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Engineering Chemistry

Master Study Guide: Spectroscopy, Stereochem, MO Theory & Thermodynamics

Module 1: Atomic Structure & Bonding

1. MO Diagram of CO & NO (Bond Order & Magnetic Property)

Carbon Monoxide (CO)

Total Electrons: 6 (from C) + 8 (from O) = 14 e⁻

Electronic Configuration:
σ1s² σ*1s² σ2s² σ*2s² π2p_x² = π2p_y² σ2p_z²

  • $N_b = 10$, $N_a = 4$
  • Bond Order: $\frac{10 - 4}{2} = \mathbf{3.0}$ (Triple bond)
  • Magnetic Property: Diamagnetic (All electrons are paired).

*Note: In CO, the σ2p_z orbital is slightly higher in energy than the π orbitals due to s-p mixing.

Nitric Oxide (NO)

Total Electrons: 7 (from N) + 8 (from O) = 15 e⁻

Electronic Configuration:
σ1s² σ*1s² σ2s² σ*2s² σ2p_z² π2p_x² = π2p_y² \mathbf{π*2p_x¹}

  • $N_b = 10$, $N_a = 5$
  • Bond Order: $\frac{10 - 5}{2} = \mathbf{2.5}$
  • Magnetic Property: Paramagnetic (1 unpaired electron in π*).

2. Particle in a 1-D Box

Describes a free particle (like an electron) confined to a 1-dimensional space of length $L$ with infinitely high potential walls ($V=0$ inside, $V=\infty$ outside).

Energy ($E_n$): $$E_n = \frac{n^2 h^2}{8mL^2}$$

Where $n = 1, 2, 3...$ (Principal quantum number). Energy is quantized. Ground state energy ($n=1$) is not zero (Zero-point energy).

Wavefunction ($\psi_n$): $$\psi_n = \sqrt{\frac{2}{L}} \sin\left(\frac{n\pi x}{L}\right)$$

The probability of finding the particle is $|\psi_n|^2$. The number of nodes is $(n-1)$.

Stereochemistry & Isomerism

1. R/S Nomenclature

Used for chiral centers. Priorities assigned via CIP (Cahn-Ingold-Prelog) atomic number rules.

  • R (Rectus): 1 → 2 → 3 path is Clockwise.
  • S (Sinister): 1 → 2 → 3 path is Counter-Clockwise.
  • Rule: If the lowest priority group (4) is on a horizontal line (Fischer) or wedge, reverse the final result!

2. E/Z & Geometrical Isomerism

Used for alkenes (C=C). Also uses CIP priority rules on each carbon.

  • Z (Zusammen): "Together" (Cis-like). High priority groups on the same side.
  • E (Entgegen): "Opposite" (Trans-like). High priority groups on opposite sides.

3. Conformations of Alkanes (n-butane & propane)

n-Butane ($CH_3-CH_2-CH_2-CH_3$): Rotation around C2-C3 bond creates 4 conformers:

  • Anti (Staggered, 180°): Most stable. Bulky $CH_3$ groups are farthest apart.
  • Gauche (Staggered, 60°): $CH_3$ groups are adjacent. Slight steric strain.
  • Eclipsed (120°): H eclipses $CH_3$. Torsional strain.
  • Fully Eclipsed (0°): Least stable. $CH_3$ completely eclipses $CH_3$. Maximum steric strain.

Propane ($CH_3-CH_2-CH_3$): Only has basic Staggered and Eclipsed forms because rotating C1-C2 always eclipses an H with a $CH_3$ group.

4. Conversions (Flying Wedge, Fischer, Sawhorse, Newman)

Wedge → Fischer

View the molecule from the top. Bonds coming out (wedges) go on the horizontal lines. Bonds going in (dashes) go on the vertical lines.

Fischer → Newman

Fischer projections are drawn in an eclipsed state. The cross intersection is the front carbon. Groups on horizontal lines point upwards/outwards in Newman.

Sawhorse → Newman

Look directly down the C-C bond of the Sawhorse. The front carbon becomes a dot, the back carbon becomes a large circle.

Spectroscopy

1. Jablonski Diagram (Photochemistry)

Illustrates the electronic states of a molecule and the transitions between them following the absorption of light.

Absorption: Molecule jumps from Singlet Ground State ($S_0$) to Excited States ($S_1, S_2$).

Internal Conversion (IC): Non-radiative transition between states of the same multiplicity (e.g., $S_2 \rightarrow S_1$).

Intersystem Crossing (ISC): Non-radiative transition between states of different multiplicity (e.g., $S_1 \rightarrow T_1$). Involves spin flip.

Fluorescence: Radiative transition $S_1 \rightarrow S_0$. Fast (nanoseconds).

Phosphorescence: Radiative transition $T_1 \rightarrow S_0$. Slow (milliseconds to hours) because it is a "forbidden" spin transition.

S₀ S₁ T₁ Absorption Fluorescence ISC Phosphorescence

2 & 3. NMR, IR & Spectroscopy Concepts

NMR: Types of Protons & Chemical Shift
  • Equivalent Protons: Protons in the exact same chemical environment produce 1 single signal. (e.g., all 6 H's in Benzene give 1 signal).
  • Chemical Shift ($\delta$): Indicates the electronic environment. Shielded protons (electron-rich) appear upfield (lower ppm). Deshielded protons (near electronegative atoms) appear downfield (higher ppm).
NMR: Pascal's Triangle & Splitting

$n+1$ Rule: The signal of a proton is split into $n+1$ peaks, where $n$ is the number of adjacent equivalent protons.

The intensity ratios of these peaks follow Pascal's Triangle:

  • n=0 (Singlet): 1
  • n=1 (Doublet): 1 : 1
  • n=2 (Triplet): 1 : 2 : 1
  • n=3 (Quartet): 1 : 3 : 3 : 1
IR & Vibrational Spectroscopy Applications

Infrared (IR) spectroscopy causes molecular vibrations (stretching and bending). It is primarily used for Functional Group Identification.
Example: A strong broad peak at ~3300 cm⁻¹ indicates an -OH group. A sharp peak at ~1700 cm⁻¹ indicates a Carbonyl (C=O) group.

5. Oxidation Number Calculation

Rules: Free elements = 0. Oxygen is usually -2 (except peroxides = -1). Hydrogen is usually +1 (except hydrides = -1). The sum of oxidation states in a neutral molecule is 0, or equal to the charge for an ion.

Module 3 & 4: Physical Chemistry

Van der Waals Equation (Real Gases)

$$\left( P + \frac{an^2}{V^2} \right) (V - nb) = nRT$$
Significance of terms (5/10 Marks):
  • $P$ and $V$: Measured pressure and volume.
  • $n$: Number of moles.
  • $a$ (Correction for Intermolecular Forces): Accounts for the attractive forces between gas molecules, which reduces the pressure they exert on the walls. High '$a$' = easy liquefaction.
  • $b$ (Correction for Volume): Represents the actual finite volume occupied by the gas molecules themselves (excluded volume).

Thermodynamics: Equilibrium Constant, $\Delta G$, $\Delta H$

Gibbs Free Energy ($\Delta G$)

$$\Delta G = \Delta H - T\Delta S$$

If $\Delta G < 0$, reaction is spontaneous. $\Delta H$ is Enthalpy (heat), $\Delta S$ is Entropy (randomness).

Relation with Equilibrium ($K_{eq}$)

$$\Delta G^\circ = -RT \ln K_{eq} = -2.303 RT \log_{10} K_{eq}$$

Used heavily in numericals to find the Equilibrium constant ($K_{eq}$) given standard free energy.

Nernst Equation Derivation

Relates the cell potential ($E$) to the standard cell potential ($E^\circ$) and the reaction quotient ($Q$).

  1. From thermodynamics, the free energy change under non-standard conditions is:
    $$\Delta G = \Delta G^\circ + RT \ln Q$$
  2. We know electrical work relates to free energy by:
    $$\Delta G = -nFE$$ and $$\Delta G^\circ = -nFE^\circ$$
  3. Substitute these into the first equation:
    $$-nFE = -nFE^\circ + RT \ln Q$$
  4. Divide the entire equation by $-nF$:
    $$E = E^\circ - \frac{RT}{nF} \ln Q$$
  5. At 298K, converting $\ln$ to $\log_{10}$ and plugging in constants ($R, T, F$), the numerical formula becomes: $$E = E^\circ - \frac{0.0591}{n} \log_{10} \left( \frac{[\text{Products}]}{[\text{Reactants}]} \right)$$

Module 5: Periodic Properties

1. Ionisation Energy (IE)

The minimum energy required to remove the most loosely bound electron from an isolated gaseous atom.

Trend: Increases across a period (due to higher effective nuclear charge). Decreases down a group (due to increased shielding and distance).

2. Electron Affinity (EA)

The energy released when an electron is added to a neutral, isolated gaseous atom to form an anion.

Trend: Becomes more negative (higher affinity) across a period. Halogens have the highest EA. Noble gases have near-zero EA.

3. Fajans' Rule

Predicts whether a chemical bond will be covalent or ionic. It states that an ionic bond gains Covalent Character when:

  • The Cation is very small.
  • The Anion is very large (highly polarizable).
  • There is a high charge on either ion.