Understanding the Nanoscale
Description:
Surface area-to-volume activity that shows how surface area and volumes even in small
amounts can add up to a lot. This lesson can be extrapolated to catalytic processes, and financial
problems in industry. This lesson utilizes a spherical model for the particles.
Level: High school geometry and up.
Discipline: Mathematics, Chemistry
Background Information:
What is a catalyst? Catalysts have the ability to change the rate of a reaction due to lowering for
the rate-limiting free energy of activation than the corresponding energy of activation. Unlike the
reagents in the reactions, which are consumed by the process, a catalyst is never consumed by the
reaction.
Concepts:
Technology, Nano particles, Metric system, Unit Conversion, Chemistry, Algebra, and
Geometry concepts
Vocabulary:
1 Nanometer = 1x10-9 meter
Nanoparticle: a particle between 1-100nm
Catalyst
Circumference
Surface area
Volume
Lesson:
In chemistry some reactions require a large amount of initial energy in order to react. For
companies trying to produce the desired product from these reactions the large amount of initial energy
costs a lot of money. In order to reduce their costs to produce cheaper products catalysts are used to
lower the initial energy need to run the reaction.
This is where nano-sized catalysts com e into play. In a chemical reaction, the only places the
reaction can take place is on the surface of the reactants/catalysts. Since the reaction takes time and
time is money to a company increasing the total amount of surface area
Part A:
Take the string your given and measure the circumference of each sphere your given. Now
convert the circumference of the sphere to the volume of the sphere. Now use the circumference to
calculate the surface area of the sphere.
Note: You can always ask students if they know these formulas, or even have them derive them on their
own.
Circumference
C=2*π*r
Volume
V= 4/3 * π * r3
Surface Area
SA = 4 * π * r2
Part B:
Now have the students count the number of spheres in each container. They can now take the
number of spheres in container and multiply it by the surface area of each sphere.
The volume of the container needs to be measured too; I prefer to have the students use water
and graduated cylinders. You can use a ruler, and since your using the same type of container you only
need measure it once.
Now take the total surface area and divide it by the volume of the container.
Now compare the surface area to volume ratio of each sphere.
Marble:
___________________
Ping Pong Ball: ___________________
Tennis Ball:
___________________
Take Home Concept:
Relate the surface area to volume ratio of something on the micron level to the level of nanoscale.
Follow-up Lab:
Hydrogen peroxide w/ MnO2
-changing the size of catalyst changes the rate of gas production.
Materials Needed:
Marbles
Tennis balls
Ping Pong balls
Plastic container
Ruler
String
Pencil
Paper
Extra: graduated cylinder and water