Introductory Chemistry: A Foundation - Zumdahl S.S., DeCoste D.J. 2019

Chemical Composition
Counting by Weighing

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These glass bottles contain silicon dioxide.

One very important chemical activity is the synthesis of new substances. Nylon, the artificial sweetener aspartame (NutraSweet®), 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 “Chemistry in Focus” segment Plastic That Talks and Listens! 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 weighing them. So let us first consider the general principle of counting by weighing.

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The Enzo Ferrari has a body made of carbon-fiber composite materials.

Counting by Weighing

Objective

· To understand the concept of average mass and explore how counting can be done by weighing.

Suppose you work in a candy store that sells gourmet jelly beans by the bean. People come in and ask for beans, beans, 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 g. If a customer asks for jelly beans, what mass of jelly beans would be required? Each bean has a mass of g, so you would need , or g ( kg). It takes just a few seconds to weigh out kg of jelly beans. It would take much longer to count out of them.

In reality, jelly beans are not identical. For example, let’s assume that you weigh beans individually and get the following results:

Chemistry in Focus Plastic That Talks and Listens!

Imagine 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 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

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 ft, making it useful for burglar alarm systems. Making the PVDF polymer piezoelectric and pyroelectric requires some very special processing, which makes it costly ( per square foot), but this seems a small price to pay for its near-magical properties.

See Problem 8.2

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 -bean sample.

The average mass of a jelly bean is g. Thus, to count out beans, we need to weigh out g of beans. This sample of beans, in which the beans have an average mass of 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:

You fill the scoop with jelly beans and dump them onto the scale, which reads 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 g of jelly beans? Comparing the average masses of the jelly beans ( g) and mints ( g), you realize that each mint has three times the mass of each jelly bean:

This means that you must weigh out an amount of mints that is three times the mass of the jelly beans:

You weigh out g of mints and put them in a bag. The customer leaves with your assurance that both the bag containing g of jelly beans and the bag containing 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.

Let’s illustrate this rather intimidating statement by using the example we just discussed. The individual components have the masses g (jelly beans) and g (mints). Consider several cases.

· Each sample contains component:

· Each sample contains components:

· Each sample contains components:

Note in each case that the ratio of the masses is always to :

This is the ratio of the masses of the individual components:

Any two samples, one of mints and one of jelly beans, that have a mass ratio of will contain the same number of components. And these same ideas apply also to atoms, as we will see in the next section.