Chapter 23.4, Problem 23.4.2PE

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 3.924Å. (a) Estimate how many platinum atoms would fit into a 2.0-nm sphere; the volume of a sphere is (4/3). Recall that 1Å= 1×10-10 m and 1nm = 1×10-9 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 (4 $\pi r^2$ and assuming that the “footprint” of one Pt atom can be estimated from its atomic diameter if 2.8 Å. (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?