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fEfGl2c,6a Atom: From Philosophical ldea to Scientific Theory The When you crush a lump of sugar, you can see that it is made up of many smaller sugar particles. You may grind these particles into a very fine powder, but each tiny piece is still sugar. Now suppose you mix the sugar powder into water. The tiny particles seem to disappear. Yet if you were to taste the solution, you'd know that the sugar is still there. W law of conservation o{ mass law ol definite proportions law of multiple p.opodions Observations like these led people to wonder about the nature of matter. Can matter be divided into piecbs forever or is it made of miniature pieces that cannot be divided at all? The particle theory of matter was supported as early as 400 B.C. by certain Greek thinkers, such as Democritus. He called nature's basic particle an atom, based on the Greek word meaning "indivisible." On the other hand, Aristotle did not believe in atoms. He thought that all matter was continuous. He lived in the generation after Democritus, and his opinion was accepted for nearly 2000 years. The opinions of Aristotle and Democritus were not based on experimental evidence. The discussion remained a philosophical one until the eighteenth century. Then scientists began to gather evidence favoring the atomic theory of matter. Three basic laws describe how matter behaves in chemical reactions. By the late 1700s, chemists agreed that elements cannot be broken down further by ordinary chemical means. They also agreed that elements combine to form compounds that have different properties from the elements that form them. They did not agree on what makes up elements, or if a compound always has the same ratio of elements in it. Sugar seerFs to disappear when it is mixed with water. Ql critical Thinldng 1. Interpret Why are the opinions of Aristolle and Democritus not considered scientific theories? ATOMS: THE EUILDING BLOCKS OF MATTER 69 Law of conservation Mass is neither created nor destroyed during ordinbry chemical reactions or physical changes. of mlss Lew of definite proportions Law of multiple proportions A compound contains the same elements in exactly the same proportions regardless of sample size or source of the compound. If two or more 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 is a ratio of small whole numbers' Toward the end of the eighteenth century scientists made several discoveries about chemical teaclions. A chemical reaction is the change of a substance or substances into one or more new substances. Using improved equipment, scientists made more exact measurements before and after reactions than ever before. In the process, they discovered some basic principles, yhich are summarized in the table' Law of Conservation of Mass Chemists measured the mass of substances before and after a reaction. The total mass of the products was always equal to the total mass of the reactants. From this evidence, chemists deduced that matter cannot be duri a reaction. a scientific law known created or as the trr* of conservatiou Law of Definite Proportions Chemists measured the mass of two elements before forming a compound with the elements. They discovered that the compound always contained the same ratio of the elements' no matter how the compound was formed. From this evidence, chemists deduced that all compounds have a fixed composition that from samole to sam le, a law known as the does not law of definite proPortions. Law of Multiple Proportions Chemists also worked with multiple compounds made from the same two elements- For example, carbon and oxygen form carbon monoxide and carbon dioxide. In carbon monoxide, there is 1.00 g of carbon for every 1.33 g of oxygen. In carbon dioxide, there is 1.00 g of carbon for every 2.66 gof oxygen' The ratio of the mass of the oxygen in the two compounds is 1 to 2' For any two such made of the same two elements, chemists found a ihe masses of the variable element via imole ratio rela this law of multiple ProPortions. 70 CHAPTER 3 Each of these salt crystals contains exactly 39.34% sodium and 60.667o chlorine by mass. sentence. The in anY products the of total mass to is equal reaction chemical 2. Complete this Compounds <ontain atomr in whole-number ratlos. In 1808, an English schoolteacher named John Dalton proposed an explanation for the three newly discovered laws He reasoned that elements were composed of atoms and that only whole numbers of atoms can combine to form compounds. His theory is summarized in the table below. l. 2. 3. 4, 5. All matter is composed of extremely small particles called atoms. Atoms of a given element are identical in size, masg and other properties. Atoms of different elements differ in these properties. Atoms cannot be subdivided, created, or destroyed. Atoms of different elements combine in simple whole-nurnber ratios to form chemical compounds. In chemical reactions, atoms are combined, separated, or rearranged. This theory provides an explanation for the law of conservation of mass during a chemical reaction. According to Statement 3, atoms cannot be divided, created, or destroyed. According to Statement 4, atoms form compounds in simple whole-number ratios. The same number of atoms is present before and after a compound forms or breaks apart_ 'o.o:- ,.:O-O Carbon. C Masg x O Massy Oxygen, Carbon monoxide, CO Massx+Massy r. Carbon monoxide, CO Carbon, Mass x Massx+Massy C In both reactions shown here. the total mass stays the same during the reaction because the mass of a carbon atom and the mass of an oxygen atom are fixed. Oxygen, O Mass y Which statement in Dalton's atomic theory implies that an atom of gold is exactly the same as any other atom of gold? ATOMS: THE BUtLDtNG BLOCKS OF MATTER '71 o.o=o (a) Carbon, C Oxygen, O Carbon monoxide, CO orygen, o orygen, o carbon dioxide, co2 (a) CO is always cornposed of one C atom and one O atom. (b) CO2 rnolecules are always composed of one C atom and two O atoms The same number of CO, molecules contain twice as many O atom$ 'o.o.O=o carbon, c Dalton's theory also provides an explanation for the law of definite proportions and the law of multiple proportions. . Statement 4 implies that a compound is always formed using atoms in the same whole-number ratio. Because an atom has a fixed masE it also follows that using twice as many atoms of an element will result in a cornpound containing twice the mass of that element. For example, carbon dioxide molecules always contain two oxygen atoms for every atom of carbon. Carbon monoxide always contains one oxygen atom for every atom of carbon. So carbon dioxide will always have twice as many oxygen atoms as carbon monoxide for every atom of carbon. Atohs can be ruHMded lnto rmallet Partklet. Dalton turned Democritus's idea abottt atoms into a scientific theory that could be tested by experiment. 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. And, as you will see in Section 3 of this chapter, a given element can have atoms with different masses However, atomic theory has not been discarded. Instead, has been modified to explain the new observations The following important concepts remain unchanged. it . A[ matter is composed of atoms. . Atoms of any one element differ in properties from atorns of another element. Ol ctiti*t rhinking 4. Infer When scientists discovered that atoms are composed of smaller particles, why didn't they reject atomic theory? i:r72: CHAPTER 3 @ VOCABULARY l. What chemical laws can be explained by Dalton s atomic theory? REVIEW 2. List the five main points of Dalton's atomic theory. 1. 2. 3. 1. 5. Critical Thinking 3. AIlAtfAilG lllFORtAIlOll Three compounds containing potassium and orygen are compared. Analysis shows that for each 1..00 g of q the compounds have 1.22 9,2.44 g, and 4.89 g of K, respectively. Show how these data support the law of multiple proportions, ATOMS: THE EUILDING BLOCKS OF MAffER ffi Elgor The Structure the Atom of The atomic theory proposed by John Dalton stated that atoms are indivisible. This idea was proven incorrect by the end of the nineteenth century. It became clear that atoms are actually cornposed of several basic types of particles. The number and arrangement of these particles determine the properties of the atom. nuclear lorces The atom is now defined as the smallest particle of anelementthut.e@ @ons. Each .egion .ontuins different types of particles, called sabato mic particles. Tlte nucleus is a very small region located at the center of the atom. The nucleus includes at least one positively charged particle called a proton and usually one or more neutral particles called neutrons. Surrounding the nucleus is a much larger region that contains negatively charged particles called electrons. Atoms contaln posltlve and negatlve partlcles. The electron was the first subatomic particle to be discovered. In the late 1800s, many experiments were performed in which electric current was passed through various gases. A gas with the same pressure as the air at Earth's surface is a poor conductor of electricity. For that reason, the scientists made sure to keep the gases in their experiments at very low pressures. For their experiments, scientists made glass tubes called cathode-ray tubes, and filled them with low-pressure gas. Metal disks were placed on either side of the tube. One disk, the cathode, was given a positive charge. The other disk, the anode, was given a negative charge. t4 CHAPTER 3 1. Draw a model showing the two regions of an atorn in the space below. I-abel the riucleus and the electron region. Cathode Rays and Electront Scientists discovered that the surface of a cathode-ray tube glowed when electric current was passed through the tube. They hypothesized that the glow was caused by a stream of particles, called a cathode ray, that traveled from the cathode to the anode. They also found that cathode rays could be deflected by a magnet or away from a negatively charged object. This led to the hypothesis that the particles in a cathode ray are negatively charged. Voltage 50urce Gas at low pressure \ "- -,-*_rq:}--- -. Cathode (metal disk) (a) Experiments carried out by English physicist Joseph John Thomson in 1897 supported this hypothesis. He was able to calculate the ratio of the charge of the particles to the mass of the particles in a cathode ray. He found that this ratio was the same. no matter what metals were used in the cathode and anode. thglatig a!!e rl!eye!!_tLheThomson concluded that all cathode rays are composed of identical negatively charged particles called electrons. The atoms in the cathode-ray experiments above were releasing electrons. This was evidence that atoms are divisible and that electrons are present in different types of atoms. (a) A simple cathode-ray tube. (b) A magnet above a cathode-ray tube deflect! the beam downward. showing that the particles in the beam must have a negative charge. Charge and MaJs of the Electron Thomson's experiments also revealed that the eiectron has a very large charge-to-mass ratio. In 1909, the American physicist Robert A. Millikan was able to measure the charge of the electron. Scientists used this information to determine the mass of an electron. They found that an electron has about one two-thousandth the mass of the smallest known atom. Thomson proposed a plum pudding model to explain the properties of the atom known at the time. Because atoms are electrically neutral, he proposed that the electrons were balanced by a "pudding" of positive charge. The electrons were embedded within this positively-charged material. The region of positive charge was also thought to contain most of the mass of the atom, since the electron has so little mass. $ conxecr Today. cxperiments have determined that the electron has a mass of9.1o9 x 1o-rrkg.This is 1/1837 the mass of the smallest type of hydrogen atom. 2. Sketch the plum pudding model proposed by Thomson. t-abel the electrons and the region of positive charge. ATOMS: THE EUILDING ELOCKS OF MATTER 75 More detail of the structure of atoms was discovered by New Zealander Emest Rutherford and his associates Hans Geiger and Ernest Marsden. They bombarded a piece of gold foil with fast-moving alpha particles, which are positively charged particles with four times the mass of a hydrogen atom. They expected the beam to pass through the foil with a very slight deflection because the mass and charge were evenly distributed in the gold foil. They were surprised when about 1 in 8000 particles deflected backwards toward the source. (a) Geiger and Marsden bombarded a thin piece of gold foil with a beam of alpha particles. (b) Some of the particles were deflected back toward their source. Rutherford hypothesized that small, densely packed bundles of matter with a positive charge must have caused the backwards deflections. The bundles had to be small because so few of the particles bounced backwards. Rutherford used the term nucleus to describe each bundle of matter. Rutherford had discovered that the volume of the nucleus was very small compared to the total volume of an atom. The source of the positive charge of an atom had been discovered. Rutherford's student, Niels Bohr, later discovered the location of the electrons in an atom. 3. What is the nucleus of an atom? 76 CHAPTER 3 e..- or Posti.re I l nanictes I Most particles passed through the gold foil undisturbed. A small number were deflectcd by the nucleus. A nucleus contains protons and neutrons. With one exception, all atomic nuclei are made of two kinds of particle$ 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 has no charge, and, like an atom, is electrically neutral. Many words derived from l-atin that end with -&t form plurals by changing the ending to -i. ThuE the plural of nucleus is nuclei arl.d the plural of radius rs radii. The one atomic nucleus that lacks a neutron is that of the simplest hydrogen atom. Its nucleus is a single proton with a single electron moving around it.A proton has a mass of I.673 x 1027 kg, which is 1836 times greater than the mass of an electron. Therefore, a proton has nearly all of the mass in the simplest hydrogen atom. The mass of a neutron is 1.675 x lTti kg, which is slightly larger than the mass of a proton. The nuclei of atoms of different elements differ in the number of protons they possess. Therefore, the number of protons determines an atom's identity. For every proton an atom has in its nucleus, the same number of electrons surrounds the nucleus. Physicists have discovered other subatomic particleq but they have little effect on the chemical properties of matter. The properties of electrons, protons, and neutrons, are summarized in the table below. 4. What quantity determines the identity of an atom? Relative Symbols electric charge Electron "-, _\" -1 0.000 5486 9.109 x 10-31 Proton p*,lH +1 t.007 276 1.673 x Io-27 1.008 665 1.675 x \0-27 Particle Neutron Mass Relative number mass (u*) "",lon *1 u (unified atomic mass unit) = 1.660 540 x Actual mass (kg) 10-27 kg ATOMS: THE EUILDtNG BLOCKS OF MATTER 77 Forces ln the Nucleus Generally, particles that have the same electric charge repel one another. Therefore, you might expect a nucleus with more than one proton in it to be unstable. However, a force exists between two protons that overcomes the electric force trying to push them apart. This force only acts when two protons are very close to one another. A similar force acts when two neutrons are very close together, or when a neutron and a proton are very close together. Together, these short-range proton-proton, neutron-neutron, and proton-neutron forces are called nuderr forces. These forces allow atoms with up to 83 positivelycharged protons in the same nucleus to be stable. The radll of atoms are exprersed ln plcometers. Because the nucleus is so small. the size of an atom is determined by the size of the region in which electrons are present. This region is sometimes thought of 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 edge - of the electron cloud. Because atomic radii are so small, they are expressed in a unit that is mote convenient for the sizes of atoms. This unit is called the picometer. Anorher unit, called lhe unified atomic mass unit, or u, is used to express the mass of atoms. 1 pm 1 u - = 10-lo cm 1.660 540 x 10-27 kg - 10-12 m To get an idea of how small a picometer is, consider that 1 cm is the same fractional part of 1000 km (about 600 mi) as 100 pm is of 1 cm. Atomic radii range from 40 pm to 270 pm across. Atomic nuclei have a much smaller radius, about 0.001 pm. Atomic nuclei are also incredibly dense, with a density of about 2 x 10la g/cm3. 0l ctiti*t Thinldng s. Calculate Verify the value for the density of an atomic nucleus given above for a spherical atom with a mass of 1 u. Recall that the volume of a sphere is given bY 78 CHAPTER 3 , :4{rt. Q6 conr.ficr In physics, there are four known fundamental forces that describe how matter interacts, These forces are the eleclromagnetic force, the gravitational force, the strong nuclear force. and the weak nuclear force. @ VOCABULARY t. Define each of the following: a. atom b. neutron nEvlEw 2. Describe one conclusion made by each scientist that led to the development of the current atomic theory. a. Thomson b. Millikan c. Rutherford 3. Compare the three subatomic particles in terms of location in the atom, masq and relative charge. tL Why is the cathode-ray tube shown earlier in this section connected to a vacuum pump? Critical Thinking 5. EVAIUATII{G lDEAlS Nuclear forces are said to hold protons and neutrons together. What is it about the composition of the nucleus that requires the concept of nuclear forces? ATOMS: THE BUILDING SLOCKS OF MAffER S -:!.sF.*L.*qs.i€i*{!F*t :.i: :ls:::i.: ailra 00, OA Or -:": .-. .: Counting Atoms Neon gas only makes up 0.002olo of the air you breathe. Yet there are 5 x 1017 atoms of neon in each breath you take. In most experiments, atoms are too small and numerous to track individually. Instead, chemists make calculations that take into account the properties of large groups of atoms. @ atomic number isotope mass number nuclide unified atomic mass unil average atomic mass mole All atoms of an element must have the same number of protonr, but not neutronJ. Avogadro's number molar mass All atoms are composed of the same basic particles. Yet all atoms are not the same. Atoms of different elements have different numbers of protons. Atoms of the same element all have the same number of protons. The atomic nmber (Z) of an element is the number of protons of each atom of that element. Turn to the large periodic table in Section 2 of the chapter "The Periodic l-aw." The periodic table square for lithium is also shown at the right. An element's atomic number is indicated above its symbol. Notice that the elements are placed in order in the periodic table according to the atomic number. At the top left is hydrogen, H, with an atomic number of 1. Next in order is helium, He, with an atomic number of 2. The next row of the periodic table includes the elements with the atomic numbers 3, 4, 5, and so on. The atomic numbers give the number of protons in an element. So all atoms of hydrogen have one proton, all atoms of helium h4ve two protons, and so on. The atomic number also identifies an element. If you ' want to know which element has atomic number 4f, you can look at the periodic table for the box with a"47" at the top. Silver, Ag, is the correct element. You then know that all silver atoms have 47 protons. Since atoms are electrically neutral, you also know that all silver atoms must also have 47 electrons. 80 CHAPTER 3 3 Li Lithium 6"941 lHel2 sl This periodic table entry shows that the atomic number of lithium is 3. 1. How many protons does every atom of hydrogen have? 2. How many protons atom of lithium have? does every Iiotopes The simplest atoms are those of hydrogen. All hydrogen atoms have only one proton. However, like many naturally occurring elements, hydrogen atoms can have different numbers of neutrons. Three types of hydrogen atorns are known. The most common type of hydrogen is sometimes calle d protiwn. It accounts for 99.9885% of the hydrogen atoms found on Earth. A protium atom has one electron and a nucleus with one proton. Another form of hydrogen is called deuterium. A deuterium atom has one electron and a nucleus with two particles: a neutron and a proton. Finally,, a tritivm atom is a hydrogen atom with one electron and a nucleus of one proton and two neutrons The names for the types of hydrogen atoms are derived from the number of particles in the nucleus. The. prefix proro- means "first," deutero- means "second," and trito- means "third." The "o" is dropped before the ending -ilm in the names of the hydrogen atoms Protium, deuterium, and tritium are isotopes of hydrogen. b{ol6 are atoms of the same element that have different masses. ls protons and electrons but a different nrrrnfsr of neutrons All isotopes of an atom are electrically neutral. A sample of an element usually consists of a mixture of its isotopes. Tin has 1.0 stable isotopeg more than any other element. Mass Number An isotope is identified by its name, such as Protium protium, or its of an isotope is atomic number and mass The &Ifd!tr the total number of protons and neutrons nucleus For example, the mass number of protium is one because there is one particle, a proton, in its nucleus. thil i[6ii-lti Deuterium 2 Neutrons Tritium 3. Use the definition of mass number to complete the table. : The three hydrogen isotopes are shown. Atomic number (number of protons) Number of neutrons Mass number (protons + neutrons) protium 1 0 I deuterium l1 tritium 12 ATOM|: THE gUtLDtNG BLOCKS OF MATTER :8t* _s+:s:_ ldentifylng lsotopes That the isotopes of hydrogen have their own names is unusual. An isotope is usually identified by specifying its mass number. There are two methods for specifying isotopes. o ln hyphen notation,lhe written with a hyphen after the name of the element. For example, in hyphen notation, tritium would be written as hydrogen-3. c A nuclear symbol is used to show the composition of an isotope's nucleus. A number to the upper left of the element symbol indicates the mass number (protons + neutrons). A number to the lower left of the element symbol indicates the atomic number (number of protons). For example, the nuclear symbol for tritium is lH. Nuclide is a general term for the specific isotope of an glggel,t For example, you could say that deuterium is a hydrogen nuclide. You could also say that hydrogen has three different nuclides. The composition of the three isotopes, or nuclides, of hydrogen and the two isotopes of helium are given in the table below. 0l mass number is criticat Thinking a. Identify A particular isotope of uranium has a nucleus with 92 protons and 143 neutrons. Identify this isotope in two different ways. s. Apply Use the information in the other columns to complete the table on the five nuclides of hydrogen and helium. lsotope 82 Nuclear symbol hydrogen-1 (protium) lH hydrogen-2 (deuterium) fH hydrogen-3 (tritium) lH helium-3 Itt. helium-4 1H. CHAPTER 3 Number Number of protons of electrons Number of neutrons How many protons, electrons, and neutrons are there in an atom of chlorine-37? soluTrolr 1 ANAIYZE Determine what information k given and unknown. Given: name of isotope is chlorine-37 Unknown: number of protong electrons, and neutrons 2 PTAN Write equations for the unknowns in terms of what is given. number of protons = number of electrons mass number : 50LVE atomic number number of neutrons + number of protons, so number of neutrons 3 : : mass number - number of protons Substitute the known values and calculate. Because the name of the isotope is chlorine-31 its mass number is 37 The element chlorine is element 17 on the periodic table, so its atomic number is 17 number of protons = number of electrons number of neutrons - 37 An atom of chlorine-37 has - 17 17 - = 17 20 electrong 17 protons, and 20 neutrons. 4 CHECK YOUR WORK Determine if the answer makes sense. The number of protons in a neutral atom equals the number of electrons. The number of protons plus the number of neutrons equals the mass number because 17 + 20 : 37. A. How many protons, electrons, and neutrons make up an atom of bromine-80? Mass number of bromine-80: Atomic number of bromine: Number of protons: Number of electrons: Number of neutrons = ATOMS: THE EU|LD|NG BLOCKS OF MATTER 83 Atoml< mars lc a relatlve measure. Masses of atorhs expressed in grams are very small. For example, an atom of oxygen-16 has amass of 2.656 x 10-2J g. It is usually more convenient to talk about the relative mass of an atom. The relative atomic mass of an atom is the mass of the atom as compared to the mass of a defined standard. Scientists use a standard measurement for comparing atomic mass. One rrnified atomic mass unit, or u, is exactly l/12 the mass-of a carbon-12 atom. In other words. one u is the nucleus of a carbon-12 atom. The value of u in grams is 1.660 540 x 10-2a g. @e [Q] .oo*,Nc cLosER 6. Deline the two parts ofthe term untfied stomic mass unit separately in your own words: unified atomic mass The mass of a hydrogen-l atom is slightly more than one unified atomic mass unit-1.007 825 u. An oxygen-16 atom has a precise mass of 15.994 91,5 u. Additional atomic masses for the isotopes of certain elements are given in the table below. Isotopes of an element do not differ significantly in their chemical behavior from the other isotopes of the element. So the three isotopes of oxygen all have the same chemical properties despite varying in mass. The table below shows some isotopes that can be found in nature. The natural abundance, or relative amount of each isotope in a sample of an element, is also given in the table. Artificial isotopes can only be created in the laboratory. They have a natural abundance of zero. lsotope Hydrogen-1 Hydrogen.2 Mass number 1 2 Percentage natural abundance 99.9885 0.0115 Unified atomic mass unit (u) 1.007 825 2.01.4 tO2 ' 12 (by definition) Average atomic mass of element {u) t.007 94 Carbon-12 Carbon-13 12 13 98.93 7.07 13.003 355 Oxygen-16 Oxygen-17 Oxygen-18 76 17 18 99.75'l 0.038 0.205 t5.994 915 t6.999 132 17.999 160 15.9994 Copper-63 Copper-65 63 69.15 65 30.85 62.929 601 64.927 794 63.546 1.32.905 447 132.905 Cesium-133 84 CHAPTER 3 133 r00 12.01.07 Aveageatomk mrrl k erdghtedrrrftrc. Chemists have found that a sample of an element will contain the same percentage of each isotope no matter where on Earth the sample is obtained. This percentage is taken into account when calculating the average atomic mass that is reported on the periodic table.The 1qq13ar3odcrl is the wei of the atomic masses of the of an element found in nature. The table on the bottom of the previous page also includes the average atomic mass for each element in the table. 7. Define the two parts of the term average atomic mass separately in your own words: average Calculatlng Average Atomic Mass The average atomic mass of an element is a weighted average. It depends on both the mass of each isotope and the natural abundance of each isotope of the element. atomic mass For example,69.150lo of the copper atoms in a sample are copper-63 atoms. This isotope has an atomic mass of 62.93 u.The remaining 30.85o/o of the sample is copper-65, which has an atomic mass of 64.93 u. The weighted average is the sum of the proportions of the mass that are taken up by each type of atom. 69.15"/" x 62.93 u - 43.52 u of copper-63 30.85"/o x 64.93 u 20.03 u of copper-65 43.52u + 20.03 u - 63.55 u In this book, an element's atomic mass is usually rounded to two decimal places before it is used in a calculation. The value is reasonable because the average atomic mass is closer to the atomic mass of copper-63 than the mass of copper-65, because copper-63 takes up the largest proportion of a natural sample of copper. The value also matches the average atomic mass in the periodic table to four significant figures. S Ctiti."t Thinking 8. Reasoning Why is the average atomic mass usually a decimal number and not a whole number like the mass number? ATOMS: fHE EUILD\NG BLOiKS OF MATTER 85 . A rrlatlve mars rcalc malcs countlng atomt poslble. The unified atomic mass unit allows scientists to compare the mass of an atom to the mass of a standard atom. The average atomic mass gives scientists a value for the average mass of an atom in a sample. Another quantity that scientists also need to determine is the number of atoms in a sample. The Mole The mole is the SI unit for the amount of a substance. The abbreviation for a mole is mol.A nolc is the amount of a substance that contains as many particl$ii ttrEre aFatoms in farm stand, you are purchasing 2 times 12,or 24 ears of corn. Similarly, a chemist might desire 1 mol of carbon or 2.567 mol of calcium. a dozen. If you buy two dozen ears of corn at a Avogadro's Number Chemists have determined that 12 g of carbon-12 contains 6.022 l4L 79 x 1.G3 atoms This means that one rnole of any atoms. This number is substance contains 6.022 I4I79 x called Avogadro's number after Amedeo Avogadro. A nineteenth-century Italian scientist, Avogadro helped explain the relationship between mass and numbers of atoms. lF For most calculations, the number given above is rounded to four significant figures. So, Aslrm nnbs is the substance, one mole of a number of and is given by 6.022 x 1#r. To get a sense of how large this number iE consider this: If every one of the 7 billion people on Earth counted one atom per second, it would take the 7 billion people about 7 million years to count all of the atoms in one mole. g. What is the SI unit for the number of particles in a sample? 10. How many particles does the SI unit for the number of particles represent? CHAPTE R 3 A penny contains about 120 mol of copper atoms, or 2.964 x 10P atoms A sample of 20 copper pennies is a little less than one mole of copper. About one molar mass of (a) carbon (graphit€), (b) iron (nails), and (c) copper (wire) is shown on each balance. Molar Mass The number of particles in one mole of a substance is given by Avogadro's number. The mass of one mole of a substance is called the molr m v written in units of g/molJhe rnolar rn-ass of an element in g/mol is equivalent to the atomic mass of the element as given on the periodic table in u. For example, the molar mass of carbon is 12.01 g/mol, the molar mass of iron is 55.84 g/mol, and the molar mass of copper is 63.55 g/mol. GramlMole Conversions Chemists use molar mass as a conversion factor in chemical calculations. For example, to find the mass of 2 mol of a substance, you would multiply 2 mol by the molar mass of the substance (in grams per mole) to obtain a value in grams. Conversions with Avogadro's Number The diagram below can be used to convert between the mass of a sample, the moles in a sample, and the number of atoms in a sample.The conversion between moles and number of atoms is performed using Avogadro's number. The following sample problems explain how to convert between all three of these quantities. 11. The periodic table gives the average atomic mass of mercury as 200.59 u. What is the mass ol one mole of mercury? rlF-+-aI -rti Mass of cbmGnt in glams The diagram shows the relationship among mass, moleq and number of atoms. ATOMS: THE EUtLDING BLOCKS OF MATTER 87 A chemist produceil 11..9 g of aluminnm' Al. How many moles of aluirinun were produced? soL[moil ' AiIALYZE Determine what information is given and unknown. Given: 11.9 g Al Unknown: amount of Al in moles 2 Determine the equation and conversion factor needed. PIAN To convert from mass to number of moles, divide by the molar mass. This is the same as using the reciprocal of molar mass as a conversion factor, as shown below. gramAl: gramsAl " ff-rluu# = moles Al 3 SOwE Substitute the known values and calculate. The molar mass of aluminum from the periodic table, rounded to four significant figures, is 26.98 g/mol. 11.egAr -tt.sext"#fu - 4 0.2141 molAl CHECK Determine if the answer makes sense. YOUR The answer and the original value have three significant figures. The answer is reasonable because 11.9 g is a little less than half of 26.98 g. WORK B. What is the mass in grams of 2.2$ mol of iron, Fe? Molar mass of iron: 2.25 molFe - 1.25 mol Fe x gFe 88 CHAPTE R 3 How many moles of silver, Ag, are in 3.01 x 104 atoms of silver? soruTtol{ 1 ANATYZE Determine what information is given and unknown. Given: 3.01 x 1023 atoms Ag Unknown: amount of Ag in moles 2 PLAN Determine the equation and. conversion factor needed, To convert from number of atoms to number of moleg divide by Avogadro's number. This is the same as using the reciprocal of Avogadro's number as a conversion factor, as shown below. moles Ag Ag atoms = Ag atoms x Avogadro's number of Ag atoms 3 SOwE moles Ag Substitute the known values and calculate. 3.10 x 1023Ag atoms :3.01 x 4 CHECK YOUR WORK 1023{g-ato-ms 0.500 mol x molAg 6.022xIG3 x Ag $*arfr Determine if the answer makes sense. The answer and the original value have three significant figures. The units cancel correctly and the number of atoms is half of Avogadro's number. c. How many atoms of aluminum, Al, are in 2.i5 mol of aluminum? Molar mass of aluminum: 2.75 molAl - 2.75 molAl x atoms Al ATOMS: THE BUILDING BLOCKS OF MATTER 89 What is the mass in grams of 1.20 x 1d atoms of copper, Cu? sonmox 1 AT{AiYZE Determine what information is given and unknown. Given: 1.20 g x 108 atoms of Cu .Unknown: mass of Cu in grams 2 Determine the equation and conversion factors needed. PIAN As shown in the diagram earlier in this section, converting from number of atoms to mass is a two-step process. To convert from number of atoms to moles, divide by Avogadro's number. To convert from moles to masg multiply by the molar mass. Cu atoms = Cu atoms x : 3 SOLVE grams Cu Substitute the known values and calculate. The molar mass of copper from the periodic table, rounded to four significant figures, is 63.55 g/mol. 63.55 s Cu 1.20 x 108 9u-atoff x 6.022 x lG3 - I.n x 10-14 g Cu 4 9u*to6s g;,olfi) CHECK Determine if the answer makes sense. YOI'R The units cancel correctly to give the answer in gtams. The order of magnitude of the answer is also reasonable because 108 divided by 1024 and then multiplied by 102 is 10-14. WORK D. How many atoms of sulfur, S, are in 4.00 g of sulfur? Molar mass of sulfur: 4.00gS-4.00gSx x S atoms , 90 ^ CHAPTER 3 VOCABULARY 1. Define the term molar mass. REVIEW 2. Complete the table at the right. 3. Write the nuclear symbol and hyphen notation for each of the following isotopes a. mass number of 28, atomic number of 14 b. 26 protons and 30 neutrons sodium-23 calcium-40 !3cu toTns tL To two decimal placeq what is the relative atomic mass and the molar mass of the element potassium, K? Determine the mass in grams of the following: a. 2.00 mol N b. 3.01 x 1023 atoms Cl 5. Determine the amount in moles of the following: a. 12.15 g mol Mg b. 1.50 x 1023 atoms F Critical Thinking 7. Al{AtlrZlilc DATA Beaker contains 222 g of silver. A contains 2.06 mol of copper, and Beaker B a. Which beaker contains the larger mass? b. Which beaker has the larger number of atoms? ATOMS: THE BUtLDtNc BLOCKS OF MATTER 9l CONVERSION FACTORS Most calculations in chemistry require that all measurements of the same quantity (mass, length, volume, temperature, and so on) be expressed in the same unit. To change the units of a quantrty, you can multiply the quantity by a conversion factor' With Sl units, such conversions are easy because units of the same quantity are related by multiples of 10, 100, 1000, or 1 million. Suppose you want to convert a given amount rn milliliters to liters. You can use the relationship 1 L= 1000 mL. From this relationship, you can 1QQQI1 6n6 derive the conversion {actors shown at the right. @ Problem-SoIaing Multiply the given amount by the conversion factor that allows the units from which you are converting to cancel out and the new units to remain' Most conversion factors are based on exact definitiong so significant figures do not measurement apply to these factors. The number of significant figures in a converted depends on the certainty of the measurement you start with. A sample of aluminum has a mass of 0.087 g. What mass in milligrams? Based on SI prefixes, You know that convetsion factors are 1 is the sample's 1000 mg. The possible 1 1000 me ano looomg --ll- g The first conversion factor cancels grams, leaving milligrams' /x 0.087 g = 0.087 looq 4g : sz g A sample of a mineral has 4.0E x 10-s mol of vanadium per kilogram the of masr. How many micromoles of vanadium per kilogram does mineral contain? l : 1 x 10-6 mol. The possible conversion factors are I x lO-n r.nol ""- I l'tol pmot "ndI x 10-6 mol gmol The second conversion factor cancels moles, leaving micromoles' -t 4.08 x 10-s mol:4.08 x 10-s ryAt ##;i - 40'8pmol Practice Problems: Chapter Review practice problems 8-10 and 13-14 92 CH APTE R 3 1L 1000 mL l. Explain each law in terms of Dalton s atomic theory. a. the law of conservation of mass h the law of definite proportions c the law of multiple proportions Z Accorditrg to the law of conservation of masg if element A has al atomic 6xss 6f I rrnifs and element B has an atomic mass of 3 units, what mass would be expected for each conpound? .. AB h A2B3 3. What is an atom? What two regions make up all atoms? * t S"mmarize Rutherford's model of the atom and explain how he developed bis model based on the results of his famous gold-fgil experiment. What are isotopes? How are the isotopes of a particular element alike and how are they different? c Complete the table at the right concerning the tblee isotopes of silicon, Si. t What is the defnition of a mole? How many particles are in one mole, and what is that number called? silkon-28 silicon-29 silicon.30 ATOMS: fHE BUILDING ATOCXS Or UArrtn o 8. What is the mass in grams of each of the following? a, 1.00 mol Li b. 1.00 rnol c. 1.00 molar mass d. 1.00 molar mass e. 6.022 x 7G3 atoms C f. 6.022 x lP atoms Ag 9. How many moles of atoms are there in each of the following? a, 6.022 x 1023 atoms Ne b. 3.011 x 1023 atorns 10. How many moles of atoms are there in each of the following? a. 3.25 x lt. ld g Pb b. 4.50 x 10-12 g O Three isotopes of argon occur in nature: l!er,l!er, and 13Ar. Calculate the average atomic mass of argon to two decimal places, given the following relative atomic masses and abundances of each of the isotopes: argon-36 (35.97 u',O.337"/"). argon 38 (3796 u10.0630/o). and argon-210 (39.96 u; 99.600%). Naturally occurring boron is 80.20"/" boron-l1 (atomic mass of 11.01 u) and 19.807o of sqme other isotopic form of boron. What must the atomic mass of this second isotope be in order to account for the 10.81 u average atomic mass of boron? (Write the answer to two decimal places) CHAPTER 3 t3. What is the mass in grams of each a. 3.011 x lF atoms F b, 1.50 x 10P atoms Mg c. 4.50 l'l x 1012 atoms Cl oftie following? d. 8.42 x 1018 atoms Br e. 25 atoms W L 1 atom Au Determine the number of atoms in each of the following. a. 5.,() g B b. 0.250 mol e. 1.00 x S f. 10-10 g Au 1.50 mol Na c. 0.0384 mol K g. 6.755 mol Pb d. 0.@5 50 g Pt lu 702 g Si AfoMs: fHE autroixe qLocKs oF MAT1ER &