Video Transcript
From smallest to largest surface
area, what is the correct order for the following images of a solid substance?
In chemistry, the surface area of a
substance is important to consider when we’re evaluating the rate of a chemical
reaction. Particles need to physically
collide in order for a reaction to occur. More collisions between particles
means that the reaction will happen more quickly. Depending on the surface area of
our reactants, the rate of a chemical reaction will change. Let’s consider two samples that
have the same amount of reactant, one where the reactant is in larger pieces and one
where the substance is in smaller pieces, perhaps ground into a powder.
When a substance is in smaller
pieces, more of the particles that make up that substance are exposed on the
surface, so the surface area is large. When the substance is in larger
pieces, not as many of the particles are exposed to the surface, so the surface area
is smaller in this case. Since particles need to collide for
a reaction to occur, the reaction will occur more quickly if more of the particles
are exposed to the surface, that is, when the substance has a larger surface
area.
In chemistry, we often see more
violent reactions with powders and fine solids than we do with reactants that exist
in larger pieces. With this in mind, we can identify
image (C) as the image with the smallest surface area. The solid substance in this image
is in one large piece. (D) must be the image with the
largest surface area, as the solid is cut into a large number of small pieces.
We can also show this
mathematically. Let’s calculate the surface area of
image (C) and image (B). Say that the cube has sides of 10
centimeters. The area of one face of the cube is
10 centimeters times 10 centimeters, or 100 centimeters squared. A cube has six faces, so the
surface area of the cube is equal to 600 centimeters squared. If we cut the cube in image (C) in
half, we’ll end up with the two cuboids in image (B). Each cuboid would have four faces
with sides of five centimeters and 10 centimeters. These faces would have an area of
50 centimeters squared.
The two remaining faces have sides
of 10 centimeters, so these sides have an area of 100 centimeters squared. So we can calculate the surface
area of one of the cuboids, which is 400 centimeters squared. We have two cuboids in image (B),
each with a surface area of 400 centimeters squared. So the total surface area of the
solid substances in image (B) is 800 centimeters squared.
As we can see from our calculation,
the surface area increases when we cut the cube into smaller pieces. So let’s finish the problem and
order these images from smallest to largest surface area. (C) will have the smallest surface
area, and the surface area will increase when we cut the cube into smaller pieces
from (B), then (A), then (E), and last is (D), the image with the largest surface
area.
The correct order of images from
smallest to largest surface area is (C), (B), (A), (E), and finally (D).
