Chemistry

Chemistry

Problem

A laboratory technician compares wires made from pure copper and pure aluminum. Both wires have identical length and cross-sectional area. Each metal is characterized by the following data. Numerical/Tabular Representation (all values at 298 K) • Valence electrons per atom: Cu = 1, Al = 3 • Measured electrical resistivity: Cu = 1.7×10−8 Ω⋅m1.7\times10^{-8}\,\Omega\cdot\text{m}, Al = 2.8×10−8 Ω⋅m2.8\times10^{-8}\,\Omega\cdot\text{m} • First-ionization energy: Cu = 745 kJ⋅mol−1745\,\text{kJ}\cdot\text{mol}^{-1}, Al = 578 kJ⋅mol−1578\,\text{kJ}\cdot\text{mol}^{-1} Use the information above to analyze how metallic bonding accounts for the observed properties of the two metals. (a) Describe, in terms of metallic bonding, why both copper and aluminum conduct electricity at room temperature. (b) Despite aluminum providing three delocalized electrons per atom, copper has the lower resistivity. Explain this observation using atomic-level arguments involving metallic bonding and electronic structure. (c) Both metals are noted for high ductility. Explain how the nature of metallic bonding allows layers of atoms in each metal to slide without fracture, and discuss how atomic size differences between Cu and Al influence their relative ease of deformation.
Intuitive explanation

Electrical conductivity in metals depends on both the number of free electrons available to carry current and how easily they move through the lattice. Copper has fewer valence electrons per atom than aluminum, yet conducts electricity better—the key insight is that resistivity reflects not just electron count but also how strongly those electrons are bound and how frequently they collide with the lattice. Copper's higher ionization energy suggests its valence electron is held more tightly, which paradoxically correlates with better conductivity, pointing to differences in crystal structure, electron mobility, and the nature of metallic bonding between these two elements.

Intuitive explanation

Electrical conductivity in metals depends on both the number of free electrons available to carry current and how easily they move through the lattice. Copper has fewer valence electrons per atom than aluminum, yet conducts electricity better—the key insight is that resistivity reflects not just electron count but also how strongly those electrons are bound and how frequently they collide with the lattice. Copper's higher ionization energy suggests its valence electron is held more tightly, which paradoxically correlates with better conductivity, pointing to differences in crystal structure, electron mobility, and the nature of metallic bonding between these two elements.

Browse the problem library