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CHAPTER 2 Atoms and Elements Objectives You will be able to do the following: 1. Given a periodic table, determine the group number for the column in which the element is found. This includes the 1-18 numbering and the common variations. For example, the second column can be numbered 2 or 2A. 2. Given a periodic table, determine the names associated with groups 1 (alkali metals), 2 (alkaline earth metals), 17 (halogens), and 18 (noble gases). 3. Write or identify the characteristics of metals. 4. Given a periodic table, determine whether an element is a metal, nonmetal, or a metalloid (semimetal). 5. Given a periodic table, determine whether an element is a representative (or main-group) element, a transition metal, or an inner transition metal. 6. Given a periodic table, write or identify the number for the period on the table to which each element belongs. 7. Given the name or symbol for an element, identify whether it is a solid, liquid, or gas at room temperature. 8. Write or identify the symbols, charges, and relative sizes of protons, neutrons, and electrons. 9. Write a description of the nuclear model of the atom. Your description should include mention of where the proton, neutron, and electron are found, the relative size of the nucleus compared to the size of the atom, and the modern description of the electron. 10. Write a description of the carbon atom, including a rough sketch representing its electrons. 11. Write an explanation for why electrons aﬀect the chemical characteristics of an atom. 12. Write an explanation for why protons aﬀect the chemical characteristics of an atom. 13. Write an explanation for why neutrons do not aﬀect the chemical characteristics of an atom. 14. Write an explanation for why atoms of the same element can have a diﬀerent number of neutrons. 15. Convert between the atomic number and the number of protons in an atom of an isotope. 16. Given an isotope’s mass number, atomic number, and charge, write its symbol. 17. Given an isotope’s symbol, determine its mass number, atomic number, and charge. 18. Given the number of protons and neutrons in an atom of an isotope, determine its mass number. 19. Given the mass number and the atomic number of an isotope, determine the number of neutrons in an atom of the isotope. 7 8 Chapter 2 Atoms and Elements 20. Given two of the following three, determine the third: (1) the number of protons in an atom, (2) the number of electrons in an atom, and (3) the charge on the atom. 21. Write or identify the diatomic elements (H2, N2, O2, F2, Cl2, Br2, and I2). 22. Write a description of the hydrogen molecule. 23. Write a general description of the structure of the following: the noble gases, hydrogen gas, nitrogen gas, oxygen gas, ﬂuorine gas, chlorine gas, bromine liquid, and iodine solid. 24. Write a brief description of the “sea of electrons” model for metallic bonding. 25. Write or identify the International System of Measurements (SI) standard units and their abbreviations for length, mass, time, temperature, and amount of substance. 26. Write a description of how the unit liter, L, is derived from the SI standard of meter. 27. Write or identify the metric base units and their abbreviations for length, mass, volume, energy, and gas pressure. 28. Convert between the preﬁx, its abbreviation, and its value for the following metric preﬁxes: giga, mega, kilo, centi, milli, micro, nano, and pico. 29. Convert between metric derived units and their abbreviations for the units derived from the SI base units and the metric preﬁxes. (For example, the abbreviation for milligram is mg.) 30. Write the relationship between the SI base units and the units derived from the metric preﬁxes. For example, 103 mm = 1 meter 31. Write a description of the relationship between mass and weight. 32. Write or identify the two factors that cause the weight of an object to change. 33. Write an explanation for why the weight of an object on the moon is less than the weight of the same object on the earth. 34. Write an explanation for why the mass of an object is the same on the moon and the earth. 35. Write the relationship between kilograms and metric tons. 36. Write conversion factors that relate the SI base units and the units derived from the metric preﬁxes. ����� For example, ���� 37. Write the English-metric conversion factors listed on Table 2.9. 38. Write an explanation for why increased temperature usually leads to decreased density for solids and liquids. 39. Write or identify the common units used to describe the density of solids, liquids, and gases. 40. Given a percentage by mass or a percentage by volume, write the conversion factor that comes from it. 41. Identify numbers in a calculation as exact or not exact. 42. Round oﬀ answers to calculations to report the correct signiﬁcant ﬁgures. 9 43. Make the following types of unit conversions using the unit analysis technique. a. Convert from one English unit to another English unit of the same type of measurement; for example, in. to ft. b. Convert from one metric unit to another metric unit of the same type of measurement; for example, mg to kg. c. Convert between metric units and English units of the same type of measurement; for example, qt to mL. d. Convert between mass and volume using density as a conversion factor. e. Convert between a cubic length type volume unit (for example, cm3) and single unit type volume; for example, mL. f. Convert between units of the part and units of the whole using percentage as a conversion factor. 44. Convert between temperature in the Celsius, Fahrenheit, and Kelvin scales. 45. Convert between the deﬁnition and the term for the following words or phrases. Chapter 2 Glossary Group (on the periodic table) All the elements in a given column on the periodic table; also called a family. Family (on the periodic table) All the elements in a given column on the periodic table; also called a group. Alkali metals Group 1 on the periodic table. Alkaline earth metals Group 2 on the periodic table. Halogens Group 17 on the periodic table. Noble gases Group 18 on the periodic table. Representative elements The elements in groups 1, 2, and 13 through 18 (the “A” groups) on the periodic table; also called main-group elements. Main-group elements The elements in groups 1, 2, and 13 through 18 (the “A” groups) on the periodic table; also called representative elements. Transition metals The elements in groups 3 through 12 (the “B” groups) on the periodic table. Inner transition elements The 28 elements at the bottom of the periodic table. Period (on the periodic table) A horizontal row on the periodic table. Atom The smallest part of an element that retains the chemical characteristics of the element. Proton A positively charged particle found in the nucleus of an atom. Electron A negatively charged particle found outside the nucleus of an atom. Neutron An uncharged particle found in the nucleus of an atom. Nucleus The extremely small, positively charged core of the atom. Ion Any charged particle, whether positively or negatively charged. Cation An ion formed from an atom that has lost one or more electrons and thus has become positively charged. Anion An ion formed from an atom that has gained one or more electrons and thus has become negatively charged. 10 Chapter 2 Atoms and Elements Isotopes Atoms that have the same number of protons but diﬀerent numbers of neutrons. They have the same atomic number but diﬀerent mass numbers. Atomic mass unit (u or amu) Unit of measurement for the masses of particles; 1/12 the mass of a carbon atom that has 6 protons, 6 neutrons, and 6 electrons. Atomic number The number of protons in an atom’s nucleus. It establishes the element’s identity. Mass number The sum of the number of protons and neutrons in an atom’s nucleus. Covalent bond A link between atoms that results from their sharing two electrons. Molecule An uncharged collection of atoms held together with covalent bonds. Diatomic Composed of paired atoms. The diatomic elements are H2, N2, O2, F2, Cl2, Br2, and I2. Allotropes Diﬀerent forms of the same element. Value A number and unit that together represent the result of a measurement or calculation. The distance of a particular race, for example, may be reported as a value of 100 meters. Unit A deﬁned quantity based on a standard. For example, in the value 100 meters, meter is the unit. Base units The seven units from which all other units in the SI system of measurement are derived. Mass The amount of matter in an object. Mass can also be deﬁned as the property of matter that leads to gravitational attractions between objects and therefore gives rise to weight. Weight A measure of the force of gravitational attraction between an object and a signiﬁcantly large body, such as the earth or the moon. Matter Anything that has mass and occupies space. Absolute zero Zero kelvins (0 K), the lowest possible temperature, equivalent to −273.15 °C. It is the point beyond which motion can no longer be decreased. Precision The closeness in value of a series of measurements of the same entity. The closer the values of the measurements, the more precise they are. Accuracy How closely a measured value approaches the true value of a property. Mass density Mass divided by volume (usually called density). Signiﬁcant ﬁgures The number of meaningful digits in a value. The number of signiﬁcant ﬁgures in a value reﬂects the value’s degree of uncertainty. A larger number of signiﬁcant ﬁgures indicates a smaller degree of uncertainty. Unit (dimensional) analysis A general technique for doing unit conversions. Conversion factor A ratio that describes the relationship between two units. 11 �� �� � � � �� �� �� �� �� � �� �� � � �� �� �� �� �� �� � � � � � � � �� � �� �� � � � � � �� �� �� � � � � � � � �� �� �� �� �� �� �� �� �� � �� �� �� �� �� �� �� �� �� �� �� �� �� �� � � �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� � � �� �� �� � �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� � �� �� � �� �� �� �� �� �� �� �� �� �� �� �� �� � �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� � �� �� �� �� �� � �� �� �� �� �� �� �� �� �� �� �� �� �� �� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� � �� �� �� �� �� �� �� �� �� �� �� ��� ��� ��� ��� ��� �� �� �� �� �� �� �� �� �� �� �� �� �� �� � �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� ��� ��� ��� � �� � �� � �� �� �� �� �� �� �� �� �� �� Figure 2.1 Periodic Table EXERCISE 2.1 - Periodic Table Complete the following table. Name Symbol Group Metal, Representative Number Solid, Number Nonmetal Element, Transition for Period Liquid, or Metal or Inner or Gas? Metalloid? Transition Metal? Al silicon Ni sulfur F cesium Hg uranium (No group number) Mn strontium 17 4 1B 5 VA metal 14 nonmetal 12 Chapter 2 Atoms and Elements EXERCISE 2.2 - Group Names What is the name of the group on the periodic table for (a) helium, (b) chlorine, (c) magnesium, and (d) sodium? Table 2.1 Some of the Characteristics of the Particles Within the Atom Particle Symbol Relative Mass in grams Mass in atomic Location in the charges mass units atom neutron n or n0 0 1.6750 x 10 −24 g 1.00867 u nucleus proton p or p+ +1 1.6726 x 10 −24 g 1.00728 u nucleus electron e− -1 9.1096 x 10 −28 g 0.000549 u outside nucleus Table 2.2 Symbols for Common Isotopes Most common 1 Aluminum cation, Al3+ 27 3+ hydrogen isotope 1H 13 Al Most abundant isotope 238 Iodine anion, I− 127 – of uranium 92U 53 I Sodium cation, Na+ 23 + Most common oxygen 16 2– 11Na anion, O2− 8O Figure 2.2 Carbon Atom ����������� ����������������������������������� ��������� ����������� ������������������������� ������������������������������������ ������������ ���������������������������������������������������� � ���������������������� ������� ������������������������������������ ���������������������������������������������������� � ������������������������������������������ � ���������������������������������������������������������� �������������������������� ������������������������� 13 ��������� ��������������� �� ���������� ����������� ����������� ������������� ������� �������� �������������� ������� ���������� ���������������� ������������ �� ������ ������������� ������������������� �� �������������� ���������� ����������������� ������������� ���������� �� �� �������������� ���������� �������������� �������� ����������� ����������� ������� ���������� ��������� ���� � ����������� � ��������� �������������� �������������������� ��������� ��������� ������������� ������������ Figure 2.3 Ions ������������������������ ����������������������� ������������������������ ����������������������������� �������� �������� �������� �������� �������� ��������� �������� ���������� ������������������������������ �������������������������������� Figure 2.4 Isotopes You can see an animation that describes the structure of some of the chemical elements at the following Web address: http://www.mpcfaculty.net/mark_bishop/element_properties.htm 14 Chapter 2 Atoms and Elements Summary of New Skills You will be asked to convert between the symbol for an isotope and the isotope’s atomic number, mass number, ionic charge, and its number of protons, neutrons, and electrons. The following describes the steps. 1. If you are given the isotope symbol, follow these guidelines to get the atomic number, mass number, and ionic charge. a. The subscript on the left of the element symbol is the atomic number. b. The superscript on the left of the element symbol is the mass number. c. The superscript on the right of the element symbol is the ionic charge. 2. Follow these guidelines to convert between atomic number, mass number, ionic charge, and the number of protons, neutrons, and electrons in the atom. a. The atomic number and the number of protons are always equal. b. The mass number is the sum of the number of protons and neutrons, so the number of neutrons can be calculated by subtracting the atomic number (the number of protons) from the mass number. c. The charge on an atom is the number of protons minus the number of electrons. ♦ For a uncharged atom, the number of electrons and protons are equal. ♦ For a positive ion, the number of electrons is equal to the number of protons minus the size of the charge. ♦ For a negative ion, the number of electrons is equal to the number of protons plus the size of the charge. EXERCISE 2.3 - Isotope Symbolism Complete the following table. Symbol Atomic Mass Number Number Number Charge number number protons neutrons electrons 59 28 Ni 32 2– 16 S 82 207 80 33 42 33 35 44 36 15 Table 2.3 Standards for the International System of Measurement Type of Standard Abbreviation Deﬁnition Measurement Unit length meter m The distance that light travels in a vacuum in 1/299,792,458 of a second mass kilogram kg The mass of a platinum-iridium alloy cylinder in a vault in France time second s The duration of 9,192,631,770 periods of the radiation emitted in a speciﬁed transition between energy levels of cesium-133 temperature kelvin K 1/273.16 of the temperature diﬀerence between absolute zero and the triple point temperature of water amount of mole mol The amount of substance that contains the substance same number of chemical units as there are atoms in 12 grams of carbon-12 electric current ampere A Current that, if maintained in two straight parallel conductors of inﬁnite length and placed 1 meter apart in a vacuum, will produce a force equal to 2 x 10−7 newton per meter. luminous intensity candela cd The luminous intensity of a black body surface 1/600,000 m2 at the normal melting point of platinum Table 2.4 Derived Units in the International System of Measurements Type of Calculated From Derived unit Redeﬁned Abbreviation Measurement from Standards area square length m2 xxxx xxxx volume cubic length m3 liter = 1 dm3 = 10−3 m3 L or l velocity length per time m xxxx xxxx s acceleration velocity per time m xxxx xxxx s2 force mass times kg m newton N acceleration s2 energy force times kg m2 joule J distance s2 gas pressure force per area kg pascal Pa m s2 16 Chapter 2 Atoms and Elements Table 2.5 Some Base Units and Their Abbreviations for the International System of Measurement Type of Measurement Base Unit Abbreviation Length meter m Mass gram g Volume liter L or l Energy joule J Gas pressure pascal Pa Table 2.6 Metric Preﬁxes Preﬁxes for Large Units Preﬁxes for Small Units Preﬁx Abbreviation Value Preﬁx Abbreviation Value giga G 10 or 1,000,000,000 9 centi c 10 −2 or 0.01 mega M 106 or 1,000,000 milli m 10 −3 or 0.001 kilo k 103 or 1000 micro µ 10 −6 or 0.000001 nano n 10 −9 or 0.000000001 pico p 10 −12 or 0.000000000001 Table 2.7 Common Units and Their Abbreviations Notice that the abbreviation for inch (in.) is the only abbreviation that ends in a period. Type of Unit Abbreviation Type of Unit Abbreviation Measurement Measurement English Mass ton ton Time year yr or year pound lb day d or day ounce oz hour h or hr English Length mile mi or mile minute min yard yd second s or sec foot ft inch in. Temperature Degree °C Celsius English Volume gallon gal Degree °F Fahrenheit quart qt kelvin K pint pt ﬂuid ﬂ oz Energy joule J ounce cubic cu ft calorie cal foot cubic cu in. dietary Cal inch calorie Table 2.8 Comparison of the Mass and Weight of a 143 Pound Person. On Earth Between Earth and Moon On the Moon Mass 65 kg 65 kg 65 kg Weight 637 N ≈O N 1/6 (637 N) = 106 N 17 EXERCISE 2.4 - Metric-Metric Conversion Factors Write conversion factors that include the following metric units. a. joule and kilojoule b. meter and centimeter c. liter and gigaliter d. gram and microgram e. gram and megagram f. pascal and millipascal Table 2.9 English-Metric Unit Conversion Factors Type of Probably most useful Also useful to know measurement to know ������� �������� ��������� �������� length ������� ����� ���� ��� ��� ������� �������� mass ���� ���� ������� �������� volume ����� ��� Table 2.10 Densities of Some Common Substances at 20 °C (unless otherwise stated) Substance Density g/mL Substance Density g/mL air at sea level 0.0012 sodium chloride (salt) 2.16 (or 1.2 g/L) Styrofoam 0.03 sulfur, S 2.07 pine wood 0.4-0.6 glass 2.4-2.8 gasoline 0.70 silicon, Si 2.32 ethanol 0.7893 aluminum, Al 2.702 olive oil 0.92 diamond 3.0-3.5 ice 0.92 titanium, Ti 4.5 water, H2O, at 20 °C 0.998204 Earth (average) 5.25 water, H2O, at 0 °C 0.999840 iron, Fe 7.86 water, H2O, at 3.98 °C 1.00000 lead, Pb 11.34 sea water 1.025 mercury, Hg 13.59 whole blood 1.05 platinum, Pt 21.45 sucrose (white sugar) 1.58 osmium, Os 22.48 bone 1.5-2.0 atomic nucleus ≈1014 sulfuric acid (concentrated) 1.84 black hole (not 20 °C) ≈1016 18 Chapter 2 Atoms and Elements Sample Study TIP-OFF After calculating a number using multiplication and division, you need to Sheet 2.1 round it oﬀ to the correct number of signiﬁcant ﬁgures. Rounding GENERAL STEPS Off Numbers Calculated STEP 1 Determine whether each value is exact or not, and ignore exact values. Using Numbers that come from deﬁnitions are exact. Multiplication Numbers in metric-metric conversion factors that are derived from and Division the metric preﬁxes are exact, such as ����� ���� Numbers in English-English conversion factors with the same type of unit (for example, both length units) top and bottom are exact, such as ������ ���� The number 2.54 in the following conversion factor is exact. ������� ����� Numbers derived from counting are exact. For example, there are exactly ﬁve toes in the normal foot. ������ ������ Values that come from measurements are never exact. We will assume that values derived from calculations are not exact unless otherwise indicated. (With one exception, the numbers relating English to metric units that you will see in this text have been calculated and rounded, so they are not exact. The exception is 2.54 cm/1 in. The 2.54 comes from a deﬁnition.) STEP 2 Determine the number of signiﬁcant ﬁgures in each value that is not exact. All non-zero digits are signiﬁcant. � � � �������� ���������������������� � � 19 Zeros between nonzero digits are signiﬁcant. ����������������������������� � � � �������� ���������������������� � � Zeros to the left of nonzero digits are not signiﬁcant. ��������������������� � � � � ����������������������������������������������� ����� � � ���������������������������������� Zeros to the right of nonzero digits in numbers that include decimal points are signiﬁcant. � � � � � ���������������������� ��������������������� ���������������������� � � � ����������������������������������������� ������������������������������������ Zeros to the right of nonzero digits in numbers without decimal points are ambiguous for signiﬁcant ﬁgures. ����������������������������� � � ������ ������������������������������� � ��������������������������������������������������� ��������������������������� � ������������ � ������������������������������������������� � � ������������� � STEP 3 When multiplying and dividing, round your answer oﬀ to the same number of signiﬁcant ﬁgures as the value containing the fewest signiﬁcant ﬁgures. If the digit to the right of the ﬁnal digit you want to retain is less than 5, round down (the last digit remains the same). ������������������������������������������������� ���������������������������������� 20 Chapter 2 Atoms and Elements If the digit to the right of the ﬁnal digit you want to retain is 5 or greater, round up (the last signiﬁcant digit increases by 1). ������������������������������������������������� �������������������������������������� �������������������������������������������������� ���������������������������������� ������������������������������������������������ ���������������������������������� EXAMPLE See Exercises 2.5, 2.6, and 2.7. Table 2.11 Numbers That Are Exact. General Category More Speciﬁc Category Examples 5 fingers Values from Counting 5 in 1 hand Numbers in English-English 12 in. Deﬁned Values Conversion Factors (with units of the 12 in 1 ft same type of measurement) Numbers in Metric-Metric 103 mm Conversion Factors (with units of the 103 in 1m same type of measurement) Some Numbers in English-Metric 2.54 cm 2.54 in Conversion Factors (rare) 1 in. Values Calculated from 10 calculated from Exact Numbers and not 5 fingers 2 hands Rounded (rare) 1 hand Table 2.12 Numbers That Are Not Exact Category Example Values from 185.0 lb from a measurement measurements Values calculated from ����� numbers that are not ���������� ���������������� ���������� exact �������� Values calculated from 27 students with As numbers that are exact, 33 from x 100 = 33% with As but for which the 82 students total answer is rounded oﬀ 21 EXERCISE 2.5 - Signiﬁcant Figures Identify whether each of the following values is exact or not. If it is not exact, write the number of signiﬁcant ﬁgures it has. a. 8.0 in 8.0 mL (derived from a measurement) b. 80 from 80 desks in a classroom (determined by counting them) 2000 lb c. 2000 in 1 ton ������� d. 453.6 in ���� 103 mg e. 103 in 1g f. 0.1067 in 0.1067 oz (from the mass of a penny calculated from its measured mass of 3.023 g) g. 0.006665 in 0.006665 lb (calculated from the mass in ounces of the penny described in part f.) h. 10 in 10% of the tablet desks in a room are for left handed people (determined by counting 8 left-handed desks and counting 80 desks total and then calculating the percentage) i. 21 from 21% of the desks have initials carved in them (determined by counting 17 desks with initials and counting 80 desks total and then calculating the percentage) j. 6.00 x 103 from the temperature of the surface of the sun, 6.00 x 103 °C. EXERCISE 2.6 - Rounding Off Answers Derived from Multiplication and Division A ﬁrst-class stamp allows you to send letters weighing up to 1 oz. (There are 16 ounces per pound.) You weigh a letter and ﬁnd it has a mass of 10.5 g. Can you mail this letter with one stamp? The unit analysis setup for converting 10.5 g to ounces is below. Identify whether each value in the setup is exact or not. Determine the number of signiﬁcant ﬁgures in each inexact value, calculate the answer, and report it to the correct number of signiﬁcant ﬁgures. ���� ����� ����������������� ������� ���� 22 Chapter 2 Atoms and Elements EXERCISE 2.7 - Rounding Off Answers Derived from Multiplication and Division The re-entry speed of the Apollo 10 space capsule was 11.0 km/s. How many hours would it have taken for the capsule to fall through 25.0 miles of the stratosphere? The unit analysis setup for this calculation is below. Identify whether each value in the setup is exact or not. Determine the number of signiﬁcant ﬁgures in each inexact value, calculate the answer, and report it to the correct number of signiﬁcant ﬁgures. ������� ������ ������� ��� ���� ��� ����� ���� ����������������� ���� ���� ����� ������ ����� ������� ���� ������ Sample Study TIP-OFF After calculating a number using addition and subtraction, you need to Sheet 2.2: round it oﬀ to the correct number of decimal positions. Rounding GENERAL STEPS Off Numbers STEP 1 Determine whether each value is exact, and ignore exact values (see Study Calculated Sheet 2.1). Using Addition STEP 2 Determine the number of decimal places for each value that is not exact. and Subtraction STEP 3 Round your answer to the same number of decimal places as the inexact value with the fewest decimal places. EXERCISE 2.8 - Rounding Off Answers Derived from Addition and Subtraction Report the answers to the following calculations to the correct number of decimal positions. Assume that each number is ±1 in the last decimal position reported. a. 684 - 595.325 = b. 92.771 + 9.3 = EXERCISE 2.9 - Rounding Off Answers The mass of a liquid can be found by ﬁrst weighing a container, adding the liquid to the container, weighing the container and the liquid, and ﬁnding the mass of the liquid by subtracting the mass of the container from the total mass of container and liquid. A container is found to have a mass of 42.6 g. When 10.2 mL of a liquid is added to the container, the mass increases to 50.7 g. What is the density of this substance? The set-up for this problem is below. Do the calculation and report your answer to the correct signiﬁcant ﬁgures. ?g 50.7 g - 42.6 g = mL 10.2 mL 23 TIP-OFF You wish to express a given value in terms of a diﬀerent unit or units. Sample Study GENERAL STEPS Sheet 2.3: STEP 1 State your question in an expression that sets the unknown unit(s) equal to Calculations one or more of the values given. Using Unit To the left of the equals sign, show the unit(s) you want in your answer. Analysis To the right of the equals sign, start with an expression composed of the given unit(s) that parallels in kind and placement the units you want in your answer. If you want a single unit in your answer, start with a value that has a single unit. If you want a ratio of two units in your answer, start with a value that has a ratio of two units, or start with a ratio of two values, each of which has one unit. Put each type of unit in the position you want it to have in the answer. STEP 2 Multiply the expression to the right of the equals sign by conversion factors that cancel unwanted units and generate the desired units. If you are not certain which conversion factor to use, ask yourself, “What is the fundamental conversion the problem requires and what conversion factor do I need to make that type of conversion?” Figure 2.5 provides a guide to useful conversion factors. STEP 3 Do a quick check to be sure you used correct conversion factors and that your units cancel to yield the desired unit(s). STEP 4 Do the calculation, rounding your answer to the correct number of signiﬁcant ﬁgures and combining it with the correct unit. 24 Chapter 2 Atoms and Elements ������������������������ ��������������������� ����������� ������������������� �������������������������� ������� ���������������������������������� ����� ������������������� ������������������ ������� ���������������������������������� ���� ����������������� ���������������� ������� ���������������������������������� ����� ������������������� ������������������� ������������ �������������������� �������������������������� ������������������������������ ���� ������ ���������������������� �������������� �������������������������� �������������� ��������������� ������������������������ ���������������� ���������������������������� ���������������� ����������������� Figure 2.5 Types of Unit Conversions Here is a summary of some of the basic types of conversions that are common in chemistry and the types of conversion factors used to make them. 25 Here are more examples of the most useful types of unit analysis conversions. EXAMPLE 2.1 - Metric-Metric Unit Conversions Convert 4567.36 micrograms to kilograms. Solution When converting from one metric unit to another, convert from the given unit to the base unit and then from the base unit to the unit that you want. ���������������������������������������������� ������������ ��� ���� ����������������������������������������������������������������������� ����� ������ ����� ����������� ������������������������������������������������ EXAMPLE 2.2 - English-Metric Unit Conversions Convert 475 miles to kilometers. Solution The conversion factor 2.54 cm/in. can be used to convert from an English to a metric unit of length. �������������������������������� ������� ������ ������� ��� ���� �������������� �������� ���� ���� ����� ������ ����� �������������������������������� ������������������������������ Memorizing other English-metric conversion factors will save you time and eﬀort. For example, if you know that 1.609 km = 1 mi, the problem becomes much easier. �������� ����������������������������������������������� ���� EXAMPLE 2.3 - Unit Conversions Using Density What is the volume in liters of 64.567 pounds of ethanol at 20 °C? Solution Pound is a mass unit, and we want volume. Density provides a conversion factor that converts between mass and volume. You can ﬁnd the density of ethanol on a table like Table 2.10. It is 0.7893 g/mL at 20 °C. ������� ���� ��� ���������������������������������������������������������������������������������������� ���� �������� ������ 26 Chapter 2 Atoms and Elements EXAMPLE 2.4 - Unit Conversions Using Percentage The label on a can of cat food tells you there are 0.94 lb of cat food per can with 0.15% calcium. If there are three servings per can, how many grams of calcium are in each serving? Solution Note that two phrases in this question can be read as “something per something” and therefore can be used as a unit analysis conversion factors. The phrase “three servings per can” leads to the ﬁrst conversion factor used below, and “0.94 lb of cat food per can” leads to the second. Percentages also provide ratios that can be used as unit analysis conversion factors. Because percentages are assumed to be mass percentages unless otherwise indicated, they tell us the number of mass units of the part for each 100 mass units of the whole. The ratio can be constructed using any unit of mass as long as the same unit is written in both the numerator and denominator. This leads to the third conversion factor in our setup. The fourth conversion factor changes pounds to grams. ����� ������������ ���������� ������� ������������������ ����������� ������� ����� ����������� ���� EXAMPLE 2.5 - Converting a Ratio of Two Units When 2.3942 kg of the sugar glucose are burned (combusted), 37.230 kJ of heat are evolved. What is the heat of combustion of glucose in J/g? (Heat evolved is described with a negative sign.) Solution When the answer you want is a ratio of two units, start your unit analysis setup with a ratio of two units. Put the correct type of unit in the correct position in the ratio. For this problem, we put the heat unit on the top and the mass unit on the bottom. ��� � � � ���������� ����� ���� �������������� ��������� ����������������� ���� ����� EXAMPLE 2.6 - Cubic Length The volume of a hydrogen atom is about 1.4 x 105 pm3. What is its volume in liters? Solution Squared or cubed units can often be converted by thinking about how to convert the single unit and squaring or cubing the conversion factors necessary to convert the single unit. 3 3 1m 102 cm 1L ? L = 1.4 × 105 pm3 = 1.4 × 10 –26 L 1012 pm 1m 103 cm3 27 For each of the following exercises, write the unit analysis set-up, calculate your answer, and report your answer with the correct signiﬁcant ﬁgures and units. EXERCISE 2.10 - UNIT ANALYSIS The average human body contains 13 gallons of water. What is this volume in quarts? EXERCISE 2.11 - UNIT ANALYSIS The diameter of a proton is 2 x 10 −15 meters. What is this diameter in nanometers? EXERCISE 2.12 - UNIT ANALYSIS The mass of an electron is 9.1093897 x 10 −31 kg. What is this mass in nanograms? EXERCISE 2.13 - UNIT ANALYSIS There are 2035 tons of sulfuric acid used to make Jell-O each year. What is this mass in kilograms? EXERCISE 2.14 - UNIT ANALYSIS A piece of Styrofoam has a mass of 88.978 g and a volume of 2.9659 L. What is its density in g/mL? EXERCISE 2.15 - UNIT ANALYSIS The density of blood plasma is 1.03 g/mL. A 70 kg adult has about 2.5 L of blood plasma. What is the mass in kilograms of the blood plasma in this person? EXERCISE 2.16 - UNIT ANALYSIS Pain information is transferred through the nervous system between 12 and 30 meters per second. If a student drops a textbook on her toe, how long will it take for the pain information with a velocity of 18 m/s to travel 6.0 feet to reach the brain? EXERCISE 2.17 - UNIT ANALYSIS An electron takes 6.2 x 10 −9 seconds to travel across a TV set that is 22 inches wide. What is the velocity of the electron in km/hr? 28 Chapter 2 Atoms and Elements EXERCISE 2.18 - UNIT ANALYSIS The mass of the ocean is about 1.8 x 1021 kg. If the ocean contains 0.041% by mass calcium ions, Ca2+, what is the mass in tons of Ca2+ in the ocean? EXERCISE 2.19 - UNIT ANALYSIS While you are at rest, your heart pumps about 5.0 liters of blood per minute. Your brain gets about 15% by volume of your blood. What volume of blood in liters is pumped through your brain in 1.0 hour of rest? EXERCISE 2.20 - UNIT ANALYSIS A normal adult has from 4 to 6 million red blood cells per mm3 of blood. Consider a person with 5.5 L of blood and 5 x 106 red blood cells per mm3 of blood. How many red blood cells does this person have? Figure 2.6 Temperature Scales ������� ������ ���������� ������������� ������ �������� ������ ��������� ��������� ��������� �������������� ���� �������� ����� ������������� ���������� ��� ���������� 29 The following is a summary of the steps for making temperature conversions. STEP 1 Write down the memorized equation for the conversion. Include the units. ������ ���������������������������������������������� ���� ���� ������������������������������� ������ ����������������������������� ����������������������������� STEP 2 Check your equation using the following criteria. • To check when converting between Celsius and Fahrenheit: Do the units cancel to yield the correct unit? Would your equation show that 32 °F equals 0 °C? • To check when converting between the Kelvin and Celsius scales, be sure that your equation will lead to a kelvin value that is larger than the degree Celsius value. STEP 3 Do the calculation and report your answer with the correct signiﬁcant ﬁgures and unit. • Remember to put the subtraction for the degree Fahrenheit to degree Celsius conversion in parentheses when you push the buttons on the calculator. • Be careful with signiﬁcant ﬁgures. EXERCISE 2.21 - Temperature Conversions a. N,N-dimethylaniline, C6H5N(CH3)2, melts at 2.5 °C. What is N,N-dimethylaniline’s melting point in °F and K? b. Benzenethiol, C6H5SH, melts at 5.4 °F. What is benzenethiol’s melting point in °C and K? c. The hottest part of the ﬂame on a Bunsen burner is found to be 2.15 × 103 K. What is this temperature in °C and °F? 30 Chapter 2 Atoms and Elements Having Trouble? The skills in this chapter build on each other. For example, to do unit conversions using unit analysis, you need to be able to write conversion factors, and to write conversion factors, you need to be familiar with units and their abbreviations for diﬀerent types of measurement. Here is a list of the major categories of tasks you need to be able to do in order to work the problems in this chapter. You should go through the list in order and be sure you have mastered each skill before you go on to the next one. You should be able to do the following. 1. Convert between the type of measurement, the SI base unit for that type of measurement, and the abbreviation for the units for length, mass, volume, energy, and gas pressure. See Table 2.5. 2. Convert between the metric preﬁxes, their abbreviations, and their values for the preﬁxes listed on Table 2.6. 3. Convert between the type of measurement, the units for that type of measurement, and the abbreviations for the units for the units listed on Table 2.7. 4. Write metric-metric conversion factors from you knowledge of the metric preﬁxes. See Table 2.8. For example, knowing the milli(m) means 10 −3 leads to the following conversion factor. 103 mm 1m 6. Write the English-metric conversion factors listed on Table 2.9. 7. Write percentage values as conversion factors. For example, the fact that water is 88.81% oxygen leads to the following conversion factor. 88.81 g 100 g H2O 8. Use the dimensional analysis format to work unit conversion problems. Be sure you can use the strategies listed in Steps 2 and 3. These will help you to do more diﬃcult problems later. 9. Use your calculator eﬃciently to calculate answers from dimensional analysis set-ups. This includes knowing how to input numbers described with scientiﬁc notation, knowing how to raise values to a power, and knowing when to use your parentheses buttons. 10. Recognize whether numbers are exact on not. 11. Round your answers to calculations to reﬂect the correct signiﬁcant ﬁgures.

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atoms and elements, atomic mass, atomic number, number of protons, the periodic table, mass number, protons and neutrons, molar mass, carbon atoms, number of electrons, ionic compounds, atomic weight, alkali metals, polyatomic ions, valence electrons

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