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In a certain industrial process involving a heterogeneous catalyst, the volume of the catalyst (in the shape of a sphere) is $10.0 \mathrm{cm}^{3}$. Calculate the surface area of the catalyst. If the sphere is broken down into eight spheres, each having a volume of $1.25 \mathrm{cm}^{3},$ what is the total surface area of the spheres? Which of the two geometric configurations of the catalyst is more effective? (The surface area of a sphere is $4 \pi r^{2}$, where $r$ is the radius of the sphere.) Based on your analysis here, explain why it is sometimes dangerous to work in grain elevators.

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Surface area of $10.0 \mathrm{cm}^{3}$ sphere is $22.4 \mathrm{cm}^{2}$ Total surface of eight $1.25 \mathrm{cm}^{3}$ spheres is $44.9 \mathrm{cm}^{2}$

Chemistry 102

Chapter 6

Chemical Kinetics

Kinetics

Rice University

University of Kentucky

University of Toronto

Lectures

22:42

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Hello. So today we're going to be looking at two different versions of catalysts, So ah, one catalyst with the volume of 10 centimeters and eight catalysts with a volume of 1.25 cubic centimeters. So you're the equations for volume and surface area, and hopefully you can see that if we know the volume, weaken caught, calculate the radius and use that to calculate the surface area. So let's get started. If we have ah, catalyst, that is in cubic centimeters. We can calculate for the radius, so radius cute is equal to two point 39 Take the Cuba crude of that and we will see that are radius is 1.3 four centimeters. So now let's take a look at our surface area. Soar Surface area is four pi times the radius squared. We've established that the radius is 1.34 centimeters. So now three multiplayer and we see that our surface area is 22 0.4 centimeter squared. So that's the surface area of this catalyst. Now let's take look at these eight smaller catalysts. Let's find the radius of each of the smaller catalysts. Leave 1.25 sequel to four thirds Pie are cute. We see her are cute is equal to 0.2 98 takes a Cuba croup. We see a radius 0.6 68 So let's find the Sofia surface area of one catalyst. So the surface area for hi r squared are are we've established a radius a 0.6 68 So now we square that times by four pi and we see the surface area of one is five 0.61 centimeters cubed, but there are eight of them, so the surface area of eight would be that multiplied by eight. So we see her surface area is 44 0.9 centimetres cute. So we see that the surface area of eight smaller catalysts is a lot greater than surface area of one big catalyst. So the more fine the catalysts. So basically the more surface area has the smaller the pieces, the greater it the better job it does, acting as a catalyst. That's why that's why I, like, say, if you dust would be more effective than pebbles. So let's think about ah, grain elevator. So in a great elevator, there's lots of fine dust. So that means that dust has a very large surface area and it would be and it's a great catalyst. It's very reactive, so that can sometimes lead to explosions in green elevators, which is why it's dangerous to work there.

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