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The mole
Learning Objectives
A checklist of concepts to learn and skills to master in this section.
Lecture Slides
Lecture Notes
Internet sites and paper references for further exploration.
Frequently Asked Questions
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Terms and definitions from the glossary are marked with an asterisk (*).

Learning objectives

  • Explain the mole concept, and convert between grams, moles, and atoms and molecules.
  • Determine mass percent composition of a sample from experimental data.
  • Determine mass percent composition of a compound from its formula.
  • Determine empirical formula* of a compound from its mass percent composition.
  • Use chemical equations to predict amounts of reactant consumed or product produced in a chemical change.
  • Define limiting reagent* and identify the limiting reagent in a chemical equation.
  • Define and distinguish theoretical yield*, actual yield*, and percent yield*. Compute percent yield from actual and theoretical yields.
  • Define molarity*. Relate molarity, moles of solute, and liters of solution.
  • Explain how a solution of a desired concentration can be prepared from solid solute or from a more concentrated stock solution.

Lecture outline

Counting molecules by weighing

moles -is, f. a shapeless mass. TRANSF.,
1. a mass of men, a large number;
2. greatness, might, power;
3. trouble, difficulty
-Cassell's Latin Dictionary
  • Why use moles?
    • many properties depend on the number of molecules in the sample, not on the mass of the sample. How can the number of molecules in the sample be measured?
    • solution: convert sample mass to daltons to molecules, using the molecular weight
    • now you can count molecules in a pure sample just by weighing the sample.
    • problem: daltons are very small units, and inconvenient; can we convert grams to molecules without using them?
    • solution: define a new unit, the mole (SI unit for amount of substance)
The official definition is "1 mole of particles is equal to the number of atoms in exactly 12g of carbon-12".
  • Defining moles
    • 1 mole of molecules has a mass equal to the molecular weight in grams.
    • examples
      • 1 mole H2O is the number of molecules in 18.015 g H2O
      • 1 mole H2 is the number of molecules in 2.016 g H2.
    • 1 mole of atoms has a mass equal to the atomic weight in grams.
    • 1 mole of particles = 6.02214 x 1023 particles for any substance!
      • Prove this by converting 1 mole to grams to daltons to particles for any substance.
  • vocabulary
    • molar mass is the mass of one mole of a substance
      • bridge between moles and grams in unit conversion problems
    • Avogadro's number is the number of molecules in one mole for any substance
      • bridge between molecules and moles in unit conversion problems

Using chemical formulas

  • molecular formulas give atom-to-atom and mole-to-mole ratios
    • example: molecular formula C6H12O6
      atom-to-atom ratios atom-to-molecule ratios mole-to-mole ratios (elements) mole-to-mole ratio (compound)
      6 atoms C
      12 atoms H

      6 atoms C
      6 atoms O

      12 atoms H
      6 atoms O

      6 atoms C
      1 molecule

      12 atoms H
      1 molecule

      6 atoms O
      1 molecule

      6 mol C
      12 mol H

      6 mol C
      6 mol O

      12 mol H
      6 mol O

      6 mol C
      1 mol C6H12O6

      12 mol H
      1 mol C6H12O6

      6 mol O
      1 mol C6H12O6

  • problems that ask you to relate one substance to another require mole-to-mole ratios
    • examples
      • How many grams of H2 can be obtained from the electrolysis of 10.0 g of H2O?
      • How many grams of CuO can be made from a piece of copper wire weighing 0.2134 g?
      • 2.04 g of carbon reacts with 5.44 g of O2 to form 7.48 g of compound. How many atoms of O per atom of C are in this compound?

Chemical formulas and elemental composition

  • mass percent: percent of total sample mass contributed by a particular component
    • determine experimentally by decomposing sample into components and weighing the separate components
      • determining water of hydration
      • combustion analysis of hydrocarbons
  • finding element mass percents from a chemical formula
    • strategy: convert the mole fraction of element in compound to a mass fraction
    • procedure
      1. Write a subscript X from the formula as (X mol element / 1 mol compound)
      2. Convert moles of element to grams (using the atomic weight)
      3. Convert moles of compound to grams (using the molar mass)
      4. Multiply by 100%
    • examples
      • To how many significant figures must you determine the percentage of carbon in a drug sample to distinguish cocaine (C17H21O4N) from aspirin (C9H8O4)?
      • Vitamin B12 is 4.34% Co. If there is only one atom of Co per molecule of vitamin, what is the molar mass of vitamin B12?
  • finding empirical formulas from element mass percents
    1. Write the mass percent as a mass (mass percent is just mass per 100 g sample).
    2. Convert each mass to moles.
    3. Divide each molar amount by the smallest molar amount.
    4. Round the mole ratios to the nearest whole number or simple fraction. Use significant figures to guide your choice of whole number or fraction!
    5. If necessary, scale the ratios so that all are whole numbers. These are the subscripts in the empirical formula.
    • examples
      • elemental analysis of a pure compound isolated from tea leaves gave the following results: 49.48% C, 5.19% H, 28.85% N, 16.48% O. What is the empirical formula of the compound?
        g element per 100 g sample moles element per 100 g sample mole ratio simplified ratio
        49.48 g C 4.11952 mol C 3.99939 4
        5.19 g H 5.1490 mol H 4.9988 5
        28.85 g N 2.05973 mol N 1.99966 2
        16.48 g O 1.03004 mol O 1 1
        ...The empirical formula is C4H5N2O (it's caffeine).
      • What is the empirical formula of a purified drug sample that is 74.27% C, 7.79% H, 12.99% N, and 4.95% O?
      • What is the empirical formula of an iron oxide that 70.0% Fe and 30.0% O?
      • What is the molecular formula of a compound that is 5.93% H and 94.07% O, with molar mass 34.015 g?

    Using Chemical Equations

    • predicting amount of substance produced or consumed in a chemical reaction
      • coefficients in balanced equation relate moles of one substance to moles of another substance in the reaction
        • example
          2C8H18(l) + 25 O2(g) = 16 CO2(g) + 18 H2O(l)


          2 mol C8H18(l) per 25 mol O2(g)
          2 mol C8H18(l) per 16 mol CO2(g)
          2 mol C8H18(l) per 18 mol H2O(l)
          25 mol O2(g) per 16 mol CO2(g)
          25 mol O2(g) per 18 mol H2O(l)
          16 mol CO2(g) per 18 mol H2O(l)

      • general problem format: Substances A and B are involved in a chemical reaction. An amount of A is given. Find the amount of B that is produced or consumed when A completely reacts.
      • strategy:
        1. Write a balanced chemical equation for the reaction.
        2. Find moles of A from given information.
        3. Convert moles of A to moles of B using mole ratios from the balanced chemical equation.
        4. Convert moles of B to desired units.
      • examples
        • Oxygen gas can be produced in the laboratory by decomposition of hydrogen peroxide (H2O2):

          2 H2O2(aq) right arrow 2 H2O(l) + O2(g)
          How many kg of O2(g) can be produced from 1.0 kg of hydrogen peroxide?

        • How many grams of oxygen gas are required to completely burn exactly 1 kg of glucose (C6H12O6)?
        • How many pounds of CO2 are produced by burning 1 gallon (5.6 lbs) of octane (C8H18)?
        • Estimate sulfur dioxide emissions (in tons per year) for a power plant that annually burns 2.5 million tons of coal that is 3% sulfur by mass.
Limiting reagent demo from Carnegie-Mellon University
  • predicting the amount of product produced (theyield) from amounts of more than one reactant
    • if reactants aren't mixed in the right mole ratio, yield is limited by one of the reactants
    • strategy
      1. compute yield for each reactant
      2. the lowest yield is the theoretical yield
      3. the reactant giving the lowest yield is the limiting reactant.
    • examples
      • Ethanol (C2H5OH) is synthesized for industrial use by the following reaction, carried out at very high pressure:

        C2H4(g) + H2O(g) right arrow C2H5OH
        What is the maximum amount of ethanol that can be produced when 1.0 kg of ethylene (C2H4) and 1.0 kg of steam are placed in the reaction vessel?

      • Some of the acid in acid rain is produced by the following reaction:

        3 NO2(g)+ H2O(l)
        2HNO3(aq) + NO(g)
        A falling raindrop weighing 0.05 g comes into contact with 1 mg of NO2. How much HNO3 can be produced?
  • why doesn't actual yield = theoretical yield?
    • impurities in reactants
    • mechanical losses
    • side reactions
      synthesis of 2, 4, 5-T
    • reversible reactions

      H2(g) + Cl2(g) right arrow 2 HCl(g)

      actual yield close to theoretical yield
      H2(g) + I2(g) l 2 HI(g) actual yield is much less than theoretical yield!
  • calculating percentage yield
    1. the actual yield must be given
    2. compute the theoretical yield
    3. percentage yield = (actual yield/theoretical yield) x 100%
    • examples
      • 0.12 g of ozone is produced per gram of oxygen gas exposed to an electric arc. What is the percent yield of ozone?
      • The fertilizer ammonium nitrate is synthesized from ammonia and nitric acid. If 17 tons of ammonia produced 63 tons of fertilizer, what is the percent yield?
  • predicting the amount of excess reactants
    • strategy
      1. find how many moles of each reactant is present before the reaction
      2. identify the limiting reactant
      3. find how much of each reactant is consumed by converting moles of limiting reactant to moles of each of the nonlimiting reactants
      4. final moles of reactant = initial moles - moles consumed
      • example
        • The following reaction is used to extract gold from pretreated gold ore:

          2 Au(CN)2-(aq) + Zn(s) right arrow 2 Au(s) + Zn(CN)42-(aq)
          If 0.654 g of powdered Zn is added to a solution that contains 2.52 g of Au(CN)2-, what masses of reactants will be left over after the reaction is complete?

    • caveats about interpreting these calculations
      • chemical equations give only mole ratios between reactants and products
      • equations are macroscopic - they don't represent actual molecular level events!
        • example: reactions with intermediates
      • equations can depict impractical or impossible reactions
        • example: formation reactions for organic molecules
      • some reactions don't run to completion: watch for the double harpoon
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General Chemistry Online! The mole

Copyright © 1997-2005 by Fred Senese
Comments & questions to fsenese@frostburg.edu
Last Revised 02/23/18.URL: http://antoine.frostburg.edu/chem/senese/101/moles/index.shtml