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21-Mat-A4 Deformation Behaviour and Properties of Materials · December 2013

Question 4 of 8: Structure and Chemical Bonding (20 marks)

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format. National Exams, December 2013 — Met-A4, Structure of Materials. Three hours, closed book, one approved calculator (Casio or Sharp). Eight questions of 20 marks each; the rubric asks for any five, and only the first five in the answer book are marked. All eight are solved here. All necessary equations and constants are provided in the exam's own appendix (reproduced where used below).

The printed exam header reads Met-A4, Structure of Materials. Only two of the eight questions (VI and VII) are genuinely diffusion/mechanical-properties content; the paper as a whole is a broad introductory materials-science survey — bonding, crystal defects, crystallography, XRD and phase diagrams — and is answered as such below.

Reference texts. The answers below are keyed to the works normally recommended for this syllabus code:

Question IV — Structure and Chemical Bonding (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

IV.1 — Primary vs. secondary bonding, and five examples

Primary bonds (ionic, covalent, metallic) involve substantial electron transfer or sharing between atoms and are strong, with bond energies typically 1–10 eV/atom (100s of kJ/mol); they set melting point, elastic stiffness and cohesive strength. Secondary (van der Waals/dipole) bonds arise from weak electrostatic attraction between permanent or induced dipoles — no electron transfer — with energies of order 0.01–0.1 eV/atom (as computed for argon in Question I.3), and they govern properties like interlayer sliding, polymer softening temperature and physisorption.

a. CsCl — ionic (large electronegativity difference, Cs 0.7 vs. Cl 3.0; Cs→Cs+ transfers its valence electron to Cl→Cl−). b. Inter-layer bonding in graphite — secondary (van der Waals); the covalent sheets themselves are bonded in-plane, but adjacent sheets are held together only by weak dispersion forces (Question II.1(b)'s companion fact). c. Iron (Fe) — metallic (delocalised valence-electron "sea" among positive ion cores, giving ductility and conductivity). d. Rubber — primarily covalent along the polymer backbone (and at sulfur cross-links after vulcanisation), with secondary (van der Waals) bonding between adjacent chains; it is this combination — strong chain bonds but weak interchain bonds — that gives rubber its large reversible elastic strain. e. Silica (SiO2) — predominantly covalent (Si–O bonds have significant covalent character, though with a notable ionic contribution from the electronegativity difference, Si 1.8 vs. O 3.5), forming the covalent SiO4 tetrahedral network that underlies the open glass structure referenced in Question II.2.

IV.2 — PVC polymerization: sketch and reaction energy

Given. Vinyl chloride monomer $C_2H_3Cl$ (structure $CH_2=CHCl$); bond energies $E(\text{C–C})=370$, $E(\text{C=C})=680$ kJ/mol.

Find. The polymerization reaction energy $\Delta E$.

nHHCCHClvinyl chloride, C₂H₃Cl⟶polymerize⋯CCH₂ClHCCH₂ClHCCH₂ClH⋯poly(vinyl chloride), –[CH₂–CHCl]ₙ–Each monomer breaks one C=C π-bond (680 kJ/mol) and forms two new C–C σ-bonds (2 × 370 kJ/mol)on average per repeat unit — the backbone that was C=C is now C–C, extended by one C–C link to each neighbour.ΔE = E(C=C) − 2E(C–C) = 680 − 2(370) = −60 kJ/mol (exothermic)
Addition polymerization of vinyl chloride: the monomer's C=C double bond becomes part of the C–C backbone, and a new C–C bond links each monomer to its neighbour.

Approach. Count bonds broken and formed per repeat unit in the long-chain limit, then $\Delta E = \sum E_{\text{broken}} - \sum E_{\text{formed}}$.

  1. Bonds broken. One C=C bond per monomer, $680$ kJ/mol (the H–C and C–Cl bonds are spectators — they are unchanged by addition polymerization).
  2. Bonds formed. The former C=C becomes a C–C single bond within the repeat unit, and — in the long-chain average — each monomer also contributes one new inter-monomer C–C bond (each link is shared 50/50 between the two monomers it joins). Net: two C–C single bonds formed per monomer, $2\times370 = 740$ kJ/mol.
  3. Reaction energy. $$\Delta E = E(\text{C=C}) - 2E(\text{C–C}) = 680 - 2(370) = \boxed{-60\ \text{kJ/mol (exothermic)}}$$

The negative sign confirms addition polymerization releases energy (consistent with why it proceeds spontaneously once initiated) — matching the typical −60 to −100 kJ/mol range reported for vinyl monomers.

IV.3 — Theoretical density of HCP cobalt

Given. HCP Co, $c/a = 1.623$, $r = 0.1253$ nm, $A_{\text{Co}} = 58.93$ g/mol, $N_A = 6.023\times10^{23}$ /mol.

Find. Theoretical density $\rho$.

Approach. Build $a$ and $c$ from $r$ and the given $c/a$, compute the hexagonal-prism cell volume ($n=6$ atoms/cell), then apply $\rho = nA_{\text{Co}}/(V_cN_A)$ (appendix).

  1. Lattice parameters. HCP atoms touch along $a$, so $a=2r$: $$\begin{aligned} a &= 2(0.1253) = 0.2506\ \text{nm} \\ c &= 1.623a = 1.623(0.2506) = 0.4067\ \text{nm} \end{aligned}$$
  2. Cell volume. The full hexagonal-prism unit cell (base area of a regular hexagon of side $a$, height $c$) holds $n=6$ atoms: $$V_c = \frac{3\sqrt3}{2}a^2c = \frac{3\sqrt3}{2}(0.2506)^2(0.4067) = 0.0664\ \text{nm}^3 = 6.64\times10^{-23}\ \text{cm}^3$$
  3. Density. $$\rho = \frac{nA_{\text{Co}}}{V_cN_A} = \frac{6(58.93)}{(6.64\times10^{-23})(6.023\times10^{23})} = \frac{353.6}{40.0} = \boxed{8.85\ \text{g/cm}^3}$$

This is within 1% of cobalt's accepted density (≈8.9 g/cm3), confirming the hard-sphere HCP model and the given $c/a$ ratio.

Question IV — final results
QuantityValue
PVC polymerization energy, $\Delta E$−60 kJ/mol (exothermic)
Co lattice parameters$a=0.2506$ nm, $c=0.4067$ nm
Theoretical density of Co, $\rho$8.85 g/cm3