions held by electrostatic attraction. Favored by large electronegativity difference; gives high melting points and conduction in molten/aqueous state.

State Fajans' rules for the covalent character of an ionic bond.

Covalent character increases with: (1) small cation, (2) large anion, (3) high charge on either ion, and (4) cations with a non-noble-gas (e.g. $d^{10}$) electron configuration. These increase polarization of the anion by the cation.

Define a covalent bond and distinguish sigma ($\sigma$) from pi ($\pi$) bonds.

A covalent bond is formed by mutual sharing of electron pairs. A $\sigma$ bond forms by head-on (axial) overlap of orbitals and is stronger; a $\pi$ bond forms by sidewise (lateral) overlap of p-orbitals and is weaker. A double bond = 1 $\sigma$ + 1 $\pi$; a triple bond = 1 $\sigma$ + 2 $\pi$.

Define a coordinate (dative) covalent bond and give an example.

A covalent bond in which both shared electrons are contributed by the same atom (the donor), while the other atom (acceptor) provides an empty orbital. Example: formation of $\ce{NH4+}$ from $\ce{NH3 + H+}$, where N donates its lone pair.

State the central postulate of VSEPR theory.

Electron pairs (bonding and lone) in the valence shell of the central atom arrange themselves as far apart as possible to minimize repulsion, determining molecular geometry. Repulsion order: lone pair-lone pair > lone pair-bond pair > bond pair-bond pair.

Using VSEPR, give the shape and bond angle for molecules of type $AB_2$, $AB_3$, $AB_4$, $AB_5$, and $AB_6$ (no lone pairs).

$AB_2$: linear, $180^\circ$. $AB_3$: trigonal planar, $120^\circ$. $AB_4$: tetrahedral, $109.5^\circ$. $AB_5$: trigonal bipyramidal, $90^\circ/120^\circ$. $AB_6$: octahedral, $90^\circ$.

Explain why the bond angle in $\ce{H2O}$ ($104.5^\circ$) is smaller than in $\ce{NH3}$ ($107^\circ$), which is smaller than in $\ce{CH4}$ ($109.5^\circ$).

All are based on tetrahedral $sp^3$ geometry. $\ce{CH4}$ has 0 lone pairs, $\ce{NH3}$ has 1, $\ce{H2O}$ has 2. More lone pairs cause greater lone pair-bond pair repulsion, compressing the bond angle progressively.

Relate the type of hybridization ($sp$, $sp^2$, $sp^3$, $sp^3d$, $sp^3d^2$) to geometry and number of electron domains.

$sp$ (2 domains): linear, $180^\circ$. $sp^2$ (3): trigonal planar, $120^\circ$. $sp^3$ (4): tetrahedral, $109.5^\circ$. $sp^3d$ (5): trigonal bipyramidal. $sp^3d^2$ (6): octahedral.

State the bonding-energy order in molecular orbital theory and give the MO filling sequence for $\ce{O2}$ and beyond.

For $\ce{O2}$, $\ce{F2}$ (and heavier): $\sigma 1s,\ \sigma^*1s,\ \sigma 2s,\ \sigma^*2s,\ \sigma 2p_z,\ (\pi 2p_x=\pi 2p_y),\ (\pi^*2p_x=\pi^*2p_y),\ \sigma^*2p_z$. For $\ce{B2}$, $\ce{C2}$, $\ce{N2}$ the $\pi 2p$ orbitals lie below $\sigma 2p_z$.

Give the molecular orbital bond order formula and explain why $\ce{O2}$ is paramagnetic.

$$\text{Bond order} = \frac{N_b - N_a}{2}$$ where $N_b$, $N_a$ are bonding and antibonding electrons. $\ce{O2}$ has 2 unpaired electrons in its $\pi^*2p$ orbitals (bond order 2), making it paramagnetic.

State the postulates of the kinetic molecular theory of gases.

Gas consists of tiny molecules in constant random motion; molecular volume is negligible vs container; no intermolecular forces; collisions are perfectly elastic; and average kinetic energy is directly proportional to absolute temperature.

State Boyle's law and Charles's law with their mathematical forms.

Boyle's law (constant $T$): $PV = \text{constant}$, i.e. $P \propto \frac{1}{V}$. Charles's law (constant $P$): $\frac{V}{T} = \text{constant}$, i.e. $V \propto T$ (absolute temperature).

State the ideal gas equation and Avogadro's law.

Ideal gas equation: $$PV = nRT$$ with $R = 0.0821\ \text{L atm mol}^{-1}\text{K}^{-1} = 8.314\ \text{J mol}^{-1}\text{K}^{-1}$. Avogadro's law: equal volumes of gases at the same $T$ and $P$ contain equal numbers of molecules ($V \propto n$).

State Dalton's law of partial pressures and Graham's law of diffusion.

Dalton: total pressure of a gas mixture equals the sum of partial pressures, $P_{\text{total}} = P_1 + P_2 + \cdots$. Graham: rate of diffusion is inversely proportional to the square root of density (or molar mass): $$\frac{r_1}{r_2} = \sqrt{\frac{M_2}{M_1}}$$

Write the van der Waals equation for real gases and explain the correction terms.

$$\left(P + \frac{an^{2}}{V^{2}}\right)(V - nb) = nRT$$ The $\frac{an^{2}}{V^{2}}$ term corrects for intermolecular attraction (lowering observed pressure), and $nb$ corrects for the finite volume occupied by the molecules.

Why do real gases deviate from ideal behavior, and under what conditions do they behave most ideally?

Deviations arise because real molecules have finite volume and exert intermolecular forces, assumptions ignored by ideal gas law. Gases behave most ideally at high temperature and low pressure, where these effects are negligible.

Define the root-mean-square (rms) speed of gas molecules and give its formula.

The square root of the mean of the squared molecular speeds: $$u_{\text{rms}} = \sqrt{\frac{3RT}{M}}$$ where $M$ is molar mass. It increases with temperature and decreases with molar mass.

Define critical temperature and explain its significance for liquefying a gas.

The critical temperature $T_c$ is the highest temperature at which a gas can be liquefied by applying pressure alone. Above $T_c$, no amount of pressure can liquefy the gas. A lower $T_c$ means a gas is harder to liquefy.