Moles and Molar Mass

11 Key excerpts on "Moles and Molar Mass"

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  eBook - ePub

  Survival Guide to General Chemistry

  • Patrick E. McMahon, Rosemary McMahon, Bohdan Khomtchouk(Authors)
  • 2019(Publication Date)
  • CRC Press

    (Publisher)

  5 An Introduction to Moles and Molar Mass

  I	GENERAL CONCEPTS

  A mole is a counting number; the value of one mole = 6.02214 ×1023 objects. In principle, this counting number can be applied to any countable object; however, in practice, the mole is used only for objects as small as atoms or molecules. One mole of pennies would cover the area of the state of Illinois to a height of about 10 miles.

  COUNTING NUMBERS

  pair = 2	dozen = 12	score = 20	gross = 144
  mole = 6.02214 ×1023

  The mole counting number is based on a specific standard. One mole is defined as equal to a number represented by the exact number of atoms present in exactly 12 grams of the isotope carbon-12. The carbon-12 standard used for the definition of one mole is the same standard used for the definition of an amu. This results in the following relationships:

  The mass of one atom of carbon-12 is exactly 12 amu (by definition).

  The mass of one mole (6.02214 × 1023 ) of carbon-12 atoms is exactly 12 grams (by definition).

  Note that the conversion factor 1.66054 × 10−24 g/amu interconverts grams and amu’s. Calculate the number of amu’s per gram:

  # a m u  i n  1 g r a m

    =  

  1   gram

  1.66054   ×  

  10

  − 24

  g/amu

  =   6

  . 0 2 2 1 4

    ×   1

  0

  2 3

  a m u / g r a m

  The number of atoms (or ions or molecules) in one mole is identical to the number of amu in one gram.

  The molar mass (MM) of an element is defined as the mass of one mole of average atoms of this element.

  The molar mass (MM = the mass of one mole of atoms) of any element is numerically equal to the average atomic mass of the element expressed in gram units; the units of MM = grams/moles.

  Recall that the mass of one average atom of an element is defined as the atomic mass (sometimes called atomic weight) and is listed in the periodic table. The definitions of amu and mole based on carbon-12, as described, produce the result that:

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  eBook - PDF

  Basics for Chemistry

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

    (Publisher)

  column gives the mass in grams of one mole of each substance. This quantity is called the molar mass or molar weight of that substance. It can be defined as: molar mass = one mole 8.3 CONVERTING MOLES TO GRAMS Thus, the molar mass of carbon is 12.0 g/mole, and the molar mass of sodium chloride is 58.5 g/mole. (A pinch of salt, which has a mass smaller than 1 g, contains about 1 0 3 mole, that is, 6 x 10 20 NaCl formula units.) The molar mass is simply the atomic, molecular, or formula weight, in grams. In summary, the mole is a measure of the amount of a substance. 1 A mole contains Avogadro's number (6.02 x 10 2 3 ) of atoms, formula units, or molecules, and 2 has a mass in grams equal to the atomic, formula, or molecular weight of the substance. Small quantities of a substance can be described in terms of the mole if we add appropriate metric prefixes. Millimole for example, means an amount that is 1/1000th of a mole (10~ 3 mole). The mole is very useful in calculations involving quantities of chemical substances. But to carry out laboratory procedures, we must often first convert moles to grams. Chemists seldom use exactly one mole of a substance. Instead, they must be able to measure some multiple or fraction of a mole and convert this quantity into grams. For example, since one mole of sodium chloride weighs 58.5 g, two moles weigh 2.00 moles x 58.5 g/mole = 117 g, three moles weigh 3.00 moles x 58.5 g/mole = 176 g, and so on. Similarly, one-half mole weighs 0.500 mole x 58.5 g/mole = 29.3 g, one-quarter mole weighs 0.250 mole x 58.5 g/mole = 14.6 g, and so on. In each case, to find the number of grams, we simply multiply the number of moles by the molar mass, which is the mass of 1 mole: The molar mass is thus used as a conversion factor in the following examples: number of grams = number of moles x 1 mole 220 mass (g) of 1 mole of substance mass (g) of 1 mole of substance

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  Basic Concepts of Chemistry

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

    (Publisher)

  The molar mass of a compound is the formula weight of the compound expressed in grams and is the mass of Avogadro’s number of molecules or ionic formula units. One important purpose of this chapter is for you to become comfortable with the conversions among moles, mass, and numbers of atoms or molecules. The two conversion factors that are used for this are the molar mass and Avogadro’s number. The formula of a compound implies a mole ratio. It can be used to determine the number of moles, the masses, and the percent composition of each element in a compound. In the reverse calculation, the empirical formula of a compound can be determined from its mass composition or percent composition. One needs to know the molar mass of a compound to determine the molecular formula from the empirical formula. The molecular formula is determined from the percent composition and the molar mass. C H A P T E R S U M M A RY Chapter Problems 173 a. C 4 H 5 b. C 8 H 10 c. 1.44 * 10 23 d. 9.50% ANSWERS TO CHAPTER 5 SYNTHESIS PROBLEM C H A P T E R P R O B L E M S Relative Masses of Particles (SECTION 5-1) 5-1. One penny weighs 2.47 g and one nickel weighs 5.03 g. What mass of pennies has the same number of coins as there are in 12.4 lb of nickels? 5-2. A small glass bead weighs 310 mg and a small marble weighs 8.55 g. A quantity of small glass beads weighs 5.05 kg. What does the same number of marbles weigh? 5-3. A piece of pure gold has a mass of 145 g. What is the mass of the same number of silver atoms? 5-4. A large chunk of pure aluminum has a mass of 212 lb. What is the mass of the same number of carbon atoms? 5-5. A piece of copper wire has a mass of 16.0 g; the same number of atoms of a precious metal has a mass of 49.1 g. What is the metal? 5-6. In the compound CuO, what mass of copper is present for each 18.0 g of oxygen? 5-7. In the compound NaCl, what mass of sodium is present for each 425 g of chlorine? 5-8.

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  Chemistry

  The Molecular Nature of Matter

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

    (Publisher)

  © Envision/Corbis Images The Mole and Stoichiometry Chapter Outline 3.1 | The Mole and Avogadro’s Number 3.2 | The Mole, Formula Mass, and Stoichiometry 3.3 | Chemical Formula and Percentage Composition 3.4 | Determining Empirical and Molecular Formulas 3.5 | Stoichiometry and Chemical Equations 3.6 | Limiting Reactants 3.7 | Theoretical Yield and Percentage Yield 3 108 After reading this chapter, you should be able to: I n this chapter we will learn the fundamentals of chemical calculations called stoichiometry (stoy-kee-AH-meh-tree), which loosely translates as “the measure of the elements.” These calculations are key for success in the chemistry laboratory. You will also find this chapter to be important for future courses in organic chemistry, biochemistry, and almost any other advanced laboratory course in the sciences. Stoichiometry involves converting chemical formulas and equations that represent individual atoms, molecules, and formula units to the laboratory scale that uses milligrams, grams, and even kilograms of these substances, just as the number of M&Ms in the bowl can be measured by weighing the M&Ms.To do this, we introduce the concept of the mole. The mole allows the chemist to scale up from the atomic/molecular level to the laboratory scale, much as a fast-food restaurant scales up the amount of ingredients from a single hamburger to mass-production as in Figure 3.1. Our stoichiometric calculations are usually conversions from one set of units to another using dimensional analysis. To be successful using dimensional analysis calculations we need two things: a knowledge of the equalities that can be made into conversion factors and a logical sequence of steps to guide us from the starting set of units to the desired units. Figure 3.6, at the end of this chapter, is a flowchart that organizes the sequence of conversion steps and the conversion factors used in stoichiometric calculations in this chapter.

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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)

  3 Amount of Substance At the end of this chapter, students should be able to: • Determine relative atomic and molecular masses using the periodic table of the elements • Explain the meaning of the mole and use Avogadro ’ s number to calculate numbers of atoms of elements or molecules of substances in a certain amount in moles • Use the equation relating the amount of substances in moles to mass and molar mass to calculate any one of these parameters knowing the other two • Calculate theoretical and actual percentage yields in chemical reactions • Calculate percentage composition by mass of elements in compounds from the molecular formula and relative atomic masses • Calculate percentage purity of compounds from analytical data relating to percentage composition • Determine the empirical and molecular formula of a compound from its percentage composition by mass • Calculate the concentration of a solution in various units, knowing its composition • Perform calculations to determine how to dilute a concentrated solution to a given molarity • Carry out calculations using titration data to determine the concentration of a solution • Use the molar gas volume to work out the mass of a certain volume of a known gas under standard conditions of temperature and pressure Foundations of Chemistry: An Introductory Course for Science Students , First Edition. Philippa B. Cranwell and Elizabeth M. Page. © 2021 John Wiley & Sons Ltd. Published 2021 by John Wiley & Sons Ltd. Companion website: www.wiley.com/go/Cranwell/Foundations 3.1 Masses of atoms and molecules Atoms join together to make molecules, and molecules react together to make different molecules or join together to make bigger molecules. In making these new substances, scientists need to know how much of one molecule or com-pound will react with another and how much product will be obtained as a result. To achieve this, we need to be able to count molecules or groups of mole-cules.

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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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  Introduction to General, Organic, and Biochemistry

  • Morris Hein, Scott Pattison, Susan Arena, Leo R. Best(Authors)
  • 2014(Publication Date)
  • Wiley

    (Publisher)

  Chemists have chosen the mole (mol) as the unit for counting atoms. The mole is a unit for counting just as a dozen or a ream or a gross is used to count: 1 dozen = 12 objects 1 ream = 500 objects 1 gross = 144 objects 1 mole = 6.022 * 10 23 objects Note that we use a unit only when it is appropriate. A dozen eggs is practical in our kitchen, a gross might be practical for a restaurant, but a ream of eggs would not be very practical. Chemists can’t use dozens, grosses, or reams because atoms are so tiny that a dozen, gross, or ream of atoms still couldn’t be measured in the laboratory. KEY TERMS Avogadro’s number mole molar mass PhotoDisc, Inc./Getty Images Oranges can be “counted” by weighing them in the store. Units of measurement need to be appropriate for the object being measured. Royalty-Free/Corbis Images Copyright John Wiley & Sons, Inc. Tom Pantages Eggs are measured by the dozen. Pencils are measured by the gross (144). Paper is measured by the ream (500 sheets). LEARNING OBJECTIVE 7.1 • The Mole 123 The number represented by 1 mol, 6.022 * 10 23 , is called Avogadro’s number, in honor of Amadeo Avogadro (1776–1856), who investigated several quantitative aspects in chemistry. It’s difficult to imagine how large Avogadro’s number really is, but this example may help: If 10,000 people started to count Avogadro’s number, and each counted at the rate of 100 numbers per minute each minute of the day, it would take them over 1 trillion (10 12 ) years to count the total number. So even the tiniest amount of matter contains extremely large numbers of atoms. Element Atomic mass Molar mass Number of atoms H 1.008 amu 1.008 g 6.022 * 10 23 Mg 24.31 amu 24.31 g 6.022 * 10 23 Na 22.99 amu 22.99 g 6.022 * 10 23 Avogadro’s number has been experimentally determined by several methods. How does it relate to atomic mass units? Remember that the atomic mass for an element is the average rela- tive mass of all the isotopes for the element.

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  A Problem-Solving Approach to Aquatic Chemistry

  • James N. Jensen(Author)
  • 2022(Publication Date)
  • Wiley

    (Publisher)

  As an example, suppose you wanted to calculate the molar mass of copper carbonate, CuCO 3 . Using the symbols defined above: M m m m cuco cu C o 3 1 1 3 ( ) ( ) ( ) . Using the relative atomic masses tabulated in Appendix A, the molar mass of CuCO 3 is (1 mol/ mol)(63.55 g/mol) + (1 mol/mol)(12.01 g/mol) + (3 mol/mol)(16.00 g/mol) = 123.56 g/ mol. Another example of the calculation of molar mass is given in Worked Example 2.2. In the older literature, the term gram molecular weight was used to refer to molar mass expressed in grams (or, more properly, in g/mol). Thus, the statements “The molar mass of water is 18 g/mol,” “The molecular weight of water is 18 g/mol,” and “The gram molecular mass of water is 18 g/mol” are identical. 2.3.4 Analytical Concentrations and Formality In some applications, molar units may seem inappropriate. For example, how would you make up a 1 M NaCl solution? When NaCl is added to water, it dissociates nearly completely to Na + and Cl – ions (see Section 1.4.2). Thus, although you might add 1 mole (about 58.44 g) of NaCl molecules to 1 liter of water, the actual number of moles of NaCl molecules in solution after a short period of time is quite small. The basic question is: Does a 1 M NaCl solution contain 1 M of NaCl molecules before any chemi- cal reactions occur or after chemical reactions occur? relative atomic mass: (atomic weight): the mass of 1 mole of an element molar mass: (molecular weight): the mass of 1 mole of a molecule or ion stoichiometric coefficient: here, the number of occur- rences of an atom in a molecule or ion Calculation of Molar Mass What is the molar mass of ferrous ammonium sulfate? Solution The molecular formula is Fe(NH 4 ) 2 (SO 4 ) 2 . One mole of ferrous ammonium sul- fate contains 1 mole of Fe, 2 moles of N, 2 moles of S, 8 moles of O, and 8 moles of H. The molar mass is M m m m m m Fe N H S O g mol g mol 2 8 2 8 1 55 85 2 14 01 .

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  Chemistry

  The Molecular Nature of Matter

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

    (Publisher)

  The equality that relates the substances is the mole-to-mole rela- tionship between glucose and O 2 given by the chemical equation. In this case, the equa- tion tells us that 1 mol C 6 H 12 O 6 3 6 mol O 2 . It is very important to realize that there is no direct conversion between the mass of C 6 H 12 O 6 and the mass of O 2 . We need to con- vert the mass of glucose to moles of glucose, then we use the mole ratio to convert moles of glucose to moles of oxygen, and finally we convert moles of oxygen to mass of oxygen. This sequence, indicating where we use the mole-to-mole equivalence, is shown below 1 mol C 6 H 12 O 6 3 6 mol O 2 1.00 g C 6 H 12 O 6 h mol C 6 H 12 O 6 h mol O 2 h g O 2 Two molar masses are used, once for converting 1.00 g of glucose to moles and again for converting moles of O 2 to grams of O 2 . Figure 3.4 outlines this flow for any stoichiometry problem that relates reactant or product masses. If we know the balanced equation for a reaction and the mass of any reac- tant or product, we can calculate the required or expected mass of any other substance in the equation. Example 3.15 shows how it works. Mass-to-mass calculations using balanced chemical equations Moles of A Moles of B Grams of Substance B Grams of Substance A Molar Mass B Molar Mass A Balanced Chemical Equation Figure 3.4 | The sequence of calculations for solving stoichiometry problems. This sequence applies to all calculations that start with the mass of one substance A and require the mass of a second substance B as the answer. Each box represents a measured or calculated quantity. Each arrow represents one of our chemical tools. 134 Chapter 3 | The Mole and Stoichiometry Portland cement is a mixture of the oxides of calcium, aluminum, and silicon. The raw material for calcium oxide is calcium carbonate, which occurs as the chief component of limestone. When calcium carbonate is strongly heated it decomposes.

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  SURVIVAL GDE GENERAL CHEM W/ MATH REVIEW

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

    (Publisher)

  Atomic weights are found on a periodic table. *The terms molar mass, molecular weight, and formula weight all apply to the same concept/calculation. Technically, the term molecular weight should be used only with covalent compounds and formula weight applies only to ionic compounds. The more generic term molar mass is used frequently in chemical literature. Sample Exercises Determining Molar Mass 1. What is the molar mass (or formula weight) of calcium phosphate, Ca 3 (PO 4 ) 2 ? The correct answer is: 310.2 g/mol Ca 3 (PO 4 ) 2 Molar mass of Ca 3 (PO 4 ) 2 = (3 x 40.08 g/mol Ca) + (4 x 2 x 16.00 g/mol O) + 2 x 30.97 g/mol P) = 310.18 g /mol Ca 3 (PO 4 ) 2 Module 4 Key Equations & Concepts 1.   ion or molecule, compound, a in atoms of weights atomic mass Molar The molar mass, molecular weight, or formula weight * are calculated by summing the atomic weights of the elements in the compound. Molar mass is the mass in grams of one mole of a substance. 2. One mole = 6.022 x 10 23 particles Avogadro’s relationship converts from the number of moles of a substance to the number of atoms, ions, or molecules of that substance and vice versa. 3. Mass of one atom of an element = mass of an element 1 mole of an element       1 mole of atoms 6.022  10 23 atoms       The mass of one atom, ion, or molecule is used to determine the mass of a few atoms, ions, or molecules of a substance. Notice that the fraction in the first set of parentheses simply is a representation of molar mass. 4. Mole ratio A compounds chemical formula is the ratio of the different types of atom in the compound. The mole ratio is used to convert from mass or moles of a compound to mass or moles of a specific atom in the compound. 34 Copyright 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-300

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  General Chemistry I as a Second Language

  Mastering the Fundamental Skills

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

    (Publisher)

  Hydrogen will be reported as 1.00794 amu and oxygen will be reported as 15.9994 amu. If we use these numbers to calculate the molar mass of H 2 O, we will get: 2(1.00794 g/mol)  (15.9994 g/mol)  18.0153 g/mol So, we see that the molar mass of any compound is a value that is known to many significant figures. In general, we will only use four or five significant figures when solving problems. 2.5 MOLAR MASS AS A CONVERSION FACTOR: INTERCONVERTING MOLES AND MASS In Chapter 1, we learned how to convert units using the factor-label method, and we saw an example of a special conversion factor that helped us convert one type of measurement into another. Specifically, we saw how to use the density of a sub- stance to convert from units of mass into units of volume, and vice versa. Although mass and volume are measured with completely different units, we were able to convert them using density as a conversion factor. In this section, we will use a similar technique; a similar type of special con- version factor. We will convert mass into moles, and vice versa, using molar mass 2.5 MOLAR MASS AS A CONVERSION FACTOR: INTERCONVERTING MOLES AND MASS 35 as a conversion factor. But this time, we don’t need to be given the conversion fac- tor—we can calculate it ourselves. When we talked about density as a special con- version factor, we saw problems where we were given the density at a certain tem- perature, and then we made our calculations. If we didn’t have the density, then we wouldn’t be able to use it as a conversion factor. But here, when we are talking about converting mass and moles, we can calculate the conversion ourselves if we are given the molecular formula. All we need is access to a periodic table, and we will be able to calculate the molar mass. And that is why the molecular formula al- ways provides us with an important piece of information when solving problems. Now let’s see how we can use the molar mass of a compound as a special conversion factor.

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