Platinum nanoparticles of diameter 2 nm are important
catalysts i...

Question

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. (b) Estimate
how many platinum atoms are on the surface of a 2.0-nm
Pt sphere, using the surface area of a sphere 14pr22 and
assuming that the 'footprint' of one Pt atom can be estimated
from its atomic diameter of 2.8 A .

Accepted Answer

Hello everyone. So in this video we're trying to calculate for the number of gold atoms on the surface of a 5. nanometer gold sphere. And we're given the equation to solve for the surface area of a sphere right over here as well as the were given the diameter of a gold item right over here. All right. First things first, we're gonna go ahead and actually calculate the cross section area of a gold atom. So let's go ahead and just label this ask ross suck of gold atom. Alright, so the equation for this is that the area is equal to pi R squared And Pi is approximately 3.14. The radius is going to be 2.92 because that's the diameter and because we have diameter of course we need to go ahead and divide this by two. Actually does not forget our units Ekstrom divided by two. Alright, plugging that into my calculator. My numerical value will be six. Yes, of course. The radius squared again. Listen to my calculator. My numerical value is 6.69 and units be angstrom squared. Now we can go ahead and calculate for the surface area of the sphere. And the equation for that is given to us right over here. So we have that the area is equal to four pi R squared. So four times 4 pi is approximately 3. radius in this case is going to be 5. nanometers right over here. And then we're gonna go ahead and divide that by two. And we want our units to to stay consistent. So I'm gonna go ahead and convert my nanometers into angstrom. So that's going to be her 190 m. Of course, all of this is going to be squared. So, plugging that into my calculator, my new american value comes up to B 7850. And then my units will be ancient squirt. So finally we're gonna go ahead and calculate for the number of gold items. So we start off with the number of regions, software for the surface area right here. So we have the 7850 action. We want this unit to be canceled. So we can go ahead and use this. So 6.69 m squared for every one gold item. So then you can see here that the angstrom squared puppy canceled. Leaving us with the unit of gold atom, which is what we want. So then this will equal to 1, gold atoms. So that's going to be your final answer for this problem is that we have 1,173 quote atoms on the surface of a 5.0 nanometer gold sphere. Thank you all so much for watching

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