Avogadro's Number and the Mole

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  Chemistry

  The Molecular Nature of Matter

  • Neil D. Jespersen, Alison Hyslop(Authors)
  • 2021(Publication Date)
  • Wiley

    (Publisher)

  The fundamental constant for the mole is Avogadro’s con- stant, 6.02214076 × 10 23 units/mole. The allows us to have the equivalency of 1 mole of X ≡ 6.02214076 × 10 23 units of X where the symbol with three horizontal lines indicates a mathematical definition. For example, for atoms of sodium the equivalency is 1 mole of Na = 6.022 × 10 23 atoms of Na For molecules such as nitrogen dioxide, NO 2 , or formula units of the compound, sodium chlo- ride, NaCl, the same ratio holds 1 mole of NO 2 = 6.022 × 10 23 molecules of NO 2 1 mole of NaCl = 6.022 × 10 23 units of NaCl The definition of the mole is especially convenient to use when discussing atoms, mole- cules, or compounds. Because these particles are so small it will be easier to use the mole to describe how much the is in a sample rather than the number of units. Now, when we want to state the amount of the substance, we use the symbol n and the unit is the mole, abbreviated mol. The Mole Concept and the Molar Mass Now that the mole has been defined in terms of the number of units, we can relate the mole to the mass of atoms, molecules, and formulas. Avogadro’s constant is the number of carbon-12 atoms in 12.000000 ± 4.5 × 10 –7 g. This allows us to have these equivalencies 1 mole of 12 C = 6.022 × 10 23 12 C atoms = 12.00 g 12 C If we weigh out 12.00 g of 12 C, then we will have 1 mole of 12 C. From this relationship and the fact that the average atomic masses in the periodic table are relative values, we can deduce that we will have a mole of atoms of any element if we weigh an amount equal to the atomic FIGURE 3.2 The SI logo showing the seven base units, including the mole, and the seven physical constants, including Avogadro’s constant, N A . kg A K cd mol s m SI h e K K cd N A Δv c NOTE Avogadro’s constant was named for Amedeo Avogadro (1776–1856), an Italian chemist who was one of the pioneers of stoichiometry. 118 CHAPTER 3 The Mole and Stoichiometry mass in grams (sometimes called the gram atomic mass).

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  Chemistry

  The Molecular Nature of Matter

  • Neil D. Jespersen, Alison Hyslop(Authors)
  • 2014(Publication Date)
  • Wiley

    (Publisher)

  Just what is that number? After much experimentation the scientific community agrees that the value, to four significant figures, is 6.022 Ž 10 23 . This value has been named Avogadro’s number. Now we can write a very important relationship between the atomic scale and the laboratory scale as 1 mole of X = 6.022 Ž 10 23 units of X The units of our chemicals can be atoms, molecules, formula units, and so on.This means that one mole of xenon atoms is the same as 6.022 Ž 10 23 atoms of Xe. Similarly, 6.022 Ž 10 23 molecules of NO 2 represents one mole of nitrogen dioxide molecules. Practice Exercise 3.1 Practice Exercise 3.2 Practice Exercise 3.3 ■ Avogadro’s number was named for Amedeo Avogadro (1776–1856), an Italian chemist who was one of the pioneers of stoichiometry. Avogadro’s number 3.1 | The Mole and Avogadro’s Number 113 Moles of A Elementary Units of A (atoms, molecules, ions) Grams of Substance A Avogadro’s Number Molar Mass A General sequence of calculations to convert between mass and elementary units of a substance. Arrows indicate which tools apply to each conversion. Using Avogadro’s Number The relationships developed above allow us to connect the laboratory scale with the atomic scale using our standard dimensional analysis calculations as shown in the next two examples. ■ Avogadro’s number is the link between the moles of a substance and its elementary units. If a problem is on the laboratory scale (atoms or molecules are not mentioned) then Avogadro’s number is not needed in the calculation. Example 3.3 Converting from the Laboratory Scale to the Atomic Scale Moles of tungsten Atoms of tungsten Grams of tungsten Tungsten wire is the filament inside most old-style incandescent light bulbs. In a typical light bulb, the tungsten filament weighs 0.635 grams.

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  Foundations of Chemistry

  An Introductory Course for Science Students

  • Philippa B. Cranwell, Elizabeth M. Page(Authors)
  • 2021(Publication Date)
  • Wiley

    (Publisher)

  Instead, it was decided to collect a certain specific number of atoms and molecules together and call this number of atoms or molecules a mole . 3.2.1 The mole The number of atoms or molecules in this fixed amount known as a mole was defined as 6.022 140 76 × 10 23 . The name given to this number is the Avogadro number , and it has the symbol L or N A . It is usually rounded to 6.02 × 10 23 . The quantity of substance that contains 6.02 × 10 23 atoms, molecules, or ions is called a mole, and its symbol is mol . Clearly, this number is huge and incredibly difficult to imagine. To grasp an idea of its magnitude, one mole of footballs would form a planet the size of the earth, and one mole of doughnuts would cover the surface of the earth to a depth of five miles! The reason this number was chosen is that if we take any element and weigh out an amount equal to its relative atomic mass in grams, we will have 6.02 × 10 23 atoms of the element: for example, in 12.0 g of carbon-12, there are 6.02 × 10 23 atoms of carbon-12; in 32.0 g of sulfur, there are 6.02 × 10 23 atoms of sulfur; and in 180.0 g of glucose, there are 6.02 × 10 23 molecules of C 6 H 12 O 6 . One mole of any substance con-tains the same number of particles but has a different mass depending on the masses of the atoms making it up. In the same way, six bananas are heavier than six satsumas, which are heavier than six blueberries (Figure 3.1). Figure 3.1 The same number of different types of fruit have different masses, as do different atoms. Source: Elizabeth Page. The Avogadro number, 6.022 140 76 × 10 23 is known extremely accurately but we will simply use the number to three significant figures in this text, i.e. 6.02 × 10 23 . 74 Amount of Substance A mole, unit mol , is the amount of substance that contains exactly 6.022 140 76 × 10 23 (the Avogadro constant) elementary entities. The term elementary entities can refer to particles such as atoms, molecules, electrons, ions, or any other entity.

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  Basic Concepts of Chemistry

  • Leo J. Malone, Theodore O. Dolter(Authors)
  • 2012(Publication Date)
  • Wiley

    (Publisher)

  C C ASSESSING THE OBJECTIVE FOR SECTION 5-1 5-2 The Mole and the Molar Mass of Elements 151 the best laboratory balance can detect nothing less than 10 -3 g, it is reasonable that we need many atoms at a time to register on our scales. Thus, we must “scale-up” the numbers of atoms so that the amounts are detectable with our laboratory instru- ments. In order to scale-up our measurements, we need an appropriate counting unit for a huge number of atoms. The number of atoms represented by the atomic mass of an element expressed in grams is a unit known as a mole. (The SI symbol is mol.) The following equality expresses the number that one mole represents. 1.000 mol = 6.022 * 10 23 objects or particles This number, 6.022 * 10 23 , is referred to as Avogadro’s number (named in honor of Amedeo Avogadro, 1776–1856, a pioneer investigator of the quantitative aspects of chemistry). Avogadro’s number has been determined experimentally by various methods. The formal definition of one mole concerns an isotope of carbon, 12 C. One mole is defined as the number of atoms in exactly 12 grams of 12 C. This number, of course, is Avogadro’s number. Thus the atomic mass of one mole of any element, expressed in grams, contains the same number of basic particles as there are in exactly 12 grams of 12 C. Avogadro’s number is not an exact, defined number such as 12 in 1 dozen or 144 in 1 gross, but it is known to many more significant figures than the four (i.e., 6.022) that are shown and used in this text. Many common counting units represent a number consistent with their use. On one hand, a baker sells a dozen doughnuts at a time because 12 is a practical number for that purpose. On the other hand, we buy a ream of computer paper, which contains 500 sheets. A ream of doughnuts and a dozen sheets of computer paper are not practical amounts to purchase for most purposes.

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  Chemistry

  Structure and Dynamics

  • James N. Spencer, George M. Bodner, Lyman H. Rickard(Authors)
  • 2011(Publication Date)
  • Wiley

    (Publisher)

  of the mole can be applied to any particle. We can talk about a mole of Mg atoms, a mole of Na + ions, a mole of electrons, or a mole of glucose molecules (C 6 H 12 O 6 ) Each time we use the term, we refer to Avogadro’s number of items. 1 mole of atoms contains 6.02  10 23 Mg atoms. 1 mole of ions contains 6.02  10 23 Na + ions. 1 mole of electrons contains 6.02  10 23 electrons. 1 mole of C 6 H 12 O 6 molecules contains 6.02  10 23 C 6 H 12 O 6 molecules. Once we know the number of elementary particles in a mole, we can deter- mine the number of particles in a sample of a pure substance by weighing the sample. To see how this is done, let’s first consider a process by which objects of known mass are counted by weighing a sample. Suppose that the mass of a dozen balls is found to be 107 grams, as shown in Figure 2.2. If a sample that contains an unknown number of balls has a mass of 178 grams. How many balls are in the unknown sample? We can build two conversion factors from our knowledge of the mass of a dozen balls. Which conversion factor should we use? A technique known as dimensional analysis can guide us to the correct conversion factor. All we have to do is keep track of what happens to the units during the calculation. If the units cancel as expected, the calculation has been set up properly. In this case, we know the mass of the unknown sample and the mass of a dozen balls. We therefore set up the calculation as follows: We can now calculate the number of balls in the sample from the fact that there are 12 balls in a dozen. In this example a dozen is analogous to a mole, and 107 grams/dozen is analo- gous to the molar mass of an element. We can use the logic developed in the example shown above to calculate the number of carbon atoms in a 1-carat diamond.

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  Basics for Chemistry

  • David A. Ucko(Author)
  • 2013(Publication Date)
  • Academic Press

    (Publisher)

  This statement is now known as Avogadro's hypothesis. Furthermore, the particles are not necessarily single atoms. They can be atoms joined together into groups, which Avogadro called molecules. For example, in the hydrogen chloride synthesis mentioned above, the equal volumes of hydrogen and chlorine gas must contain the same numbers of molecules. Furthermore, these molecules must be diatomic (H 2 and Ch) in order to produce twice the volume, and therefore twice the number of molecules, of hydrogen chloride (2HCI). Unfortunately, Avogadro's ideas were ignored for nearly 50 years. They did not begin to catch on until his countryman Stanislao Canniz-zaro presented them at the First International Chemical Congress at Karlsruhe, Germany, in 1860. Today, the number of particles in a mole, 6.02 x t023, is called Avogadro's number in his honor. ASIDE . . . If you stacked Avogadro's number of sheets of paper on top of each other, they would reach from the Earth to a nearby star. depending on the mass of the individual unit. Think of a mole of feathers and a mole of marbles. The number of each is the same (Avogadro's number), but the mole of marbles weighs much more because each marble is heavier than each feather. In the same way, a mole of oxygen atoms and a mole of hydrogen atoms each contains Avogadro's number of atoms, but the mole of oxygen atoms weighs 16 times as much as the mole of hydrogen atoms. The reason is, of course, that each atom of oxygen (16.0 amu) weighs 16 times as much as each hydrogen atom (1.0 amu) because of the greater number of protons and neutrons in the oxygen nucleus. Avogadro's number is the basis for the mole because it makes calculating the mass or weight of one mole very easy.

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  eBook - ePub

  Regents Chemistry--Physical Setting Power Pack Revised Edition

  • Barron's Educational Series, Albert S. Tarendash(Authors)
  • 2021(Publication Date)
  • Barrons Educational Services

    (Publisher)

  Chapter 6 , we will see that the mole has a third face: the volume of a gas under certain specified conditions.

  One mole refers to Avogadro’s number (NA = 6.02 × 1023 ) of particles of anything. For example, 1 mole of silver refers to 6.02 × 1023 atoms of Ag, while 1 mole of CO2 refers to 6.02 × 1023 molecules of CO2 . And 1 mole of slices of pizza? That’s correct, 6.02 × 1023 slices!

  One mole of particles has a special mass associated with it: the formula mass of the substance expressed in grams. For example, 1 mole of H2 O has a mass of 18.00 grams (because its formula mass is 18.00 u). In this context, we refer to 1 mole as the molar mass (also known as the gram-formula mass), whose units are grams per mole (g/mol). In this book, we will use these two terms interchangeably and we will use the symbol ℳ to represent them. If the formula happens to be that of an element, such as calcium, the molar mass will refer to the atomic mass of the element; if the formula represents a molecule or an ionic compound, the molar mass will refer to the formula mass of the substance.

  Problem

  Calculate the molar mass of each of the following:

  1. Ne
  2. Cl2
  3. SO3
  4. KBr

  Solutions

  1. We use the atomic mass of Ne: ℳ = 20.18 g/mol.
  2. We calculate the molar mass of Cl2 : ℳ = 70.91 g/mol.
  3. We calculate the molar mass of SO3 : ℳ = 80.07 g/mol.
  4. We calculate the molar mass of KBr: ℳ = 118.0 g/mol.

  Try It Yourself

  Calculate the molar mass of CaCO3 .

  Answer

  ℳ = 100.1 g/mol

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  4.5 PROBLEMS INVOLVING A SINGLE SUBSTANCE

  We can solve a variety of problems involving a single substance because any substance can be represented by a chemical formula, and any formula can be associated with the mole concept. For example, the formula H2 SO4 can be interpreted as follows: 1 mole of H2 SO4 contains 2 moles of H atoms, 1 mole of S atoms, and 4 moles of O atoms. Similarly, 1 mole of CaCl2 contains 1 mole of Ca2+ ions and 2 moles of Cl–

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  Understanding Basic Chemistry

  The Learner's Approach

  • Kim Seng Chan, Jeanne Tan(Authors)
  • 2014(Publication Date)
  • WSPC

    (Publisher)

  CHAPTER 4

  MOLE CONCEPT, FORMULA, AND STOICHIOMETRY

  In Chapter 3 , we learned that matter is made up of fundamental particles such as an atom, ion, or molecule. But these particles are extremely small objects, both in size and mass. If the mass of a small toothpick is about 1.00 × 10−2 g, the mass of a hydrogen atom (1.67 × 10−24 g) is 1.67 × 1022 times lighter than the mass of the toothpick. Or if your mass is 10 kg, you are about 5.97 × 1024 times lighter than the mass of our planet Earth.

  Atoms and molecules react in specific ratios to form compounds. In the laboratory, however, chemists work with bulk quantities of reactants, which are measured by mass. They need to know the relationship between the mass of a given sample and the number of atoms or molecules contained in that mass of a given sample. So, how do scientists know the number of particles in the mass of a matter in the laboratory? How many ions are present in a tablespoon of salt? How many molecules are present in a dew drop? How many atoms are present in a speck of sand? A standard for counting such small particles is needed!

  4.1 The Mole

  This standard is known as the “mole.” The mole is based upon the carbon-12 isotope. In the beginning, scientists asked the following question: how many carbon-12 atoms are needed to have a mass of exactly 12 g (recall that scientists had already developed the concept of relative atomic mass)? So, what is this number?

  The number is known as the Avogadro’s number, L or NA , in honor of Amedeo Avogadro, though the number was not formulated by him. In fact, he just conceptualized the idea. Thus, L is defined as:

  Careful measurements yield a value of 6.022141 × 1023 mol−1 . It is difficult to imagine how large this number is. Let us try: if you have 6.02 × 1023 one-dollar notes and each day you spend $1,000, you are going to need 6.02 × 1020 days or 1.64 × 1018 years to finish it. The age of Earth is just about 4.54 × 109

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  Chemistry

  With Inorganic Qualitative Analysis

  • Therald Moeller(Author)
  • 2012(Publication Date)
  • Academic Press

    (Publisher)

  23 grains of rice would weigh 13.2 quadrillion tons and fill a cube 146 miles long on each side.

  EXAMPLE 2.4

  How many ozone molecules and how many oxygen atoms are present in 48.00 g of ozone, O3 ?

  The molecular weight of ozone is (3 atoms)(15.999 amu/atom) = 48.00 amu; thus in 48.00 g of ozone there will be an Avogadro’s number of molecules. Each molecule contains three oxygen atoms, so the number of oxygen atoms is

  The 48.00 g sample of ozone contains 6.022 × 1023 molecules and 1.807 × 1024 oxygen atoms.

  The mole . The mole is the most meaningful unit of measure for the amounts of substances that are represented by chemical formulas or that take part in chemical reactions. One mole represents a definite number of particles, or entities. We speak of a mole of ions, a mole of atoms, a mole of electrons, a mole of molecules—theoretically, even a mole of butterflies. The mole is one of the seven basic SI units (Section 1.6 ). Here is the complete SI definition of a mole:

  The mole is the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kg (12 g) of carbon-12.

  Note: When the mole is used, the elementary entities must be specified and may be atoms, ions, electrons, other particles, or specified groups of such particles.

  In other words, as we said above, the mole is an Avogadro’s number of anything.

  The symbol often used for the amount of substance expressed in moles is n and the substance can be specified by writing it as a subscript. For example,

  One mole of hydrogen	n H2 = 1 mole
  One-half mole of calcium atoms	n Ca = 0.5 mole
  Two moles of phosphorus pentachloride	n PCl5 = 2 moles

  In calculations where only one kind of entity is expressed in moles, the subscript is often omitted. The SI system recommends the abbreviation mol for mole. We have chosen to write mole instead.

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  SURVIVAL GDE GENERAL CHEM W/ MATH REVIEW

  • Charles Atwood(Author)
  • 2016(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  Avogadro’s relationship 36 Copyright 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-300 © 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. TIPS The first four modules are foundations of chemistry. Understanding these modules is essential to your chemistry progress. Module 4 Module 1 Module 2 Module 3 A commonly encountered problem for students is deciding where to start on mole problems. If you have trouble getting started, focus on the given information. All of the examples in this module began by using the mass or number of moles stated in the question. You will frequently use some combination of molar masses, Avogadro’s relationship, and mole ratio to solve mole problems. Select which entity to use first by looking at the unit given in the problem then determine, using dimensional analysis, how to cancel that unit. Pay attention to vocabulary! Keep in mind the differences between atoms, ions, and molecules, and pay attention to which of the three the question is asking about. 37 Copyright 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-300 © 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Study Tip #5 1. Read your textbook daily Constantly refresh your memory about chemistry. When you sit down to study leave outside influences behind. Do not look at your cell phone, check Facebook, etc. 2. Do NOT work the practice test or homework over and over! This falsely convinces you that you understand the material when all you are doing is memorizing a set of steps. If your instructor changes the problem you will be lost.

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  General Chemistry I as a Second Language

  Mastering the Fundamental Skills

  • David R. Klein(Author)
  • 2015(Publication Date)
  • Wiley

    (Publisher)

  If we were to dump out the contents of one of these barrels, and then take apart all of the structures, we would have over 36 million individual Lego pieces from one barrel alone. We said before, that our analogy uses individual Lego pieces to represent atoms, and Lego structures to represent molecules. Now we have added a new term: a barrel, which represents the term “mole”. A mole is just a large number (a bar- rel) of molecules. In our Lego analogy, each barrel had 6,022,042 (or 6.022042  10 6 ) Lego structures. Well, it turns out that a mole of molecules is a lot larger than a barrel of Lego structures. The number is actually 17 orders of magnitude larger (100,000,000,000,000,000 times larger). So, there are 6.022042  10 23 molecules in a mole. Since most of our calculations will involve other numbers that have fewer significant figures, let’s make things simpler, and let’s use fewer significant figures. From now on, we will use the number 6.022  10 23 . The “mole” is a very important term. It is the SI unit that is used to measure the number of molecules in a substance. For example, when we measure the num- ber of molecules, we report our answer as 3.72 mol, or 5.3 mol, etc. As we have already discovered, one mole is defined as 6.022042  10 23 molecules. This num- ber is also called Avogadro’s number. It is clearly a VERY large number. The term “mole” is the term that we use to connect our macroscopic world to the world of very small atoms and molecules. EXERCISE 2.10. Count the number of oxygen atoms in 3.45 moles of H 2 SO 4 . Answer: This might seem like simple math, and you might be tempted to do this in your head. But you need to get into the habit of always using the factor-label method to solve the problem. You will see many more problems that are not so easy to do in your head, so you need to get practice using the factor-label method now. In addition, the factor-label method serves as a way to double-check your answer.

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  Chemistry for Today

  General, Organic, and Biochemistry

  • Spencer Seager, Michael Slabaugh, Maren Hansen, , Spencer Seager, Spencer Seager, Michael Slabaugh, Maren Hansen(Authors)
  • 2021(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  (Section 2.4) 5 Use isotope percent abundances and masses to calculate atomic weights of elements. (Section 2.5) 6 Use the mole concept to obtain relationships between number of moles, number of grams, and number of atoms for ele- ments, and use those relationships to obtain factors for use in factor-unit calculations. (Section 2.6) 7 Use the mole concept and molecular formulas to obtain relationships between number of moles, number of grams, and number of atoms or molecules for compounds, and use those relationships to obtain factors for use in factor-unit calculations. (Section 2.7) Rick Loomis/Los Angeles Times/Getty Images Copyright 2022 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. Atoms and Molecules 47 WE INTRODUCED SOME FUNDAMENTAL ideas about matter, atoms, mol- ecules, measurements, and calculations in Chapter 1. In this chapter, these ideas are applied, the mole is defined, and the quantitative nature of chemistry becomes more apparent. A system of symbols is introduced that simplifies the way atoms and molecules are represented. 2.1 Symbols and Formulas Learning Objective 1 Use symbols for chemical elements to write formulas for chemical compounds. In Chapter 1, we defined elements as homogeneous pure substances made up of identical atoms. At least 118 different elements are known to exist. This leads to the conclusion that a minimum of 118 different kinds of atoms exist. Eighty-eight of the elements are natu- rally occurring and therefore are found in Earth’s crust, oceans, or atmosphere. The others are synthetic elements produced in the laboratory.

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