Atomic Structure and Mass - Observations in Science

Observations in Science

2.2 Atomic Structure and Mass

The comparison of polyethylene, poly(vinyl chloride), and poly(vinylidene chloride) demonstrates that the identity of the atoms in a molecule can have a tremendous im- pact on that molecule’s properties. Let’s begin our exploration by examining the structure of atoms, so that we can address the question of how a chlorine atom differs from a hydrogen atom. To do that, we’ll need to zoom in one more level, to the realm of subatomic particles.

Fundamental Concepts of the Atom

Our current model of the structure of atoms has been accepted for nearly a century, but it took great creativity and many ingenious experiments to develop. The atom is composed of a small, compact core called the nucleus surrounded by a disperse cloud of electrons. The nucleus is composed of two types of particles: protons and neu- trons. There is so much space between the electrons and the nucleus that it is impos- sible to show it to scale in an illustration. Consider Figure 2.3(a), which is similar to pictures you’ve seen before in high school chemistry or physical science books. The fi gure shows the relative positions of the protons, neutrons, and electrons. But if the protons and neutrons were actually the size shown, then the electrons would be hun- dreds of meters away. Another misunderstanding promoted by this type of illustration is the picture of electrons following regular orbits around the nucleus. A better model of atomic structure views the electrons as clouds of negative charge that surround the nucleus, as opposed to particles that orbit around it in an orderly way (Figure 2.3(b)).

We will examine the structure of atoms in much greater detail in Chapter 6.

Orbit

Electron

Nucleus

(a) (b)

Figure 2.3 ❚ Atoms have often been depicted as resembling a solar system: the nucleus is at the center, and the electrons orbit around it, as seen here in (a). Although such pictures do help to emphasize the way that protons, neutrons, and electrons are distributed in the atom, they cannot illustrate accurately the currently accepted model of atomic structure. Instead, we depict the electrons as clouds of negative charge surrounding the nucleus, as shown in (b). In such pictures, the density of the small dots is related to the probability of fi nding an electron at a particular location.

Now we turn our attention to the numbers of protons, neutrons, and electrons in the atom. Electric charge provides an important constraint on these numbers. Protons are positively charged, electrons are negatively charged, and neutrons are neutral. At- oms themselves are also electrically neutral, so the numbers of protons and electrons present must be such that their charges will cancel each other. You may know from physics that the SI unit of charge is the coulomb (C). Experiments have shown that the electrical charges on a proton and an electron are equal and opposite. Every electron carries a charge of −1.602 × 10⁻¹⁹ C, whereas every proton carries a charge of +1.602 × 10⁻¹⁹ C. So for an atom to remain neutral, the numbers of electrons and protons must be equal. Because neutrons have no charge, the number of neutrons present is not restricted by the requirement for electrical neutrality. For most elements, the number of neutrons can vary from one atom to another, as we’ll see.

Atomic Number and Mass Number

The number of protons in a particular atom, referred to as the atomic number, identi- fi es the element. Carbon atoms make up the backbone of nearly all polymers, so we will consider them fi rst. The atomic number of carbon is six, which tells us that a neutral carbon atom has six protons. Electrical neutrality requires that a carbon atom also must have six electrons. The great majority of carbon atoms—roughly 99%—also contain six neutrons. But some carbon atoms contain seven or even eight neutrons. Atoms of the same element that have different numbers of neutrons are called isotopes. Protons and electrons govern nearly all of the important chemical properties of atoms, so generally isotopes cannot be separated chemically. But the existence and even the relative abundance of isotopes can be proven by careful examinations of the mass of atoms.

Protons and neutrons have similar masses; each is nearly 2000 times more mas- sive than the electron. So the mass of any atom is concentrated in its nucleus. Indi- vidual atoms are so small and light that reporting their masses in conventional units such as kilograms or grams is not convenient. Instead we use a unit that is appropriate to the atomic scale: the atomic mass unit or amu.

1 amu = 1.6605 × 10⁻²⁴ g

Both the neutron and the proton have masses very close to one amu. The mass of a neutron is 1.009 amu, and that of a proton is 1.007 amu. The mass of an electron, in contrast, is just 0.00055 amu. So for many practical purposes, we can determine the mass of an atom simply by counting the number of protons and neutrons. That number will be the mass in amu, to a fairly reasonable approximation. Because of this, the combined total of protons and neutrons is called the mass number of the atom.

Because isotopes are atoms of the same element with different numbers of neutrons, they will have the same atomic number but different mass numbers.

Isotopes

How do we know that these isotopes exist? Modern instruments called mass spec- trometers provide direct experimental evidence. The fi rst important function of a mass spectrometer is to take a stream of microscopic particles—atoms or molecules—and

“sort them” according to mass. (Figure 2.4 explains how the instrument does this.) Once the particles have been separated by mass, the second key function of the mass spectrometer is to measure accurately the number of particles with a given mass. The data are usually presented as a “mass spectrum.” Any time we refer to a spectrum, we will be noting a measurement that is made over a range of values of some variable. In this case that variable is mass, so the mass spectrum is really just a plot showing the number of particles detected as a function of mass. When a peak is seen at a particular mass, it means that the sample analyzed has some component with that mass.

Figure 2.5 shows such a mass spectrum for a sample of carbon. Looking at the graph, we immediately see a large peak centered at mass 12. That represents the isotope Protons and neutrons are themselves

made up of even smaller particles, known as quarks.

Protons and neutrons are themselves made up of even smaller particles, known as quarks.

We generally depict the charges in units of the electron charge, so that the charge of an electron is written as 1− and that of a proton is written as 1+.

The atomic mass unit is also referred to as a dalton and is sometimes abbreviated as u.

called carbon-12, whose nucleus contains six protons and six neutrons. This isotope is actually used to defi ne the amu: an atom of carbon-12 has a mass of exactly 12 amu. But if we look at the mass spectrum closely, we also see a much smaller peak centered near mass 13. This tells us that there is a small amount of a second isotope, carbon-13, with seven neutrons. Comparing the relative sizes of the two peaks, we could determine that the carbon-12 isotope accounts for roughly 99% of the carbon atoms. More accurate measurement gives a value of 98.93%, with just 1.07% of carbon-13. It is also possible to determine that the exact mass of the carbon-13 isotope is 13.0036 amu. Because any sample we measure will always contain vast numbers of atoms, these same percentages, or isotopic abundances, will be found in any naturally occurring sample of carbon.

Atomic Symbols

All the information about the structure of the atom, which we have just discussed, can be written in scientifi c shorthand, using atomic symbols. The general atomic symbol can be written as

Z E

A number of radioactive isotopes of carbon are also known. The most common of these is ¹⁴C. Its abundance is measured in the carbon dating of archaeological objects.

Figure 2.4 ❚ The schematic diagram shown here illustrates the key principles in the functioning of a mass spectrometer. A stream of gas to be analyzed enters at the left, and an electron gun causes some of the atoms to lose an electron, forming charged particles called ions. These ions are then accelerated to the right by an electric fi eld, so that a beam of ions passes into a magnetic fi eld. The magnetic fi eld defl ects the ions, and the extent of that defl ection depends on the charge to mass ratio of each ion. For a given charge, lighter particles are defl ected more severely than heavier ones. So if the sample contained both ⁴He⁺ and ¹²C⁺ ions, as shown here, the helium ions would be defl ected much more than the carbon ions. This allows a slit to select ions of a particular charge to mass ratio, which then strike a detector. The current at this detector produces a signal that is proportional to the number of ions found with the desired charge to mass ratio, and this in turn is related to the amount of the parent gas molecule that entered the spectrometer.

Detector

Beam of ⁴He⁺ ions

Beam of ¹²C⁺ ions Accelerating

plates

Gas inlet Electron gun

Magnet

Slit Collector

–

12 13 14 15

10 11

Mass (amu)

Signal

Figure 2.5 ❚ A sketch of the mass spectrum of elemental carbon is shown. The large peak is due to ¹²C, and the smaller peak to the right is

13C. The size of the ¹³C peak here is somewhat exaggerated; it would actually be just 1/99 the size of the

12C peak.

Here E represents the atomic symbol for the element in question, the superscript A is the mass number, and the subscript Z is the atomic number. The symbol for carbon-12, for example, is ¹² ₆ C.

Many atomic symbols are fairly obviously derived from the name of the element, such as the use of C for carbon in our example. For other elements, the symbol is based on the Latin name. The symbol for iron, for example, is Fe, derived from the Latin name ferrum. An atom of iron with 26 protons and 30 neutrons is represented as ⁵⁶ ₂₆ Fe. A listing of some common elements whose symbols are not based on their English names is provided in Table 2.1. A full list of elements and their symbols can be found in Appendix A at the back of this book.

Atomic Masses

When you look at an entry in the periodic table, you see some of the information we’ve just defi ned, such as the atomic symbol and atomic number. Most periodic tables include additional information as well. Almost always, the atomic mass is given.

This number provides the average mass in amu of an atom of the element. If you look up carbon in the periodic table inside the back cover of this book, you will fi nd the box shown in Figure 2.6. The atomic mass appears under the symbol: 12.011.

But we have already said that the mass of an atom of carbon-12 is exactly 12 amu, and that of carbon-13 is 13.0036 amu. So the value of 12.011 does not seem to be the mass of any individual atom of carbon. Then how are atomic masses defi ned and determined?

The atomic mass is defi ned as the average mass of an atom of a particular element. Carbon has two stable isotopes with masses of 12.0000 and 13.0036 amu, respectively. So why is the average mass 12.011 and not something closer to 12.5?

The answer is that when we take the average mass, we must account for the relative abundance of each isotope. Suppose that we could measure the mass of a 100-atom sample. Based on the isotopic abundances, we would expect to have 99 atoms of carbon-12 and only a single atom of carbon-13. In any sample that we can actually weigh, the number of atoms will be far greater than 100. Even using the best avail- able laboratory balances, the smallest quantity of matter that can be weighed is about a nanogram, or 10⁻⁹ g. A nanogram of carbon would contain more than 10¹³ atoms.

For such large numbers of atoms, it is safe to assume that the fraction of each isotope present will be determined by the natural abundances. For carbon, the fact that we only need to consider two stable isotopes makes the calculation fairly simple. We can The term “ferrous metals” refers to

iron or alloys such as steel that contain signifi cant amounts of iron.

The term “ferrous metals” refers to iron or alloys such as steel that contain signifi cant amounts of iron.

Table

❚

^2.1

Names and symbols of some common elements whose symbols are not related to their English names

Name Symbol (name origin)

Gold Au (aurum)

Iron Fe (ferrum)

Lead Pb (plumbum)

Mercury Hg (hydrargyrum)

Silver Ag (argentum)

Sodium Na (natrium)

Atomic number

6 C 12.011

Symbol Relative atomic mass Figure 2.6 ❚ Entry for carbon from a periodic table. The atomic number (6) and the atomic mass (12.011) are shown, along with the symbol for the element (C).

Some tables may display additional information, and the exact layout may vary from one table to another.

But once you are familiar with the table itself, usually it is easy to interpret whatever data are shown.

multiply the mass by the fractional abundance to weight each isotope’s contribution to the atomic mass.

Carbon-12: 12.0000 × 0.9893 = 11.87 Carbon-13: 13.0036 × 0.0107 = 0.139

Weighted average mass = 11.87 + 0.139 = 12.01

The value of 12.011 found in the periodic table is obtained using additional signifi - cant fi gures on the isotopic abundance numbers.

E X A M P L E P RO B L E M 2 .1

The chlorine present in PVC has two stable isotopes. ³⁵Cl with a mass of 34.97 amu makes up 75.77% of the natural chlorine found. The other isotope is ³⁷Cl, whose mass is 36.95 amu. What is the atomic mass of chlorine?

Strategy To determine the atomic mass, we must calculate the average mass weighted by the fractional abundance of each chlorine isotope. Because there are only two stable isotopes, their abundances must add up to 100%. So we can calculate the abundance of ³⁷Cl from the given abundance of ³⁵Cl.

Solution First, we calculate the abundance of the chlorine-37 isotope:

Abundance of ³⁷Cl = 100% − 75.77% = 24.23%

Now we can calculate the contribution of each isotope to the atomic mass.

35Cl: 34.97 × 0.7577 = 26.50

37Cl: 36.95 × 0.2423 = 8.953

Weighted average mass = 26.50 + 8.953 = 35.45 So the atomic mass of chlorine is 35.45 amu.

Analyze Your Answer Based on the relative percentages, we should be able to decide if this answer makes sense. The individual isotopes have masses of roughly 35 and 37, so a 50/50 ratio would lead to an average mass of about 36. But the actual abundance of the ³⁵Cl isotope is greater than that of ³⁷Cl, so the average mass should be closer to 35. Thus our answer of 35.45 seems reasonable. And of course we can check the answer by consulting a periodic table.

Discussion Some elements have several stable isotopes, but we can always do the same type of calculation by accounting for the mass and fractional abundance of each isotope.

Check Your Understanding There are three naturally occurring isotopes of the element silicon, which is widely used in producing computer chips. Given the masses and abundances below, calculate the atomic mass of silicon.

Isotope Abundance Mass

28Si 92.2% 27.977 amu

29Si 4.67% 28.977 amu

30Si 3.10% 29.974 amu

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