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O
ne very important chemical activity is the synthesis of new substances. Nylon, the artificial sweetener aspartame, Kevlar used in
bulletproof vests and the body parts of exotic cars, polyvinyl chloride (PVC) for plastic water pipes, Teflon, Nitinol (the alloy that remembers
its shape even after being severely distorted), and so many other materials
that make our lives easier—all originated in some chemist’s laboratory. Some
of the new materials have truly amazing properties such as the plastic that
listens and talks, described in the “Chemical Impact” on page 155. When
a chemist makes a new substance, the first order of business is to identify it. What is its composition? What is its chemical formula?
In this chapter we will learn to determine a compound’s formula. Before we can do that, however, we need to think about counting atoms.
How do we determine the number of each type of atom in a substance so
that we can write its formula? Of course, atoms are too small to count individually. As we will see in this chapter, we typically count atoms by weigh- This Italian car has composite
ing them. So let us first consider the general principle of counting by weighing. body parts.
Counting by Weighing
Objective: To understand the concept of average mass and explore how
counting can be done by weighing.
S
uppose you work in a candy store that sells gourmet jelly beans by the
bean. People come in and ask for 50 beans, 100 beans, 1000 beans, and
so on, and you have to count them out—a tedious process at best. As a good
problem solver, you try to come up with a better system. It occurs to you
that it might be far more efficient to buy a scale and count the jelly beans
by weighing them. How can you count jelly beans by weighing them? What
information about the individual beans do you need to know?
Assume that all of the jelly beans are identical and that each has a mass
of 5 g. If a customer asks for 1000 jelly beans, what mass of jelly beans would
be required? Each bean has a mass of 5 g, so you would need 1000 beans 5 g/bean, or 5000 g (5 kg). It takes just a few seconds to weigh
out 5 kg of jelly beans. It would take much longer to
count out 1000 of them.
In reality, jelly beans are not identical. For
example, let’s assume that you weigh 10 beans
individually and get the following results:
Bean
Mass
1
2
3
4
5
6
7
8
9
10
5.1
5.2
5.0
4.8
4.9
5.0
5.0
5.1
4.9
5.0
g
g
g
g
g
g
g
g
g
g
Jellybeans can be
counted by weighing.
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MATH
To find an average, add up all
the individual measurements
and divide by the number of
measurements.
Can we count these nonidentical beans by weighing? Yes. The key piece of
information we need is the average mass of the jelly beans. Let’s compute the
average mass for our 10-bean sample.
total mass of beans
Average mass number of beans
5.1 g 5.2 g 5.0 g 4.8 g 4.9 g 5.0 g 5.0 g 5.1 g 4.9 g 5.0 g
10
50.0
5.0 g
10
The average mass of a jelly bean is 5.0 g. Thus, to count out 1000 beans, we
need to weigh out 5000 g of beans. This sample of beans, in which the beans
have an average mass of 5.0 g, can be treated exactly like a sample where all
of the beans are identical. Objects do not need to have identical masses to
be counted by weighing. We simply need to know the average mass of the
objects. For purposes of counting, the objects behave as though they were all
identical, as though they each actually had the average mass.
Suppose a customer comes into the store and says, “I want to buy a bag
of candy for each of my kids. One of them likes jelly beans and the other
one likes mints. Please put a scoopful of jelly beans in a bag and a scoopful
of mints in another bag.” Then the customer recognizes a problem. “Wait!
My kids will fight unless I bring home exactly the same number of candies
for each one. Both bags must have the same number of pieces because they’ll
definitely count them and compare. But I’m really in a hurry, so we don’t
have time to count them here. Is there a simple way you can be sure the bags
will contain the same number of candies?”
You need to solve this problem quickly. Suppose you know the average
masses of the two kinds of candy:
Jelly beans: average mass 5 g
Mints: average mass 15 g
You fill the scoop with jelly beans and dump them onto the scale, which
reads 500 g. Now the key question: What mass of mints do you need to give
the same number of mints as there are jelly beans in 500 g of jelly beans?
Comparing the average masses of the jelly beans (5 g) and mints (15 g), you
realize that each mint has three times the mass of each jelly bean:
15 g
3
5g
This means that you must weigh out an amount of mints that is three times
the mass of the jelly beans:
3 500 g 1500 g
You weigh out 1500 g of mints and put them in a bag. The customer leaves
with your assurance that both the bag containing 500 g of jelly beans and
the bag containing 1500 g of mints contain the same number of candies.
In solving this problem, you have discovered a principle that is very important in chemistry: two samples containing different types of components,
A and B, both contain the same number of components if the ratio of the sample
masses is the same as the ratio of the masses of the individual components of A
and B.
154
Chapter 6 Chemical Composition
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Let’s illustrate this rather intimidating statement by using the example
we just discussed. The individual components have the masses 5 g (jelly beans)
and 15 g (mints). Consider several cases.
●
Each sample contains 1 component:
Mass of mint 15 g
Mass of jelly bean 5 g
●
Each sample contains 10 components:
15 g
10 mints 150 g of mints
mints
5g
10 jelly beans 50 g of jelly beans
jelly beans
●
Each sample contains 100 components:
15 g
100 mints 1500 g of mints
mints
5g
100 jelly beans 500 g of jelly beans
jelly beans
Science, Technology, and Society
Plastic That Talks and Listens
I
magine a plastic so “smart” that it can be used to
sense a baby’s breath, measure the force of a
karate punch, sense the presence of a person 100 ft
away, or make a balloon that sings. There is a plastic film capable of doing all these things. It’s called
polyvinylidene difluoride (PVDF), which has the structure
F
F
C
F
C
H
F
C
H
C
H
H
When this polymer is processed in a particular way,
it becomes piezoelectric and pyroelectric. A piezoelectric substance produces an electric current when
it is physically deformed or, alternatively, undergoes
a deformation when a current is applied. A pyroelectric material is one that develops an electrical potential in response to a change in its temperature.
Because PVDF is piezoelectric, it can be used to
construct a paper-thin microphone; it responds to
sound by producing a current proportional to the
deformation caused by the sound waves. A ribbon
of PVDF plastic one-quarter of an inch wide could
be strung along a hallway and used to listen to all
the conversations going on as people walk through.
On the other hand, electric pulses can be applied
to the PVDF film to produce a speaker. A strip of
PVDF film glued to the inside of a balloon can play
any song stored on a microchip attached to the
film—hence a balloon that can sing “happy birthday” at a party. The PVDF film also can be used to
construct a sleep apnea monitor, which, when
placed beside the mouth of a sleeping infant, will
set off an alarm if the breathing stops, thus helping
to prevent sudden infant death syndrome (SIDS).
The same type of film is used by the U.S. Olympic
karate team to measure the force of kicks and
punches as the team trains. Also, gluing two strips
of film together gives a material that curls in response to a current, creating an artificial muscle. In
addition, because the PVDF film is pyroelectric, it
responds to the infrared (heat) radiation emitted by
a human as far away as 100 ft, making it useful for
burglar alarm systems. Making the PVDF polymer
piezoelectric and pyroelectric requires some very
special processing, which makes it costly ($10 per
square foot), but this seems a small price to pay for
its near-magical properties.
6.1 Counting by Weighing
155