A student wishes to estimate the concentration of conduction electrons in two metals

CHEMISTRY · Multi-part · AP · Chemistry · Compound Structure and Properties · Compound Structure and Properties

Problem

A student wishes to estimate the concentration of conduction electrons in two metals, sodium and aluminum. Relevant data are provided. Numerical/Tabular Representation • Density: Na=0.97 g⋅cm−3Na = 0.97\,\text{g}\cdot\text{cm}^{-3}, Al=2.70 g⋅cm−3Al = 2.70\,\text{g}\cdot\text{cm}^{-3} • Molar mass: Na=22.99 g⋅mol−1Na = 22.99\,\text{g}\cdot\text{mol}^{-1}, Al=26.98 g⋅mol−1Al = 26.98\,\text{g}\cdot\text{mol}^{-1} • Avogadro’s constant: NA=6.022×1023 mol−1N_{A} = 6.022 \times 10^{23}\,\text{mol}^{-1} Assume that all valence electrons in each metal behave as delocalized conduction electrons. (a) Calculate the number of metal atoms per cubic centimeter for sodium and for aluminum. (b) Using your results from part (a) and the stated valence electron counts (1 for Na, 3 for Al), determine the concentration of conduction electrons (electrons cm−3\text{cm}^{-3}) for each metal. (c) If the mean free path of an electron were identical in both metals, predict which metal would exhibit the higher electrical conductivity. Justify your answer with reference to your calculated electron concentrations and the metallic bonding model.

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