Atoms: The Building Blocks of Matter - Chapter 3 PDF

CHAPTER 3 Atoms: The Building Blocks of Matter (c) ©Drs. Ali Yazdani & Daniel J. Hornbaker/Photo Researchers, Inc; (br) DOE Photo Online Chemistry...

CHAPTER 3 Atoms: The Building Blocks of Matter (c) ©Drs. Ali Yazdani & Daniel J. Hornbaker/Photo Researchers, Inc; (br) DOE Photo Online Chemistry HMDScience.com Section 1 Online Labs include: The Atom: From Conservation of Mass Philosophical Idea to Studying What You Can’t See Scientific Theory SECTION 2 Premium Content The Structure of the Atom SECTION 3 Why It Matters Video Counting Atoms HMDScience.com Atoms  Section 1 The Atom: From Main Ideas Three basic laws describe how Philosophical Idea matter behaves in chemical reactions. Compounds contain atoms in to Scientific Theory whole-number ratios. Atoms can be subdivided into smaller particles. Key Terms law of conservation of mass law of definite proportions law of multiple proportions > Virginia standards CH.2.i The student will investigate and When you crush a lump of sugar, you can see that it is made up of many smaller understand that the placement of elements on particles of sugar. You may grind these particles into a very fine powder, but each the periodic table is a function of their atomic tiny piece is still sugar. Now suppose you dissolve the sugar in water. The tiny structure. The periodic table is a tool used for the investigations of: historical and quantum particles seem to disappear completely. Even if you look at the sugar-water solution models. through a powerful microscope, you cannot see any sugar particles. Yet if you were CH.1.EKS-16; CH.1.EKS-26; CH.2.EKS-16 to taste the solution, you’d know that the sugar is still there. Observations like these led early philosophers to ponder the fundamental nature of matter. Is it continuous and infinitely divisible, or is it divisible only until a basic, invisible particle that cannot be divided further is reached? The particle theory of matter was supported as early as 400 bce by certain Greek thinkers, such as Democritus. He called nature’s basic particle an atom, based on the Greek word meaning “indivisible.” Aristotle was part of the generation that succeeded Democritus. His ideas had a lasting impact on Western civilization, and he did not believe in atoms. He thought that all matter was continuous, and his opinion was accepted for nearly 2000 years. Neither the view of Aristotle nor that of Democritus was supported by experimental evidence, so each remained under speculation until the eighteenth century. Then scientists began to gather evidence favoring the atomic theory of m ­ atter. Main Idea Three basic laws describe how matter behaves in chemical reactions. Virtually all chemists in the late 1700s accepted the modern definition of an element as a substance that cannot be further broken down by ordinary chemical means. They also assumed that these elements combined to form compounds that have different physical and chemical properties than those of the elements that make them. What troubled them, however, was the understanding of just exactly how the different substances could combine with one another to form new ones, what we know as chemical reactions. Most historians date the foundation of modern chemistry to this time when scientists finally began to ascribe rules to how matter interacts. Atoms: The Building Blocks of Matter 63 Figure 1.1 In the 1790s, the study of matter was revolutionized by a new empha- sis on the quantitative analysis of chemical reactions. Aided by improved Table Salt Crystals Each of balances, investigators began to accurately measure the masses of the the salt crystals shown here contains elements and compounds they were studying. This led to the discovery of exactly 39.34% sodium and 60.66% several basic laws. One of these laws was the law of conservation of mass, chlorine by mass. which states that mass is neither created nor destroyed during ordinary chemical reactions or physical changes. This discovery was soon followed by the assertion that, regardless of where or how a pure chemical com- pound is prepared, it is composed of a fixed proportion of elements. For example, sodium chloride, also known as ordinary table salt, as shown in Figure 1.1, always consists of 39.34% by mass of the element sodium, Na, and 60.66% by mass of the element chlorine, Cl. The fact that a chemical compound contains the same elements in exactly the same proportions by mass regardless of the size of the sample or source of the compound is known as the law of definite proportions. It was also known that two elements sometimes combine to form more than one compound. For example, the elements carbon and oxygen form two compounds, carbon dioxide and carbon monoxide. Consider samples of each of these compounds, each containing 1.00 g of carbon. In carbon dioxide, 2.66 g of oxygen combine with 1.00 g of carbon. In carbon monoxide, 1.33 g of oxygen combine with 1.00 g of carbon. The ratio of the masses of oxygen in these two compounds is 2.66 to 1.33, or 2 to 1. This illustrates the law of multiple proportions: If two or more different com- pounds are composed of the same two elements, then the ratio of the masses of the second element combined with a certain mass of the first element is always a ratio of small whole numbers. Main Idea Compounds contain atoms in whole-number ratios. In 1808, an English schoolteacher named John Dalton proposed an explanation that encompassed all these laws. He reasoned that el­ements were composed of atoms and that only whole numbers of atoms can combine to form compounds. His theory can be summed up by the following statements. 1. All matter is composed of extremely small particles called atoms. 2. Atoms of an element are identical in size, mass, and other properties; atoms of different elements differ in size, mass, and other properties. ©Thomas J. Peterson/Photographer’s Choice/Getty Images 3. Atoms cannot be subdivided, created, or destroyed. 4. Atoms of different elements combine in simple whole-number ratios to form chemical compounds. 5. In chemical reactions, atoms are combined, separated, or rearranged. Dalton’s atomic theory explains the law of conservation of mass through the concept that chemical reactions involve merely the combi- nation, separation, or rearrangement of atoms and that during reactions atoms are not subdivided, created, or destroyed. Figure 1.2, on the next page, illustrates this idea for the formation of carbon monoxide from carbon and oxygen. 64 Chapter 3 Figure 1.2 Atoms and the Law of Conservation of Mass + = = + Carbon, C Oxygen, O Carbon monoxide, CO Carbon monoxide, CO Carbon, C Oxygen, O Mass x Mass y Mass x + Mass y Mass x + Mass y Mass x Mass y  (a) An atom of carbon, C, and an atom of oxygen, O, can  (b) The reverse holds true in a reaction in which a combine chemically to form a molecule of carbon CO molecule is broken down into its elements. monoxide, CO. The mass of the CO molecule is equal to the mass of the C atom plus the mass of the O atom. Figure 1.3 Law of Multiple Proportions + = + + = Carbon, C Oxygen, O Carbon monoxide, CO Carbon, C Oxygen, O Oxygen, O Carbon dioxide, CO2 (a) CO molecules are always composed of (b) CO2 molecules are always composed of one C atom one C atom and one O atom. and two O atoms. Note that a molecule of carbon dioxide contains twice as many oxygen atoms as does a molecule of carbon monoxide. Figure 1.3 illustrates how Dalton’s atomic theory explained the other laws. The law of definite proportions results from the fact that a given chemical compound always contains the same combinations of atoms. As for the law of multiple proportions, in the case of the carbon oxides, the 2-to-1 ratio of oxygen masses results because carbon dioxide always contains twice as many atoms of oxygen (per atom of carbon) as does carbon monoxide. Main Idea Atoms can be subdivided into smaller particles. By relating atoms to the measurable property of mass, Dalton turned Democritus’s idea into a scientific theory that could be tested by experi­ ment. But not all aspects of Dalton’s atomic theory have proven to be correct. For example, today we know that atoms are divisible into even smaller particles (although the law of conservation of mass still holds true for chemical reactions). And, as you will see in Section 3, we know that a given element can have atoms with different masses. Atomic theory has not been discarded—only modified! The important concepts that (1) all matter is composed of atoms and that (2) atoms of any one element differ in properties from atoms of another element remain unchanged. Atoms: The Building Blocks of Matter 65  Constructing a Model Question and masses of some known Materials How can you construct a model of objects outside the can. Then can covered by a sock sealed an unknown object by (1) making compare your estimates of with tape inferences about an object that these objects with actual one or more objects that fit in is in a closed container and measurements using a metric the container (2) touching the object without ruler and a balance. metric ruler seeing it? balance Discussion Safety Procedure 1. Scientists often use more than  ear safety W Record all of your results in a one method to gather data. goggles and an data table. How was this illustrated in the apron. 1. Your teacher will provide you investigation? with a can that is covered by a 2. Of the observations you made, sock sealed with tape. Without which were qualitative and unsealing the container, try to which were quantitative? determine the number of objects inside the can as well 3. Using the data you gathered, as the mass, shape, size, draw a model of the unknown composition, and texture of object(s) and write a brief each object. To do this, you summary of your conclusions. may carefully tilt or shake the can. Record your observations in a data table. 2. Remove the tape from the top of the sock. Do not look inside the can. Put one hand through the opening, and make the same observations as in step 1 by handling the objects. To make more-accurate estimations, practice estimating the sizes Section 1 Formative ASSESSMENT Reviewing Main Ideas Critical Thinking 1. List the five main points of Dalton’s 3. ANALYZING INFORMATION Three atomic theory. compounds containing potassium and oxygen are compared. Analysis shows that for each 2. What chemical laws can be explained by 1.00 g of O, the compounds have 1.22 g, 2.44 g, Dalton’s theory? and 4.89 g of K, respectively. Show how these data support the law of multiple proportions. Atoms: The Building Blocks of Matter 67 careers in Chemistry Physical Chemist P hysical chemists focus on understanding the physical properties of atoms and molecules. They are driven by a curiosity of what makes things work at the level of atoms, and they enjoy being challenged. In addition to chemistry, they study mathematics and physics extensively. Laboratory courses involving experience with electronics and optics are typically part of their training. Often, they enjoy working with instruments and computers. Physical chemists can be experimentalists or theoreticians. They use sophisticated instruments to make measurements or high-powered computers to perform intensive calculations. This STM image shows a “corral” of iron atoms The instruments used include lasers, electron microscopes, on a copper surface. nuclear magnetic resonance spectrometers, mass spectrometers, and particle accelerators. Physical chemists work in industry, government laboratories, research institutes, and academic institutions. Because physical Surface chemistry is a developing subdiscipline in physical chemists work on a wide range of problems, taking courses chemistry, and STM is an important tool in the field. in other science disciplines is important. Scientists use STM to study surface reactions, such as those that take place in catalytic converters. Other areas of Scanning Tunneling Microscopy research in which STM is useful include semiconductors and For years, scientists have yearned for the ability to “see” microelectronics. Usually, STM is used with materials that individual atoms. Because atoms are so small, this had been conduct, but it has also been used to study biological nothing more than a dream. Now, the scanning tunneling molecules, such as DNA. microscope, STM, gives scientists the ability to look at One innovative application of STM is the ability to position individual atoms. It was invented in 1981 by Gerd Binnig and individual atoms. The figure shows the result of moving Heinrich Rohrer, scientists working for IBM in Zurich, individual atoms. First, iron atoms were placed on a copper Switzerland. They shared the 1986 Nobel Prize in physics for surface. Then, individual iron atoms were picked up by the their discovery. probe and placed in position. The result is a “quantum The basic principle of STM is based on the current that corral” of 48 iron atoms on the surface of copper. The ©IBM Almaden Research Center/Peter Arnold Images/Photolibrary exists between a metallic needle that is sharpened to a diameter of the corral is about 14 nm. single atom, the probe, and a conducting sample. As the probe passes above the surface of the sample at a distance Questions of one or two atoms, electrons can “tunnel” from the needle tip to the sample’s surface. The probe moves across, or 1. In addition to chemistry, what kinds of courses are “scans,” the surface of the sample. When the probe comes important for a student interested in a physical close to the electrons of an individual atom, a signal is chemistry career? produced. A weaker signal is produced between atoms. 2. What part of an atom is detected by STM? These signals build a topographical (hill and valley) “map” of conducting and nonconducting regions. The resulting map shows the position and spacing of atoms. 66  Section 2 Main Ideas Atoms contain positive and The Structure of the Atom negative particles. Atoms have small, dense, positively-charged nuclei. Key Terms A nucleus contains protons and atom neutrons. nuclear force The radii of atoms are expressed in picometers. Although John Dalton thought atoms were indivisible, investigators in the late 1800s proved otherwise. As scientific advances allowed a deeper exploration of matter, it became clear that atoms are actually composed of smaller particles and that the number and arrangement of these particles within an atom determine that > Virginia standards atom’s chemical properties. Therefore, today we define an atom as the smallest particle of an element that retains the chemical properties of that e ­ lement. CH.2 The student will investigate and understand that the placement of elements on All atoms consist of two regions. The nucleus is a very small region located at the the periodic table is a function of their atomic center of an atom. In every atom, the nucleus is made up of at least one positively structure. The periodic table is a tool used for charged particle called a proton and usually one or more neutral particles called the investigations of: CH.2.a average atomic mass, mass number, neutrons. Surrounding the nucleus is a region occupied by negatively charged and atomic number. particles called electrons. This region is very large compared with the size of the CH.2.c mass and charge characteristics of nucleus. Protons, neutrons, and electrons are referred to as subatomic particles. subatomic particles. CH.1.EKS-26; CH.2.EKS-6; CH.2.EKS-16 Main Idea Atoms contain positive and negative particles. The first discovery of a subatomic particle came in the late 1800s. At that Figure 2.1 time, many experiments were performed in which electric current was passed through various gases at low pressures. (Gases at atmospheric Structure of a Cathode-Ray pressure don’t conduct electricity well.) These experi­ments were carried Tube Particles pass through the out in glass tubes, like the one shown in Figure 2.1, that had been hooked tube from the cathode, the metal disk up to a vacuum pump. Such tubes are known as cathode-ray tubes. connected to the negative terminal of the voltage source, to the anode, the metal disk connected to the positive terminal. Cathode Rays and Electrons Investigators noticed that when current was passed through the tube, the surface of the tube directly opposite the cathode glowed. They hypothesized that the glow was caused by a stream of particles, which Voltage source they called a cathode ray. The ray traveled from the cathode to the anode when current was passed through the tube. Experiments devised to test this Gas at low pressure Cathode ray hypothesis revealed the following ­observations: 1. Cathode rays were deflected by a magnetic field in the same manner as a wire carrying electric – + current, which was known to have a negative charge (see Figure 2.2 on the next page). Cathode Anode 2. The rays were deflected away from a negatively (metal disk) (metal disk) charged object. 68 Chapter 3  These observations led to the hypothesis Figure 2.2 that the particles that compose cathode rays are negatively charged. This hypothesis was Finding Negative Particles Holding a magnet near a strongly supported by a series of experiments cathode-ray tube (attached to a vacuum pump) causes negatively- carried out in 1897 by the English physicist charged particles in the beam to be deflected. Joseph John Thomson. In one investigation, he was able to measure the ratio of the charge of cathode-ray particles to their mass. He found that this ratio was always the same, regardless of the metal used to make the cathode or the nature of the gas inside the cathode-ray tube. Thomson concluded that all cathode rays must be composed of identical negatively charged particles, which were named ­electrons. Cathode Anode Charge and Mass of the Electron Cathode rays have identical properties regardless of the element used to produce them. Therefore, it was concluded that electrons are present in atoms of all elements. Thus, cathode-ray experiments provided evidence that atoms are divisible and that one of the atom’s basic constituents is the negatively charged ­electron. Thomson’s experiment also revealed that the electron has a very large charge-to-mass ratio. In 1909, experiments conducted by the American physicist Robert A. Millikan measured the charge of the electron. Scientists used this information and the charge-to- mass ratio of the electron to determine that the mass of the electron is about one two-thousandth the mass of the simplest type of hydrogen atom, which is the smallest atom known. More-accurate experiments conducted since then indicate that the electron has a mass of 9.109 × 10-31 kg, or 1/1837 the mass of the simplest type of hydrogen atom. Based on what was learned about electrons, two other inferences were made about atomic structure. 1. Because atoms are electrically neutral, they must contain a positive charge to balance the negative electrons. 2. Because electrons have so much less mass than atoms, atoms must contain other particles that account for most of their mass. Thomson proposed a model for the atom that is called the plum pudding model (after the English dessert). He believed that the negative cHECK FOR UNDERSTANDING electrons were spread evenly throughout the positive charge of the rest of Analyze Why is it necessary to use the atom. This arrangement is like seeds in a watermelon: the seeds are experiments such as those of spread throughout the fruit but do not contribute much to the overall J.J. Thomson and Robert A. Millikan to mass. However, shortly thereafter, new experiments disproved this model. infer information about electrons? Still, the plum pudding model was an important step forward in our modern understanding of the atom, as it represents the first time scien- tists tried to incorporate the then-revolutionary idea that atoms were not, strictly speaking, indivisible. Atoms: The Building Blocks of Matter 69  Main Idea Atoms have small, dense, positively charged nuclei. cHECK FOR UNDERSTANDING More detail of the atom’s structure was provided in 1911 by New Zealander Explain What did Rutherford expect to Ernest Rutherford and his associates Hans Geiger and Ernest Marsden. happen when he fired alpha particles at The scientists bombarded a thin piece of gold foil with fast-moving alpha the gold foil? particles, which are positively charged particles with about four times the mass of a hydrogen atom. Geiger and Marsden assumed that mass and charge were uniformly distributed throughout the atoms of the gold foil, as one would expect from the plum pudding model. They expected the alpha particles to pass through with only a slight deflection, and for the vast majority of the particles, this was the case. However, when the scientists checked for the possibility of wide-angle deflections, they were shocked to find that roughly 1 in 8000 of the alpha particles had actually been de- flected back toward the source (see Figure 2.3). As Rutherford later ex- claimed, it was “as if you had fired a 15-inch [artillery] shell at a piece of tissue paper and it came back and hit you.” After thinking about the startling result for a few months, Rutherford finally came up with an explanation. He reasoned that the deflected alpha particles must have experienced some powerful force within the atom. And he figured that the source of this force must occupy a very small amount of space because so few of the total number of alpha particles had been affected by it. He concluded that the force must be caused by a very densely packed bundle of matter with a positive electric charge. Rutherford called this positive bundle of matter the nucleus (see Figure 2.4 on the next page). Rutherford had discovered that the volume of a nucleus was very small compared with the total volume of an atom. In fact, if the nucleus were the size of a marble, then the size of the atom would be about the size of a football field. But where were the electrons? This question was not answered until Rutherford’s student, Niels Bohr, proposed a model in which electrons surrounded the positively charged nucleus as the planets surround the sun. Bohr’s model is discussed in a later chapter. Figure 2.3 Screen to detect deflected particles Thin gold foil Lead box containing radioactive Particles (a) (b) source of fast-moving particles deflected by foil a) Geiger and Marsden bombarded a thin piece of gold foil b) Some of the particles were deflected by the gold foil with a narrow beam of alpha particles. back toward their source. 70 Chapter 3  Figure 2.4 Small deflection Finding the Nucleus Rutherford reasoned that each atom in the gold foil contained a small, dense, positively charged nucleus sur­rounded by electrons. A small number of the alpha particles directed toward the foil were deflected Beam of Electrons by the tiny nu­cleus (red arrows). Most of positive surround Nucleus the particles passed through undisturbed particles nucleus Large deflection (black arrows). Main Idea A nucleus contains protons and neutrons. Except for the nucleus of the simplest type of hydrogen atom (discussed in the next section), all atomic nuclei are made of two kinds of particles, protons and neutrons. A proton has a positive charge equal in magnitude to the negative charge of an electron. Atoms are electrically neutral because they contain equal numbers of protons and electrons. A neutron is electrically neutral. The simplest hydrogen atom consists of a single-proton nucleus with a single electron moving about it. A proton has a mass of 1.673 × 10-27 kg, which is 1836 times greater than the mass of an electron and 1836/1837, or virtually all, of the mass of the simplest hydrogen atom. All atoms besides the simplest hydrogen atom also have neutrons. The mass of a neutron is 1.675 × 10-27 kg—slightly larger than that of a proton. The nuclei of atoms of different elements differ in their number of protons and, therefore, in the amount of positive charge they possess. Thus, the number of protons determines that atom’s identity. Physicists have identified other subatomic particles, but particles other than elec- trons, protons, and neutrons have little effect on the chemical properties of matter. Figure 2.5 on the next page summarizes the properties of electrons, protons, and neutrons. Forces in the Nucleus Generally, particles that have the same electric charge repel one another. Therefore, we would expect a nucleus with more than one proton to be unstable. However, when two protons are extremely close to each other, there is a strong attraction between them. In fact, as many as 83 protons can exist close together to help form a stable nucleus. A similar attraction exists when neutrons are very close to each other or when protons and neutrons are very close together. These short-range proton-­neutron, proton-proton, and neutron-neutron forces hold the nuclear particles together and are referred to as nuclear forces. Atoms: The Building Blocks of Matter 71  Figure 2.5 Properties of Subatomic Particles Relative electric Relative mass Particle Symbols charge Mass number (u*) Actual mass (kg) Electron ​ 0 ​e e -, ​  -1 -1 0 0.000 5486 9.109 × 10-31 Proton p+, ​  ​11​H +1 1 1.007 276 1.673 × 10-27 Neutron n°, ​  ​10​n 0 1 1.008 665 1.675 × 10-27 *1 u (unified atomic mass unit) = 1.660 5402 × 10-27 kg Main Idea The radii of atoms are expressed in picometers. It is convenient to think of the region occupied by the electrons as an electron cloud—a cloud of negative charge. The radius of an atom is the distance from the center of the nucleus to the outer portion of this electron cloud. Because atomic radii are so small, they are expressed using a unit that is more convenient for the sizes of atoms. This unit is the picometer. The abbreviation for the picometer is pm (1 pm = 10-12 m = 10-10 cm). To get an idea of how small a picometer is, consider that 1 cm is the same fractional part of 103 km (about 600 mi) as 100 pm is of 1 cm. Atomic radii range from about 40 to 270 pm. By contrast, the nuclei of atoms have much smaller radii, about 0.001 pm. Nuclei also have incredibly high densities, about 2 × 108 metric tons/cm3. Section 2 Formative ASSESSMENT Reviewing Main Ideas 3. Compare the three subatomic particles in terms of location in the atom, mass, and relative charge. 1. Define each of the following: a. atom 4. Why are cathode-ray tubes, like the one in Figure 2.1, connected to a vacuum pump? b. electron c. nucleus Critical Thinking d. proton e. neutron 5. EVALUATING IDEAS Nuclear forces are said to hold protons and neutrons together. What 2. Describe one conclusion made by each of the is it about the composition of the nucleus that following scientists that led to the development requires the concept of nuclear forces? of the current atomic theory: a. Thomson b. Millikan c. Rutherford 72 Chapter 3  Section 3 Counting Atoms Main Ideas All atoms of an element must have the same number of Key Terms protons, but not neutrons. atomic number nuclide mole isotope unified atomic mass unit Avogadro’s number Atomic mass is a relative mass number average atomic mass molar mass measure. Average atomic mass is a Consider neon, Ne, the gas used in many illuminated signs. Neon is a minor component of the atmosphere. In fact, dry air contains only about 0.002% neon. weighted value. And yet there are about 5 × 1017 atoms of neon present in each breath you inhale. A relative mass scale makes In most experiments, atoms are much too small to be measured individually. Chemists can analyze atoms quantitatively, however, by knowing fundamental counting atoms possible. properties of the atoms of each element. In this section, you will be introduced to some of the basic properties of atoms. You will then discover how to use this information to count the number of atoms of an element in a sample with a known mass. You will also become familiar with the mole, a special unit used by chemists > Virginia standards to express amounts of particles, such as atoms and molecules. CH.2 The student will investigate and understand that the placement of elements on the periodic table is a function of their atomic Main Idea structure. The periodic table is a tool used for the investigations of: All atoms of an element must have the same number CH.2.a average atomic mass, mass number, of protons, but not neutrons. and atomic number. CH.2.b isotopes, half lives, and radioactive decay. All atoms contain the same particles. Yet all atoms are not the same. CH.4.a The student will investigate and Atoms of different elements have different numbers of protons. Atoms understand that quantities in a chemical of the same element all have the same number of protons. The reaction are based on molar relationships. Key concepts include: Avogadro's principle and atomic number (Z) of an element is the number of protons of each atom molar volume. of that element. CH.2.EKS-2; CH.2.EKS-3; CH.4.EKS-1 Look at a periodic table. In most, an element’s atomic number is indicated above its s­ ymbol, and the elements are placed in order of increasing atomic number. Hydrogen, H, is at the upper left of the table and has an atomic number of 1. All atoms of the element hydrogen have one proton. Next in order is helium, He, which has two protons. Lithium, Li, has three protons (see Figure 3.1); beryllium, Be, has four protons; and so on. The atomic number identifies an element. If the number of protons in the nucleus of an atom were to change, that atom would become a different element. Figure 3.1 Isotopes Atomic Numbers The atomic number in this periodic table entry But just because all hydrogen atoms, for example, have only a single reveals that an atom of lithium has proton, it doesn't mean they all have the same number of neutrons, or three protons in its nucleus. even any neutrons at all. In fact, three types of hydrogen atoms are known. The most common type of hydrogen is sometimes called protium. It accounts for 99.9885% of the hydrogen atoms found on Earth, and its 3 nucleus consists of only a single proton. Another type of hydrogen, Li Lithium deuterium, accounts for 0.0115% of Earth’s hydrogen atoms; its nucleus 6.941 has one proton and one neutron. The third form of hydrogen, tritium, has [He]2s1 one proton and two neutrons in its nucleus. Tritium is radioactive so it is not very common at all on Earth; however, it is still hydrogen. Atoms: The Building Blocks of Matter 73 Figure 3.2 Three Isotopes of Hydrogen The nuclei of different isotopes of the same element have the same number of protons but different numbers of neutrons. 1 Neutron 2 Neutrons 1 Proton 1 Proton 1 Proton Protium Deuterium Tritium Protium, deuterium, and tritium are isotopes of hydrogen. Isotopes are atoms of the same element that have different masses. The isotopes of a particular element all have the same number of protons and electrons but different numbers of neutrons. In all three isotopes of hydrogen, shown in Figure 3.2, the positive charge of the single proton is balanced by the negative charge of the electron. Most of the elements consist of mixtures of isotopes. Tin has 10 stable isotopes, for example—the most of any element. The atoms in any sample of an element you may find most likely will be a mixture of several isotopes in various proportions. The detection of these isotopes and determination of their relative proportions has become extremely precise. So precise that scientists can determine where some elements come from by measuring the percentages of different isotopes in a sample. Mass Number Identifying an isotope requires knowing both the name or atomic number of the element and the mass of the isotope. The mass number is the total number of protons and neutrons that make up the nucleus of an isotope. The three isotopes of hydrogen described earlier have mass numbers 1, 2, and 3, as shown in Figure 3.3. Figure 3.3 Mass Numbers of Hydrogen Isotopes Atomic number Number of Mass number (number of protons) neutrons (protons + neutrons) Protium 1 0 1+0=1 Deuterium 1 1 1+1=2 Tritium 1 2 1+2=3 74 Chapter 3  Identifying Isotopes There are two methods for specifying isotopes. In the first, the mass number appears with a hyphen after the name of the element. Tritium, for example, is written as hydrogen-3. We call this method hyphen notation. The uranium isotope with mass number 235, commonly used as fuel for nuclear power plants, is known as uranium-235. The second method shows the composition of a nucleus using the isotope’s nuclear symbol. So uranium-235 is shown as ​  ​235 92​U. The superscript indicates the mass number (protons + neutrons). The subscript indicates the atomic number (number of protons). The number of neutrons is found by subtracting the atomic number from the mass number. mass number – atomic number = number of neutrons 235 (protons + neutrons) – 92 protons = 143 neutrons Figure 3.4 gives the names, symbols, and compositions of the isotopes of hydrogen and helium. Nuclide is a general term for a specific isotope of an element. Figure 3.4 Isotopes of Hydrogen and Helium Nuclear Number of Number of Number of Isotope symbol protons electrons neutrons Hydrogen-1 (protium) ​  11​ ​H 1 1 0 Hydrogen-2 (deuterium) ​  21​ ​H 1 1 1 Hydrogen-3 (tritium) ​  31​ ​H 1 1 2 Helium-3 ​  32​ ​He 2 2 1 Helium-4 ​  42​ ​He 2 2 2 Sub-Atomic Particles Sample Problem A How many protons, electrons, and neutrons are there in an atom of chlorine-37? Analyze Given: name and mass number of chlorine-37 Unknown: numbers of protons, electrons, and neutrons PLAN atomic number = number of protons = number of electrons mass number = number of neutrons + number of protons Continued Atoms: The Building Blocks of Matter 75  Sub-Atomic Particles (continued) Solve The mass number of chlorine-37 is 37. Consulting the periodic table reveals that chlorine’s atomic number is 17. Therefore we know that atomic number = number of protons = number of electrons = 17 protons and 17 electrons number of neutrons = mass number - atomic number = 37 - 17 = 20 neutrons An atom of chlorine-37 is made up of 17 electrons, 17 protons, and 20 neutrons. CHECK YOUR The number of protons in a neutral atom equals the number of electrons. The WORK sum of the protons and neutrons equals the given mass number (17 + 20 = 37). Answers in Appendix E 1. How many protons, electrons, and neutrons make up an atom of bromine-80? 2. Write the nuclear symbol for carbon-13. 3. Write the hyphen notation for the isotope with 15 electrons and 15 neutrons. Main Idea Atomic mass is a relative measure. Masses of atoms expressed in grams are very small. As we shall see, an atom of oxygen-16, for example, has a mass of 2.656 × 10–23 g. For most chemical calculations it is more convenient to use relative atomic masses. As you learned when you studied scientific measurement, scientists use standards of measurement that are constant and are the same every- where. In order to set up a relative scale of atomic mass, one atom has been arbitrarily chosen as the standard and assigned a mass value. The masses of all other atoms are expressed in relation to this standard. The standard used by scientists to compare units of atomic mass is the carbon-12 atom, which has been arbitrarily assigned a mass of exactly 12 unified atomic mass units, or 12 u. One unified atomic mass unit, or 1 u, is exactly 1/12 the mass of a carbon-12 atom. The atomic mass of any other atom is determined by comparing it with the mass of the carbon-12 atom. The hydrogen-1 atom has an atomic mass of about 1/12 that of the carbon‑12 atom, or about 1 u. The precise value of the atomic mass of a hydrogen‑1 atom is 1.007 825 u. An oxygen‑16 atom has about 16/12 (or 4/3) the mass of a ­carbon-12 atom. Careful measurements show the atomic mass of ­oxygen‑16 to be 15.994 915 u. The mass of a magne- sium-24 atom is found to be slightly less than twice that of a carbon-12 atom. Its atomic mass is 23.985 042 u. 76 Chapter 3  Some additional examples of the atomic masses of the naturally occurring isotopes of several elements are given in Figure 3.5 on the next page. Isotopes of an element may occur naturally, or they may be made in the laboratory (artificial isotopes). Although isotopes have different masses, they do not differ significantly in their chemical behavior. The masses of subatomic particles can also be expressed on the atomic mass scale (see Figure 2.5). The mass of the electron is 0.000 548 6 u, that of the proton is 1.007 276 u, and that of the neutron is Discovery of Element 43 1.008 665 u. Note that the proton and neutron masses are close, but not The discovery of element 43, equal, to 1 u. You have learned that the mass number is the total number technetium, is credited to Carlo Perrier of protons and neutrons that make up the nucleus of an atom. You can and Emilio Segrè, who artificially now see that the mass number and relative atomic mass of a given produced it in 1937. However, nuclide are quite close to each other. They are not identical, because the scientists have found minute traces proton and neutron masses deviate slightly from 1 u and the atomic of technetium in the Earth's crust that masses include electrons. Also, as you will read in a later chapter, a small result from the fission of uranium. amount of mass is changed to energy in the creation of a nu­cleus from its Astronomers have also discovered protons and ­neutrons. technetium in S-type stars. Main Idea Average atomic mass is a weighted value. Most elements occur naturally as mixtures of isotopes, as indicated in Figure 3.5 (see next page). Scientists determine the average mass of a sample of an element's isotopes by determining the percentages of each of the isotopes and then giving the proper weight to each value. Average atomic mass is the weighted average of the atomic masses of the naturally occurring isotopes of an element. Unlike atomic number, average atomic mass is a statistical calculation. Different samples of the same element can differ in their relative abundance of isotopes. The following is an example of how to calculate a weighted average. Suppose you have a box containing two sizes of marbles. If 25% of the marbles have masses of 2.00 g each and 75% have masses of 3.00 g each, how is the weighted average calculated? You could count the number of each type of marble, calculate the total mass of the mixture, and divide by the total number of marbles. If you had 100 marbles, the calculations would be as follows: 25 marbles × 2.00 g = 50 g 75 marbles × 3.00 g = 225 g Adding these masses gives the total mass of the marbles. 50 g + 225 g = 275 g Dividing the total mass by 100 gives an average marble mass of 2.75 g. A simpler method is to multiply the mass of each marble by the decimal fraction representing its percentage in the mixture. Then add the products. 25% = 0.25     75% = 0.75 (2.00 g × 0.25) + (3.00 g × 0.75) = 2.75 g Atoms: The Building Blocks of Matter 77  Figure 3.5 Atomic Masses and Abundances of Several Naturally Occurring Isotopes Percentage natural Average atomic Isotope Mass number abundance Atomic mass (u) mass of element (u) Hydrogen-1 1 99.9885    1.007 825    1.007 94 Hydrogen-2 2    0.0115    2.014 102 Carbon-12 12 98.93 12 (by definition) Carbon-13 13    1.07 13.003 355 12.0107 Oxygen-16 16 99.757 15.994 915 15.9994 Oxygen-17 17    0.038 16.999 132 Oxygen-18 18    0.205 17.999 160 Copper-63 63 69.15 62.929 601 63.546 Copper-65 65 30.85 64.927 794 Cesium-133 133 100 132.905 447 132.905 Uranium-234 234    0.0054 234.040 945 Uranium-235 235    0.7204 235.043 922 238.029 Uranium-238 238 99.2742 238.050 784 Calculating Average Atomic Mass The average atomic mass of an element depends on both the mass and the relative abundance of each of the element’s isotopes. For example, naturally occurring copper consists of 69.15% copper-63, which has an atomic mass of 62.929 601 u, and 30.85% copper-65, which has an atomic mass of 64.927 794 u. The average atomic mass of copper can be calcu- lated by multiplying the atomic mass of each isotope by its relative abundance (expressed in decimal form) and adding the results. 0.6915 × 62.929 601 u + 0.3085 × 64.927 794 u = 63.55 u The calculated average atomic mass of naturally occurring copper is 63.55 u. The average atomic mass is included for the elements listed in Figure 3.5. As illustrated in the table, most atomic masses are known to four or more significant figures. In this book, an element’s atomic mass is usually rounded to two decimal places before it is used in a calculation. Main Idea A relative mass scale makes counting atoms possible. Premium The relative atomic mass scale makes it possible to know how many Content atoms of an element are present in a sample of the element with a Chemistry measurable mass. Three very important concepts—the mole, Avogadro’s HMDScience.com number, and molar mass—provide the basis for relating masses in grams Avogadro's Number to numbers of atoms. 78 Chapter 3 The Mole Figure 3.6 The mole is the SI unit for amount of substance. A mole (abbreviated mol) is Molar Mass Shown is approximately the amount of a substance that contains as many particles as there are atoms one molar mass of each of three elements. in exactly 12 g of carbon-12. The mole is a counting unit, just like a dozen is. We don’t usually buy 12 or 24 ears of corn; we order one dozen or two dozen. Similarly, a chemist may want 1 mol of carbon, or 2 mol of iron, or 2.567 mol of calcium. In the sections that follow, you will see how the mole relates to masses of atoms and c­ ompounds. Avogadro’s Number The number of particles in a mole has been experimentally determined in a number of ways. The best modern value is 6.022 141 79 × 1023. This means that exactly 12 g of carbon-12 contains 6.022 141 79 × 1023 carbon‑12 atoms. The number of particles in a mole is known as Avogadro’s number, named for the nineteenth-century Italian scientist Amedeo Avogadro, whose ideas were crucial in explaining the relationship between mass (a) carbon (graphite) and numbers of atoms. Avogadro’s number—6.022 141 79 × 1023—is the number of particles in exactly one mole of a pure substance. For most pur- poses, Avogadro’s number is rounded to 6.022 × 1023. To get a sense of how large Avogadro’s number is, consider the following: If every person living on Earth (6.8 billion people) worked to count the atoms in one mole of an element, and if each person counted continuously at a rate of one atom per second, it would take about 3 million years for all the atoms to be counted. Molar Mass An alternative definition of mole is the amount of a substance that contains Avogadro’s number of particles. Can you calculate the approximate mass of one mole of helium atoms? You know that a mole of carbon-12 atoms has a (b) iron (nails) mass of exactly 12 g and that a carbon-12 atom has an atomic mass of 12 u. The atomic mass of a helium atom is 4.00 u, which is about one-third the mass of a carbon-12 atom. It follows that a mole of helium atoms will have about one-third the mass of a mole of carbon-12 atoms. Thus, one mole of helium has a mass of about 4.00 g. The mass of one mole of a pure substance is called the molar mass of that substance. Molar mass is usually written in units of g/mol. The molar mass of an element is numerically equal to the atomic mass of the element in unified atomic mass units (which can be found in the periodic table). For example, the molar mass of lithium, Li, is 6.94 g/mol, while the molar mass of mercury, Hg, is 200.59 g/mol (rounding each value to two decimal places). The molar mass of an element contains one mole of atoms. For example, 4.00 g of helium, 6.94 g of lithium, and 200.59 g of mercury all contain a mole of atoms. Figure 3.6 shows molar masses of (c) copper (wire) three common ­elements. Atoms: The Building Blocks of Matter 79 Figure 3.7 Relating Mass to the Number of Atoms The diagram shows the relationship between mass in grams, amount in moles, and number of atoms of an element in a sample. molar mass 1 mol = of element × = × 1 mol Amount 6.022 x 10 23 atoms of element Mass of element 1 mol 6.022 x 10 23 atoms = Number of atoms × molar mass = in moles × in grams of element 1 mol of element Gram/Mole Conversions Chemists use molar mass as a conversion factor in chemical calculations. For example, the molar mass of helium is 4.00 g He/mol He. To find how many grams of helium there are in two moles of helium, multiply by the molar mass. 4.00g He 2.00 mol He × _ ​   ​= 8.00 g He 1 mol He Figure 3.7 shows how to use molar mass, moles, and Avogadro’s number to relate mass in grams, amount in moles, and number of atoms of an element. Sub-Atomic Particles Sample Problem B What is the mass in grams of 3.50 mol of the element copper, Cu? Analyze Given: 3.50 mol Cu Unknown: mass of Cu in grams PLAN amount of Cu in moles ⟶ mass of Cu in grams According to Figure 3.7, the mass of an element in grams can be calculated by multiplying the amount of the element in moles by the element’s molar mass. grams Cu moles Cu × _​   ​= grams Cu moles Cu Solve The molar mass of copper from the periodic table is rounded to 63.55 g/mol. 63.55 g Cu 3.50 mol Cu × _ ​   ​= 222 g Cu 1 mol Cu CHECK YOUR Because the amount of copper in moles was given to three significant figures, WORK the answer was rounded to three significant figures. The size of the answer is reasonable because it is somewhat more than 3.5 times 60. Continued 80 Chapter 3  Sub-Atomic Particles (continued) Answers in Appendix E 1. What is the mass in grams of 2.25 mol of the element iron, Fe? 2. What is the mass in grams of 0.375 mol of the element potassium, K? 3. What is the mass in grams of 0.0135 mol of the element sodium, Na? 4. What is the mass in grams of 16.3 mol of the element nickel, Ni? Premium Content Gram/Mole Conversions Learn It! Video HMDScience.com Sample Problem C A chemist produced 11.9 g of aluminum, Al. Solve It! Cards HMDScience.com How many moles of aluminum were ­produced? Analyze Given: 11.9 g Al Unknown: amount of Al in moles PLAN mass of Al in grams ⟶ amount of Al in moles As shown in Figure 3.7, amount in moles can be obtained by dividing mass in grams by molar mass, which is mathematically the same as multiplying mass in grams by the reciprocal of molar mass. moles Al  ​= moles Al grams Al × ​ _ grams Al Solve The molar mass of aluminum from the periodic table is rounded to 26.98 g/mol. ​ 1 mol Al  ​= 0.441 mol Al 11.9 g Al × _ 26.98 g Al CHECK YOUR The answer is correctly given to three significant figures. The answer is reason- WORK able because 11.9 g is somewhat less than half of 26.98 g. Answers in Appendix E 1. How many moles of calcium, Ca, are in 5.00 g of calcium? 2. How many moles of gold, Au, are in 3.60 × 10-5 g of gold? 3. How many moles of zinc, Zn, are in 0.535 g of zinc? Atoms: The Building Blocks of Matter 81  Conversions with Avogadro’s Number CHECK FOR UNDERSTANDING Avogadro’s number can be used to find the number of atoms of an Describe Although using the element from the amount in moles or to find the amount of an element in mole unit of measurement is often moles from the number of atoms. While these types of problems are less preferable for doing calculations to common in chemistry than converting between amount in moles and using Avogadro’s number, at other mass in grams, they are useful in demonstrating the meaning of times, using Avogadro’s number is Avogadro’s number. Note that in these calculations, Avogadro’s number necessary. Describe a circumstance is expressed in units of atoms per mole. under which this is true. Premium Content Conversions with Avogadro’s Number Solve It! Cards HMDScience.com Sample Problem D How many moles of silver, Ag, are in 3.01 × 1023 atoms of silver? Analyze Given: 3.01 × 1023 atoms of Ag Unknown: amount of Ag in moles PLAN number of atoms of Ag ⟶ amount of Ag in moles From Figure 3.7, we know that number of atoms is converted to amount in moles by dividing by Avogadro’s number. This is equivalent to multiplying numbers of atoms by the reciprocal of Avogadro’s number. moles Ag Ag atoms × ​ ___     ​= moles Ag    Avogadro’s number of Ag atoms 1 mol Ag Solve 3.01 × 1023 Ag atoms × __ ​        ​= 0.500 mol Ag 6.022 × 1023 Ag atoms CHECK YOUR The answer is correct—units cancel correctly and the number of atoms is WORK one-half of Avogadro’s number. Answers in Appendix E 1. How many moles of lead, Pb, are in 1.50 × 1012 atoms of lead? 2. How many moles of tin, Sn, are in 2500 atoms of tin? 3. How many atoms of aluminum, Al, are in 2.75 mol of ­aluminum? Conversions with Avogadro’s Number Sample Problem E What is the mass in grams of 1.20 × 108 atoms of copper, Cu? Analyze Given: 1.20 × 108 atoms of Cu Unknown: mass of Cu in grams Continued 82 Chapter 3 Conversions with Avogadro's Number (continued) PLAN number of atoms of Cu ⟶ amount of Cu in moles ⟶ mass of Cu in grams As indicated in Figure 3.7, the given number of atoms must first be converted to amount in moles by dividing by Avogadro’s number. Amount in moles is then multiplied by molar mass to yield mass in grams. moles Cu grams Cu Cu atoms × ___ ​          ​× _ ​   ​= grams Cu Avogadro’s number of Cu atoms moles Cu Solve The molar mass of copper from the periodic table is rounded to 63.55 g/mol. 1.20 × 108 Cu atoms × __ ​  1 mol    Cu   ​× ​ 63.55 g Cu _ ​= 1.27 × 10-14 g Cu 6.022 × 1023 Cu atoms 1 mol Cu CHECK YOUR Units cancel correctly to give the answer in grams. The size of the answer is WORK reasonable—108 has been divided by about 1024 and multiplied by about 102. 1. What is the mass in grams of 7.5 × 1015 atoms of nickel, Ni? 2. How many atoms of sulfur, S, are in 4.00 g of ­sulfur? 3. What mass of gold, Au, contains the same number of atoms as 9.0 g of aluminum, Al? Section 3 Formative ASSESSMENT Reviewing Main Ideas 4. To two decimal places, what is the relative atomic mass and the molar mass of the element 1. Explain each of the following: potassium, K? a. atomic number 5. Determine the mass in grams of the following: b. mass number a. 2.00 mol N c. relative atomic mass b. 3.01 × 1023 atoms Cl d. average atomic mass e. mole 6. Determine the amount in moles of the following: f. Avogadro’s number a. 12.15 g Mg g. molar mass b. 1.50 × 1023 atoms F h. isotope Critical Thinking 2. Determine the number of protons, electrons, and neutrons in each of the following isotopes: 7. ANALYZING DATA Beaker A contains 2.06 mol a. sodium-23 of copper, and Beaker B contains 222 grams of silver. Which beaker contains the larger mass? b. calcium-40 Which beaker has the larger number of atoms? c. 64 ​ ​Cu 22 108​ d. ​ 47 Ag 3. Write the nuclear symbol and hyphen notation for each of the following isotopes: a. mass number of 28 and atomic number of 14 b. 26 protons and 30 neutrons Atoms: The Building Blocks of Matter 83 Math Tutor Conversion Factors Most calculations in chemistry require that all measurements The correct strategy is to multiply the given amount (in mL) by of the same quantity (mass, length, volume, temperature, and the conversion factor that allows milliliter units to cancel out so on) be expressed in the same unit. To change the units of a and liter units to remain. Using the second conversion factor quantity, you can multiply the quantity by a conversion factor. will give you the units you want. With SI units, such conversions are easy because units of the These conversion factors are based on an exact definition same quantity are related by multiples of 10, 100, 1000, or (1000 mL = 1 L exactly), so significant figures do not apply to 1 million. Suppose you want to convert a given amount in these factors. The number of significant figures in a converted milliliters to liters. You can use the relationship 1 L = 1000 mL. measurement depends on the certainty of the measurement From this relationship, you can derive the following conversion you start with. factors. 1000 mL ​ _  ​and _​  1 L  ​ 1L 1000 mL Sample Problem A sample of aluminum has a mass of 0.087 g. What is the sample’s mass in milligrams? Based on SI prefixes, you know that 1 g = 1000 mg. Therefore, the possible conversion factors are _1000 mg 1g ​   ​and ​ _ ​ 1g 1000 mg The first conversion factor cancels grams, leaving milligrams. 1000 mg 0.087 g × ​ _  ​= 87 mg 1g Notice that the values 0.087 g and 87 mg each have two significant figures. A sample of a mineral has 4.08 × 10‑5 mol of vanadium per kilogram of mass. How many micromoles of vanadium per kilogram does the mineral contain? The prefix micro‑ specifies _______ ​ 1 0001 000 ​or 1 × 10‑6 of the base unit. So, 1 µmol = 1 × 10‑6 mol. The possible conversion factors are 1 µmol × 10‑6 mol ​ __     ​and ​ 1__  ​ ‑6 1 × 10 mol 1 µmol The first conversion factor will allow moles to cancel and micromoles to remain. 1 µmol 4.08 × 10‑5 mol × __ ​      ​= 40.8 µmol 1 × 10‑6 mol Notice that the values 4.08 × 10‑5 mol and 40.8 µmol each have three significant figures. 1. Express each of the following measurements in the units indicated. a. 2250 mg in grams b. 59.3 kL in liters 2. Use scientific notation to express each of the following measurements in the units indicated. a. 0.000 072 g in micrograms b. 3.98 × 106 m in kilometers 84 Chapter 3  Summary Premium Content Chapter 3 Interactive Review HMDScience.com Review Games Concept Maps Section 1 The Atom: From Philosophical Idea to Key Terms Scientific Theory The idea of atoms has been around since the time of the ancient Greeks. law of conservation of mass In the nineteenth century, John Dalton proposed a scientific theory of law of definite proportions atoms that can still be used to explain properties of most chemicals today. law of multiple proportions Matter and its mass cannot be created or destroyed in chemical reactions. The mass ratios of the elements that make up a given compound are always the same, regardless of how much of the compound there is or how it was formed. If two or more different compounds are composed of the same two elements, then the ratio of the masses of the second el­ement combined with a certain mass of the first element can be expressed as a ratio of small whole numbers. Section 2 The Structure of the Atom Key Terms Cathode-ray tubes supplied evidence of the existence of electrons, which atom are negatively charged subatomic particles that have relatively little mass. nuclear forces Rutherford found evidence for the existence of the atomic nucleus by bombarding gold foil with a beam of positively charged particles. Atomic nuclei are composed of protons, which have an electric charge of +1, and (in all but one case) neutrons, which have no electric charge. Atomic nuclei have radii of about 0.001 pm (pm = picometers; 1 pm × 10‑12 m), and atoms have radii of about 40 –270 pm. Section 3 Counting Atoms Key Terms The atomic number of an element is equal to the number of protons of an atomic number atom of that element. isotope The mass number is equal to the total number of protons and neutrons that mass number make up the nucleus of an atom of that element. nuclide The unified atomic mass unit (u) is based on the carbon‑12 atom and unified atomic mass unit is a convenient unit for measuring the mass of atoms. It equals 1.660 540 × 10‑24 g. average atomic mass mole The average atomic mass of an element is found by calculating the weighted average of the atomic masses of the naturally occurring isotopes Avogadro’s number of the element. molar mass Avogadro’s number is equal to approximately 6.022 × 1023. A sample that contains a number of particles equal to Avogadro’s number contains a mole of those particles. Chapter Summary 85 Chapter 3 Review Section 1 8. Copy and complete the following table concerning The Atom: From Philosophical the three isotopes of silicon, Si. (Hint: See Sample Problem A.) Idea to Scientific Theory Number of Number of number of REVIEWing main Ideas Isotope protons electrons neutrons 1. Explain each of the following in terms of Dalton’s Si-28 atomic theory: Si-29 a. the law of conservation of mass Si-30 b. the law of definite proportions c. the law of multiple proportions 9. a. What is the atomic number of an element? b. What is the mass number of an isotope? 2. According to the law of conservation of mass, if c. In the nuclear symbol for deuterium,​  21​ ​H, identify element A has an atomic mass of 2 mass units and the atomic number and the mass number. element B has an atomic mass of 3 mass units, what mass would be expected for compound AB? for 10. What is a nuclide? compound A2B3? 11. Use the periodic table and the information that follows to write the hyphen notation for each isotope Section 2 described. The Structure of the Atom a. atomic number = 2, mass number = 4 b. atomic number = 8, mass number = 16 REVIEWing main Ideas c. atomic number = 19, mass number = 39 3. a. What is an atom? 12. a. What nuclide is used as the standard in the b. What two regions make up all atoms? relative scale for atomic masses? b. What is its assigned atomic mass? 4. Describe at least four properties of electrons that were determined based on the experiments of 13. What is the atomic mass of an atom if its mass is Thomson and Millikan. approximately equal to the following? 1 ​that of carbon-12 a. ​ _ 5. Summarize Rutherford’s model of the atom, and 3 explain how he developed this model based on the b. 4.5 times as much as carbon-12 results of his famous gold-foil experiment. 14. a. What is the definition of a mole? 6. What number uniquely identifies an element? b. What is the abbreviation for mole? c. How many particles are in one mole? Section 3 d. What name is given to the number of particles in Counting Atoms a mole? REVIEWing main Ideas 15. a. What is the molar mass of an element? b. To two decimal places, write the molar masses of 7. a. What are isotopes? carbon, neon, iron, and uranium. b. How are the isotopes of a particular element alike? c. How are they different? 16. Suppose you have a sample of an element. a. How is the mass in grams of the element converted to amount in moles? b. How is the mass in grams of the element converted to number of atoms? 86 Chapter 3  Chapter review Practice Problems Mixed Review 17. What is the mass in grams of each of the following? REVIEWing main Ideas (Hint: See Sample Problems B and E.) a. 1.00 mol Li 24. Determine the mass in grams of each of the following: b. 1.00 mol Al a. 3.00 mol Al c. 1.00 molar mass Ca b. 2.56 × 1024 atoms Li d. 1.00 molar mass Fe c. 1.38 mol N e. 6.022 × 1023 atoms C d. 4.86 × 1024 atoms Au f. 6.022 × 1023 atoms Ag e. 6.50 mol Cu f. 2.57 × 108 mol S 18. How many moles of atoms are there in each of the g. 1.05 × 1018 atoms Hg following? (Hint: See Sample Problems C and D.) a. 6.022 × 1023 atoms Ne 25. Copy and complete the following table concerning b. 3.011 × 1023 atoms Mg the properties of subatomic particles. c. 3.25 × 105 g Pb d. 4.50 × 10‑12 g O Mass Actual Relative Particle Symbol number mass charge 19. Three isotopes of argon occur in nature—​  36 ​18​Ar,​  38 ​18​Ar, 40 and​  18 Ar. Calculate the average atomic mass of argon ​ ​ Electron to two decimal places, given the following relative Proton atomic masses and abundances of each of the isotopes: Neutron argon-36 (35.97 u; 0.337%), argon-38 (37.96 u; 0.063%), and argon-40 (39.96 u; 99.600%). 26. a. How is a unified atomic mass unit (u) related to the mass of one carbon-12 atom? 20. Naturally occurring boron is 80.20% boron-11 b. What is the relative atomic mass of an atom? (atomic mass = 11.01 u) and 19.80% of some other isotopic form of boron. What must the atomic mass of 27. a. What is the nucleus of an atom? this second isotope be in order to account for the b. Who is credited with the discovery of the atomic 10.81 u average atomic mass of boron? (Write the nucleus? answer to two decimal places.) c. Identify the two kinds of particles that make up the nucleus. 21. How many atoms are there in each of the following? a. 1.50 mol Na 28. How many moles of atoms are there in each of the b. 6.755 mol Pb following? c. 7.02 g Si a. 40.1 g Ca b. 11.5 g Na 22. What is the mass in grams of each of the following? c. 5.87 g Ni a. 3.011 × 1023 atoms F d. 150 g S b. 1.50 × 1023 atoms Mg e. 2.65 g Fe c. 4.50 × 1012 atoms Cl f. 0.007 50 g Ag d. 8.42 × 1018 atoms Br g. 2.25 × 1025 atoms Zn e. 25 atoms W h. 50 atoms Ba f. 1 atom Au 29. State the law of multiple proportions, and give an 23. Determine the number of atoms in each of the example of two compounds that illustrate the law. following: a. 5.40 g B 30. What is the approximate atomic mass of an atom if its b. 0.250 mol S mass is c. 0.0384 mol K a. 12 times that of carbon-12? d. 0.025 50 g Pt ​ 1 ​that of carbon-12? b. _ 2 e. 1.00 × 10‑10 g Au 31. What is an electron? Chapter Review 87 Chapter review 38. Trace the development of the electron microscope, CRITICAL THINKING and cite some of its many uses. 32. Organizing Ideas Using two chemical compounds as 39. The study of atomic structure and the nucleus an example, describe the difference between the law produced a new field of medicine called nuclear of definite proportions and the law of multiple medicine. Describe the use of radioactive tracers to proportions. detect and treat diseases. 33. Constructing Models As described in Section 2, the structure of the atom was determined from observations made in painstaking experimental ALTERNATIVE ASSESSMENT research. Suppose a series of experiments revealed that when an electric current is passed through gas at 40. Observe a cathode-ray tube in operation, and write a low pressure, the surface of the cathode-ray tube description of your observations. opposite the anode glows. In addition, a paddle 41. Performance Assessment Using colored clay, build a wheel placed in the tube rolls from the anode toward model of the nucleus of each of carbon’s three the cathode when the current is on.