Private: Chapter Two
Key Terms, Key Equations, Summaries, and Exercises (Chapter 2)
Key Terms
- alpha particle (α particle)
- positively charged particle consisting of two protons and two neutrons
- anion
- negatively charged atom or molecule (contains more electrons than protons)
- atomic mass
- average mass of atoms of an element, expressed in amu
- atomic mass unit (amu)
- (also, unified atomic mass unit, u, or Dalton, Da) unit of mass equal to 112 of the mass of a 12C atom
- atomic number (Z)
- number of protons in the nucleus of an atom
- cation
- positively charged atom or molecule (contains fewer electrons than protons)
- chemical symbol
- one-, two-, or three-letter abbreviation used to represent an element or its atoms
- Dalton (Da)
- alternative unit equivalent to the atomic mass unit
- Dalton’s atomic theory
- set of postulates that established the fundamental properties of atoms
- electron
- negatively charged, subatomic particle of relatively low mass located outside the nucleus
- empirical formula
- formula showing the composition of a compound given as the simplest whole-number ratio of atoms
- fundamental unit of charge
- (also called the elementary charge) equals the magnitude of the charge of an electron (e) with e = 1.602 × 10−19 C
- ion
- electrically charged atom or molecule (contains unequal numbers of protons and electrons)
- isomers
- compounds with the same chemical formula but different structures
- isotopes
- atoms that contain the same number of protons but different numbers of neutrons
- law of constant composition
- (also, law of definite proportions) all samples of a pure compound contain the same elements in the same proportions by mass
- law of definite proportions
- (also, law of constant composition) all samples of a pure compound contain the same elements in the same proportions by mass
- law of multiple proportions
- when two elements react to form more than one compound, a fixed mass of one element will react with masses of the other element in a ratio of small whole numbers
- mass number (A)
- sum of the numbers of neutrons and protons in the nucleus of an atom
- molecular formula
- formula indicating the composition of a molecule of a compound and giving the actual number of atoms of each element in a molecule of the compound.
- neutron
- uncharged, subatomic particle located in the nucleus
- nucleus
- massive, positively charged center of an atom made up of protons and neutrons
- proton
- positively charged, subatomic particle located in the nucleus
- spatial isomers
- compounds in which the relative orientations of the atoms in space differ
- structural formula
- shows the atoms in a molecule and how they are connected
- structural isomer
- one of two substances that have the same molecular formula but different physical and chemical properties because their atoms are bonded differently
- unified atomic mass unit (u)
- alternative unit equivalent to the atomic mass unit
Key Equation
average mass=∑𝑖(fractional abundance×isotopic mass)𝑖
Summaries
2.1 Early Ideas in Atomic Theory
The ancient Greeks proposed that matter consists of extremely small particles called atoms. Dalton postulated that each element has a characteristic type of atom that differs in properties from atoms of all other elements, and that atoms of different elements can combine in fixed, small, whole-number ratios to form compounds. Samples of a particular compound all have the same elemental proportions by mass. When two elements form different compounds, a given mass of one element will combine with masses of the other element in a small, whole-number ratio. During any chemical change, atoms are neither created nor destroyed.
2.2 Evolution of Atomic Theory
Although no one has actually seen the inside of an atom, experiments have demonstrated much about atomic structure. Thomson’s cathode ray tube showed that atoms contain small, negatively charged particles called electrons. Millikan discovered that there is a fundamental electric charge—the charge of an electron. Rutherford’s gold foil experiment showed that atoms have a small, dense, positively charged nucleus; the positively charged particles within the nucleus are called protons. Chadwick discovered that the nucleus also contains neutral particles called neutrons. Soddy demonstrated that atoms of the same element can differ in mass; these are called isotopes.
2.3 Atomic Structure and Symbolism
An atom consists of a small, positively charged nucleus surrounded by electrons. The nucleus contains protons and neutrons; its diameter is about 100,000 times smaller than that of the atom. The mass of one atom is usually expressed in atomic mass units (amu), which is referred to as the atomic mass. An amu is defined as exactly 112 of the mass of a carbon-12 atom and is equal to 1.6605 × 10−24 g.
Protons are relatively heavy particles with a charge of 1+ and a mass of 1.0073 amu. Neutrons are relatively heavy particles with no charge and a mass of 1.0087 amu. Electrons are light particles with a charge of 1− and a mass of 0.00055 amu. The number of protons in the nucleus is called the atomic number (Z) and is the property that defines an atom’s elemental identity. The sum of the numbers of protons and neutrons in the nucleus is called the mass number and, expressed in amu, is approximately equal to the mass of the atom. An atom is neutral when it contains equal numbers of electrons and protons.
Isotopes of an element are atoms with the same atomic number but different mass numbers; isotopes of an element, therefore, differ from each other only in the number of neutrons within the nucleus. When a naturally occurring element is composed of several isotopes, the atomic mass of the element represents the average of the masses of the isotopes involved. A chemical symbol identifies the atoms in a substance using symbols, which are one-, two-, or three-letter abbreviations for the atoms.
2.4Chemical Formulas
A molecular formula uses chemical symbols and subscripts to indicate the exact numbers of different atoms in a molecule or compound. An empirical formula gives the simplest, whole-number ratio of atoms in a compound. A structural formula indicates the bonding arrangement of the atoms in the molecule. Ball-and-stick and space-filling models show the geometric arrangement of atoms in a molecule. Isomers are compounds with the same molecular formula but different arrangements of atoms. A convenient amount unit for expressing very large numbers of atoms or molecules is the mole. Experimental measurements have determined the number of entities composing 1 mole of substance to be 6.022 × 1023, a quantity called Avogadro’s number. The mass in grams of 1 mole of substance is its molar mass.
Exercises
2.1 Early Ideas in Atomic Theory
In the following drawing, the green spheres represent atoms of a certain element. The purple spheres represent atoms of another element. If the spheres of different elements touch, they are part of a single unit of a compound. The following chemical change represented by these spheres may violate one of the ideas of Dalton’s atomic theory. Which one?
Which postulate of Dalton’s theory is consistent with the following observation concerning the weights of reactants and products? When 100 grams of solid calcium carbonate is heated, 44 grams of carbon dioxide and 56 grams of calcium oxide are produced.
Identify the postulate of Dalton’s theory that is violated by the following observations: 59.95% of one sample of titanium dioxide is titanium; 60.10% of a different sample of titanium dioxide is titanium.
Samples of compound X, Y, and Z are analyzed, with results shown here.
| Compound | Description | Mass of Carbon | Mass of Hydrogen |
|---|---|---|---|
| X | clear, colorless, liquid with strong odor | 1.776 g | 0.148 g |
| Y | clear, colorless, liquid with strong odor | 1.974 g | 0.329 g |
| Z | clear, colorless, liquid with strong odor | 7.812 g | 0.651 g |
Do these data provide example(s) of the law of definite proportions, the law of multiple proportions, neither, or both? What do these data tell you about compounds X, Y, and Z?
2.2 Evolution of Atomic Theory
The existence of isotopes violates one of the original ideas of Dalton’s atomic theory. Which one?
How are electrons and protons similar? How are they different?
Predict and test the behavior of α particles fired at a “plum pudding” model atom.
(a) Predict the paths taken by α particles that are fired at atoms with a Thomson’s plum pudding model structure. Explain why you expect the α particles to take these paths.
(b) If α particles of higher energy than those in (a) are fired at plum pudding atoms, predict how their paths will differ from the lower-energy α particle paths. Explain your reasoning.
(c) Now test your predictions from (a) and (b). Open the Rutherford Scattering simulation and select the “Plum Pudding Atom” tab. Set “Alpha Particles Energy” to “min,” and select “show traces.” Click on the gun to start firing α particles. Does this match your prediction from (a)? If not, explain why the actual path would be that shown in the simulation. Hit the pause button, or “Reset All.” Set “Alpha Particles Energy” to “max,” and start firing α particles. Does this match your prediction from (b)? If not, explain the effect of increased energy on the actual paths as shown in the simulation.
Predict and test the behavior of α particles fired at a Rutherford atom model.
(a) Predict the paths taken by α particles that are fired at atoms with a Rutherford atom model structure. Explain why you expect the α particles to take these paths.
(b) If α particles of higher energy than those in (a) are fired at Rutherford atoms, predict how their paths will differ from the lower-energy α particle paths. Explain your reasoning.
(c) Predict how the paths taken by the α particles will differ if they are fired at Rutherford atoms of elements other than gold. What factor do you expect to cause this difference in paths, and why?
(d) Now test your predictions from (a), (b), and (c). Open the Rutherford Scattering simulation and select the “Rutherford Atom” tab. Due to the scale of the simulation, it is best to start with a small nucleus, so select “20” for both protons and neutrons, “min” for energy, show traces, and then start firing α particles. Does this match your prediction from (a)? If not, explain why the actual path would be that shown in the simulation. Pause or reset, set energy to “max,” and start firing α particles. Does this match your prediction from (b)? If not, explain the effect of increased energy on the actual path as shown in the simulation. Pause or reset, select “40” for both protons and neutrons, “min” for energy, show traces, and fire away. Does this match your prediction from (c)? If not, explain why the actual path would be that shown in the simulation. Repeat this with larger numbers of protons and neutrons. What generalization can you make regarding the type of atom and effect on the path of α particles? Be clear and specific.
2.3 Atomic Structure and Symbolism
In what way are isotopes of a given element always different? In what way(s) are they always the same?
Write the symbol for each of the following ions:
(a) the ion with a 1+ charge, atomic number 55, and mass number 133
(b) the ion with 54 electrons, 53 protons, and 74 neutrons
(c) the ion with atomic number 15, mass number 31, and a 3− charge
(d) the ion with 24 electrons, 30 neutrons, and a 3+ charge
Write the symbol for each of the following ions:
(a) the ion with a 3+ charge, 28 electrons, and a mass number of 71
(b) the ion with 36 electrons, 35 protons, and 45 neutrons
(c) the ion with 86 electrons, 142 neutrons, and a 4+ charge
(d) the ion with a 2+ charge, atomic number 38, and mass number 87
Open the Build an Atom simulation and click on the Atom icon.
(a) Pick any one of the first 10 elements that you would like to build and state its symbol.
(b) Drag protons, neutrons, and electrons onto the atom template to make an atom of your element.
State the numbers of protons, neutrons, and electrons in your atom, as well as the net charge and mass number.
(c) Click on “Net Charge” and “Mass Number,” check your answers to (b), and correct, if needed.
(d) Predict whether your atom will be stable or unstable. State your reasoning.
(e) Check the “Stable/Unstable” box. Was your answer to (d) correct? If not, first predict what you can do to make a stable atom of your element, and then do it and see if it works. Explain your reasoning.
Open the Build an Atom simulation
(a) Drag protons, neutrons, and electrons onto the atom template to make a neutral atom of Oxygen-16 and give the isotope symbol for this atom.
(b) Now add two more electrons to make an ion and give the symbol for the ion you have created.
Open the Build an Atom simulation
(a) Drag protons, neutrons, and electrons onto the atom template to make a neutral atom of Lithium-6 and give the isotope symbol for this atom.
(b) Now remove one electron to make an ion and give the symbol for the ion you have created.
Determine the number of protons, neutrons, and electrons in the following isotopes that are used in medical diagnoses:
(a) atomic number 9, mass number 18, charge of 1−
(b) atomic number 43, mass number 99, charge of 7+
(c) atomic number 53, atomic mass number 131, charge of 1−
(d) atomic number 81, atomic mass number 201, charge of 1+
(e) Name the elements in parts (a), (b), (c), and (d).
The following are properties of isotopes of two elements that are essential in our diet. Determine the number of protons, neutrons and electrons in each and name them.
(a) atomic number 26, mass number 58, charge of 2+
(b) atomic number 53, mass number 127, charge of 1−
Give the number of protons, electrons, and neutrons in neutral atoms of each of the following isotopes:
(a) 105B
(b) 19980Hg
(c) 6329Cu
(d) 136C
(e) 7734Se
Give the number of protons, electrons, and neutrons in neutral atoms of each of the following isotopes:
(a) 73Li
(b) 12552Te
(c) 10947Ag
(d) 157N
(e) 3115P
Click on the site and select the “Mix Isotopes” tab, hide the “Percent Composition” and “Average Atomic Mass” boxes, and then select the element boron.
(a) Write the symbols of the isotopes of boron that are shown as naturally occurring in significant amounts.
(b) Predict the relative amounts (percentages) of these boron isotopes found in nature. Explain the reasoning behind your choice.
(c) Add isotopes to the black box to make a mixture that matches your prediction in (b). You may drag isotopes from their bins or click on “More” and then move the sliders to the appropriate amounts.
(d) Reveal the “Percent Composition” and “Average Atomic Mass” boxes. How well does your mixture match with your prediction? If necessary, adjust the isotope amounts to match your prediction.
(e) Select “Nature’s” mix of isotopes and compare it to your prediction. How well does your prediction compare with the naturally occurring mixture? Explain. If necessary, adjust your amounts to make them match “Nature’s” amounts as closely as possible.
An element has the following natural abundances and isotopic masses: 90.92% abundance with 19.99 amu, 0.26% abundance with 20.99 amu, and 8.82% abundance with 21.99 amu. Calculate the average atomic mass of this element.
Average atomic masses listed by IUPAC are based on a study of experimental results. Bromine has two isotopes, 79Br and 81Br, whose masses (78.9183 and 80.9163 amu, respectively) and abundances (50.69% and 49.31%, respectively) were determined in earlier experiments. Calculate the average atomic mass of bromine based on these experiments.
Variations in average atomic mass may be observed for elements obtained from different sources. Lithium provides an example of this. The isotopic composition of lithium from naturally occurring minerals is 7.5% 6Li and 92.5% 7Li, which have masses of 6.01512 amu and 7.01600 amu, respectively. A commercial source of lithium, recycled from a military source, was 3.75% 6Li (and the rest 7Li). Calculate the average atomic mass values for each of these two sources.
The average atomic masses of some elements may vary, depending upon the sources of their ores. Naturally occurring boron consists of two isotopes with accurately known masses (10B, 10.0129 amu and 11B, 11.00931 amu). The actual atomic mass of boron can vary from 10.807 to 10.819, depending on whether the mineral source is from Turkey or the United States. Calculate the percent abundances leading to the two values of the average atomic masses of boron from these two countries.
The 18O:16O abundance ratio in some meteorites is greater than that used to calculate the average atomic mass of oxygen on earth. Is the average mass of an oxygen atom in these meteorites greater than, less than, or equal to that of a terrestrial oxygen atom?
2.4 Chemical Formulas
Explain why the symbol for an atom of the element oxygen and the formula for a molecule of oxygen differ.
Explain why the symbol for the element sulfur and the formula for a molecule of sulfur differ.
Write the molecular and empirical formulas of the following compounds:
(a)
(b)
(c)
(d)
Determine the empirical formulas for the following compounds:
(a) caffeine, C8H10N4O2
(b) sucrose, C12H22O11
(c) hydrogen peroxide, H2O2
(d) glucose, C6H12O6
(e) ascorbic acid (vitamin C), C6H8O6
Determine the empirical formulas for the following compounds:
(a) acetic acid, C2H4O2
(b) citric acid, C6H8O7
(c) hydrazine, N2H4
(d) nicotine, C10H14N2
(e) butane, C4H10
Open the Build a Molecule simulation and select the “Larger Molecules” tab. Select an appropriate atom’s “Kit” to build a molecule with two carbon and six hydrogen atoms. Drag atoms into the space above the “Kit” to make a molecule. A name will appear when you have made an actual molecule that exists (even if it is not the one you want). You can use the scissors tool to separate atoms if you would like to change the connections. Click on “3D” to see the molecule, and look at both the space-filling and ball-and-stick possibilities.
(a) Draw the structural formula of this molecule and state its name.
(b) Can you arrange these atoms in any way to make a different compound?
Use the Build a Molecule simulation to repeat Exercise 2.34, but build a molecule with two carbons, six hydrogens, and one oxygen.
(a) Draw the structural formula of this molecule and state its name.
(b) Can you arrange these atoms to make a different molecule? If so, draw its structural formula and state its name.
(c) How are the molecules drawn in (a) and (b) the same? How do they differ? What are they called (the type of relationship between these molecules, not their names)?
Use the Build a Molecule simulation to repeat Exercise 2.34, but build a molecule with three carbons, seven hydrogens, and one chlorine.
(a) Draw the structural formula of this molecule and state its name.
(b) Can you arrange these atoms to make a different molecule? If so, draw its structural formula and state its name.
(c) How are the molecules drawn in (a) and (b) the same? How do they differ? What are they called (the type of relationship between these molecules, not their names)?
Write a sentence that describes how to determine the number of moles of a compound in a known mass of the compound if we know its molecular formula.
Compare 1 mole of H2, 1 mole of O2, and 1 mole of F2.
(a) Which has the largest number of molecules? Explain why.
(b) Which has the greatest mass? Explain why.
Which contains the greatest mass of oxygen: 0.75 mol of ethanol (C2H5OH), 0.60 mol of formic acid (HCO2H), or 1.0 mol of water (H2O)? Explain why.
Which contains the greatest number of moles of oxygen atoms: 1 mol of ethanol (C2H5OH), 1 mol of formic acid (HCO2H), or 1 mol of water (H2O)? Explain why.
Calculate the molar mass of each of the following compounds:
(a) hydrogen fluoride, HF
(b) ammonia, NH3
(c) nitric acid, HNO3
(d) silver sulfate, Ag2SO4
(e) boric acid, B(OH)3
Calculate the molar mass of each of the following:
(a) S8
(b) C5H12
(c) Sc2(SO4)3
(d) CH3COCH3 (acetone)
(e) C6H12O6 (glucose)
Calculate the empirical or molecular formula mass and the molar mass of each of the following minerals:
(a) limestone, CaCO3
(b) halite, NaCl
(c) beryl, Be3Al2Si6O18
(d) malachite, Cu2(OH)2CO3
(e) turquoise, CuAl6(PO4)4(OH)8(H2O)4
Calculate the molar mass of each of the following:
(a) the anesthetic halothane, C2HBrClF3
(b) the herbicide paraquat, C12H14N2Cl2
(c) caffeine, C8H10N4O2
(d) urea, CO(NH2)2
(e) a typical soap, C17H35CO2Na
Determine the number of moles of compound and the number of moles of each type of atom in each of the following:
(a) 25.0 g of propylene, C3H6
(b) 3.06 × 10−3 g of the amino acid glycine, C2H5NO2
(c) 25 lb of the herbicide Treflan, C13H16N2O4F (1 lb = 454 g)
(d) 0.125 kg of the insecticide Paris Green, Cu4(AsO3)2(CH3CO2)2
(e) 325 mg of aspirin, C6H4(CO2H)(CO2CH3)
Determine the mass of each of the following:
(a) 0.0146 mol KOH
(b) 10.2 mol ethane, C2H6
(c) 1.6 × 10−3 mol Na2 SO4
(d) 6.854 × 103 mol glucose, C6 H12 O6
(e) 2.86 mol Co(NH3)6Cl3
Determine the number of moles of the compound and determine the number of moles of each type of atom in each of the following:
(a) 2.12 g of potassium bromide, KBr
(b) 0.1488 g of phosphoric acid, H3PO4
(c) 23 kg of calcium carbonate, CaCO3
(d) 78.452 g of aluminum sulfate, Al2(SO4)3
(e) 0.1250 mg of caffeine, C8H10N4O2
Determine the mass of each of the following:
(a) 2.345 mol LiCl
(b) 0.0872 mol acetylene, C2H2
(c) 3.3 × 10−2 mol Na2 CO3
(d) 1.23 × 103 mol fructose, C6 H12 O6
(e) 0.5758 mol FeSO4(H2O)7
The approximate minimum daily dietary requirement of the amino acid leucine, C6H13NO2, is 1.1 g. What is this requirement in moles?
Determine the mass in grams of each of the following:
(a) 0.600 mol of oxygen atoms
(b) 0.600 mol of oxygen molecules, O2
(c) 0.600 mol of ozone molecules, O3
A 55-kg woman has 7.5 × 10−3 mol of hemoglobin (molar mass = 64,456 g/mol) in her blood. How many hemoglobin molecules is this? What is this quantity in grams?
Determine the number of atoms and the mass of zirconium, silicon, and oxygen found in 0.3384 mol of zircon, ZrSiO4, a semiprecious stone.
Determine which of the following contains the greatest mass of hydrogen: 1 mol of CH4, 0.6 mol of C6H6, or 0.4 mol of C3H8.
Determine which of the following contains the greatest mass of aluminum: 122 g of AlPO4, 266 g of Al2Cl6, or 225 g of Al2S3.
Diamond is one form of elemental carbon. An engagement ring contains a diamond weighing 1.25 carats (1 carat = 200 mg). How many atoms are present in the diamond?
The Cullinan diamond was the largest natural diamond ever found (January 25, 1905). It weighed 3104 carats (1 carat = 200 mg). How many carbon atoms were present in the stone?
One 55-gram serving of a particular cereal supplies 270 mg of sodium, 11% of the recommended daily allowance. How many moles and atoms of sodium are in the recommended daily allowance?
A certain nut crunch cereal contains 11.0 grams of sugar (sucrose, C12H22O11) per serving size of 60.0 grams. How many servings of this cereal must be eaten to consume 0.0278 moles of sugar?
A tube of toothpaste contains 0.76 g of sodium monofluorophosphate (Na2PO3F) in 100 mL.
(a) What mass of fluorine atoms in mg was present?
(b) How many fluorine atoms were present?
Which of the following represents the least number of molecules?
(a) 20.0 g of H2O (18.02 g/mol)
(b) 77.0 g of CH4 (16.06 g/mol)
(c) 68.0 g of CaH2 (42.09 g/mol)
(d) 100.0 g of N2O (44.02 g/mol)
(e) 84.0 g of HF (20.01 g/mol)