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 Å.
Estimate how many platinum atoms would fit into a 2.0-nm sphere; the volume of a sphere is (4/3)πr3. Recall that 1 Å = 1 x 10–10 m and 1 nm = 1 x 10–9 m. Estimate how many platinum atoms are on the surface of a 2.0-nm Pt sphere, using the surface area of a sphere (4πr2) and assuming that the "footprint" of one Pt atom can be estimated from its atomic diameter of 2.8 Å.
Using your results, calculate the percentage of Pt atoms that are on the surface of a 2.0-nm nanoparticle.
Frequently Asked Questions
What scientific concept do you need to know in order to solve this problem?
Our tutors have indicated that to solve this problem you will need to apply the Unit Cell concept. You can view video lessons to learn Unit Cell. Or if you need more Unit Cell practice, you can also practice Unit Cell practice problems.