Platinum nanoparticles of diameter -2 nm are important catalysts in carbon monoxide oxidation to carbon dioxide. Platinum crystallizes in a face-centered cubic arrangement with an edge length of 3.924 A. (a) Estimate how many platinum atoms would fit into a 2.0-nm sphere: the volume of a sphere is (4/3)tt/3. Recall that 1 Ae = 1 x 10-10 m and 1 nm = 1 x 10-9 m. (b) Estimate how many platinum atoms are on the surface of a 2.0-nm Pt sphere, using the surface area of a sphere (4nr2) and assuming that the "footprint* of one Pt atom can be estimated from its atomic diameter of 2.8 A. (c) Using your results from (a) and (b), calculate the percentage of Pt atoms that are on the surface of a 2.0-nm nanoparticle, (d) Repeat these calculations for a 5.0-nm platinum nanoparticle, (e) Which size of nanoparticle would you expect to be more catalytically active and why?

VSEPR Valence Shell Electron Pair Repulsion Theory (VSEPR) is a qualitative theory that allows us to predict the geometry of molecules based upon their Lewis structures. This model looks at the repulsion of different electron regions (either bonding or non-bonding) and chooses a geometry that minimizes their repulsions. Valence Bond Theory The valence bond model is a quantum mechanical model for understanding bonding in molecules. However, now it is mostly used by chemists as a means to describe the bonding with organic systems qualitatively. The idea is that bonds form between atoms as a result of the overlap of atomic orbitals. This leads to what we would call a localized bonding picture. You can point to a bond in a molecule and say what types of atomic orbitals lead to that parti