Platinum nanoparticles of diameter ∼2 nm are importantcatalysts in carbon monoxide oxidation to carbondioxide. Platinum crystallizes in a face-centered cubicarrangement with an edge length of 3.924 Å. (a) Estimatehow many platinum atoms would fit into a 2.0-nmsphere; the volume of a sphere is (4/3)π r3. Recall that1 A° = 1 x 10-10 m and 1 nm = 1 x 10-9 m. (b) Estimatehow many platinum atoms are on the surface of a 2.0-nmPt sphere, using the surface area of a sphere (4π r2) andassuming that the “footprint” of one Pt atom can be estimatedfrom its atomic diameter of 2.8 A° . (c) Using yourresults from (a) and (b), calculate the percentage of Pt atomsthat 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 tobe more catalytically active and why?
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. (a) Estimate
how many platinum atoms would fit into a 2.0-nm
sphere; the volume of a sphere is (4/3)π r3. Recall that
1 A° = 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 (4π r2) 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?
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