Question 31 (2 points) Nanoparticles are defined by the United States (US) Nanotechnology Initiative as particles that are approximately what size? A) 0.1-1 nm B) 1-100 nm C) 100 nm and larger
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Nanotechnology has become an important field, with applications ranging from high-density data storage to the design of "nano machines." One common building block of nanostructured architectures is manganese oxide nanoparticles. The particles can be formed from manganese oxalate nanorods, the formation of which can be described as follows: $$\begin{aligned} &\mathrm{Mn}^{2+}(a q)+\mathrm{C}_{2} \mathrm{O}_{4}^{2-}(a q) \rightleftharpoons \mathrm{MnC}_{2} \mathrm{O}_{4}(a q)\\ &K_{1}=7.9 \times 10^{3} \end{aligned}$$ $$\begin{aligned} &\mathrm{MnC}_{2} \mathrm{O}_{4}(a q)+\mathrm{C}_{2} \mathrm{O}_{4}^{2-}(a q) \rightleftharpoons \mathrm{Mn}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{2}^{2-}(a q)\\ &K_{2}=7.9 \times 10^{1} \end{aligned}$$ Calculate the value for the overall formation constant for $\mathrm{Mn}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{2}^{2-}$ $$ K=\frac{\left[\mathrm{Mn}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{2}^{2-}\right]}{\left[\mathrm{Mn}^{2+}\right]\left[\mathrm{C}_{2} \mathrm{O}_{4}^{2-}\right]^{2}} $$
Platinum nanoparticles of diameter $\sim 2 \mathrm{nm}$ are important catalysts in carbon monoxide oxidation to carbondioxide. 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 $(4 / 3) \pi r^{3} .$ Recall that $1 \hat{\mathrm{A}}=1 \times 10^{-10} \mathrm{m}$ and $1 \mathrm{nm}=1 \times 10^{-9} \mathrm{m} .$ (b) Estimate how many platinum atoms are on the surface of a $2.0-\mathrm{nm}$ Pt sphere, using the surface area of a sphere $\left(4 \pi r^{2}\right)$ 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?
Platinum nanoparticles of diameter $\sim 2 \mathrm{nm}$ are important catalysts in carbon monoxide oxidation to carbon dioxide. Platinum crystallizes in a face-centered cubic arrangement with an edge length of $3.924 \AA$. (a) Estimate how many platinum atoms would fit into a $2.0-\mathrm{nm}$ sphere; the volume of a sphere is $(4 / 3) \pi r^{3}$. Recall that $1 \AA=1 \times 10^{-10} \mathrm{~m}$ and $1 \mathrm{nm}=1 \times 10^{-9} \mathrm{~m} .$ (b) Estimate how many platinum atoms are on the surface of a $2.0-\mathrm{nm} \mathrm{Pt}$ sphere, using the surface area of a sphere $\left(4 \pi r^{2}\right)$ and assuming that the "footprint" of one $\mathrm{Pt}$ atom can be estimated from its atomic diameter of $2.8 \AA$. (c) Using your results from (a) and (b), calculate the percentage of $\mathrm{Pt}$ atoms that are on the surface of a $2.0-\mathrm{nm}$ 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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