• A picture of a mole holding an Erlenmeyer flask.

    Textbook Reading: 

    Holt "Chemistry" Ch.3 S.4 p 100-103 & Ch. 7 S. 3 p 246-247
    Silberberg "Chemistry" Ch.3 S.1 

    A Mole Is 

    • A convenient unit for counting atoms & molecules.  Equal to 6.022 x 1023 items.
      • A mole is analogous to a dozen, which is 12 of something, only it's much larger than a dozen.
    • One mole of any element has a mass in grams equal to the atomic mass of the element on the Periodic Table.
      • One mole of carbon has a mass of 12.01 grams.
      • One mole of uranium has a mass of 238.03 grams.
      • They both have the same # of atoms, but uranium atoms have more mass than carbon atoms.
    • One mole of any compound has a mass in grams equal to the sum of atomic masses of the elements in that compound.
      • One mole of NaCl has a mass of 22.99 + 35.45 = 58.44 g
      • One mole of H2O has a mass of (2 x 1.008) + 15.999 = 18.015 g
      • One mole of Ca(OH)2 has a mass of 40.08 + 2 x (15.999 + 1.008) = 74.049 g
        • Note that we multiply subscripts by every atom inside the parentheses!
        • You could also rewrite it as CaO2H2 before adding it up.
    • One mole of any gas, at STP (Standard Temperature and Pressure, 0°C and 1 atm), has a volume of 22.4 L.
      • This is the molar volume of a gas.

     

    A Molar Mass is

    • The mass of one mole of any substance.
    • The molar mass of a substance has units of grams per mole
      • The molar mass of carbon is 12.011 g/mol
      • The molar mass of H2O is 18.015 g/mol

     

    Chemical Formulas are Ratios of Moles

    • The formula H2O means 1 mole of water contains 2 moles of H atoms and 1 mole of O atoms
    • We can write the mole ratios (2 mol H/1 mol H2O) and (1 mol O/1 mol H2O)

     

    A Percentage is 100 x Part / Whole

    • If 100 grams of a compound contains 45 grams of element Q, the compound is 45% Q.
    • Percent means "per hundred" in Latin.
    • What if we have 47 grams of a compound containing 7.0 grams of element Z? 
    • 100 x 7 / 47 = 15% Z
    • The percentages of all parts of anything must add up to 100%.

     

    Use the Molar Mass to Convert between Grams and Moles

    How many atoms are in 5.000 moles of H2O?  How many moles are in 185.12 g of Ca(OH)2?

     5.000 mol H2O x 18.015 g H2O = 90.08 g H2O
                        1 mol H2O

    185.12 g Ca(OH)2 x 1 mol Ca(OH)2 = 2.5000 mol Ca(OH)2
                    74.049 g Ca(OH)2

    Note that we multiply by the molar mass to convert moles to grams.  When we want to go from grams to moles, we 'flip' the molar mass upside down.  The rule of factor label calculations is that a unit on the top of a fraction cancels the same unit on the bottom of another fraction.  

     

    Use Avogadro's Number, 6.022 x 1023/mol, to Convert between Moles and # of atoms or molecules

    How many atoms are in 5.000 moles of Au?  How many moles are in 2.831 x 1025 molecules of H2O?

    5.000 mol Au x 6.022E23 atoms Au = 3.011E24 atoms Au 
                            1 mol Au 

    2.831E25 molecules H2O x _          1 mol H2O = 47.01 mol H2O 
                           6.022E23 molecules H2O

    Note that we multiply by Avogardo's # to convert moles to #atoms or #molecules (depending on whether substance is an element or a compound).  When we want to go from #atoms/molecules to moles, we flip Avogadro's # to the bottom.  Again in factor label calculations a unit on top of a fraction cancels the same unit on the bottom of another fraction.

     

    Use Chemical Formulas to Convert between Moles of Atoms and Moles of a Compound

    How many moles of Se are in 5.00 moles of Al2Se3?

    5.00 mol Al2Se3  x 3 mol Se = 15.0 mol Se
                   1 mol Al2Se3

    How many moles of P4O10 can you make out of 10.0 moles of P?

    10.0 mol P x 1 mol P4O10 = 2.50 mol P4O10
                 4 mol P

    Combine Molar Mass, Avogadro's Number, Molar Volume of a Gas, Chemical Formulas to Solve Multi-Step Problems

    We can do as many steps as we need in a factor label calculation.  The general rule is that you cancel out the unit you are given in the denominator, and put the unit you are converting to into the numerator, so the bottom unit of a step often cancels the top unit of the step before it.

    How many atoms are in 1.00 gram of Magnesium?

    1.00 g Mg x 1 mol Mg x 6.022E23 atoms Mg = 2.48E22 atoms Mg
               24.3 g Mg            1 mol Mg

    What is the mass of 1.00 L of SF6 gas at STP?  

    1.00 L SF6 x  1 mol SF6 x 146 g SF6 = 6.52 g SF6
                 22.4 L SF6   1 mol SF6

    How many moles of Na2SO4 can you make out of 137.94 g of Na?   

    137.94 g Na x 1 mol Na x 1 mol Na2SO4 = (137.94/45.98) = 3.000 mol Na2SO4
                22.99 g Na   2 mol Na

    (Note that when we do a factor label calculation, we need to multiply all the numerators together and divide them by the product of all the denominators.  The numerators multiply to 137.94, the denominators multiply to 45.98).  

    How many grams of gold (Au) are in 151.7 g of AuCl3?

    151.7 g AuCl3 x       1 mol AuCl3 x    1 mol Au x 196.97 g Au = 98.51 g Au
                      303.325 g AuCl3   1 mol AuCl3      1 mol Au

    Percent Composition of a Compound from the Formula

    We saw in the previous problem that 151.7 g of AuCl3 contains 98.51 g Au.  What is the % of Au in this compound?  What is the % of Cl?

    100 x 98.51 / 151.7 = 64.94% Au
%Cl = 100 - 64.94 = 35.06% Cl

    There is an easier way to find the % composition of a compound!  We can just assume we have 1 mole of the compound and add up the molar masses of all the elements which make it up.  For each element, 100 x part / whole will give the %.

    1 mol Au x 196.967 g Au = 196.967 g Au
               1 mol Au
    
3 mol Cl x 35.453 g Cl =  106.358 g Cl
              1 mol Cl

                       total: 303.325 g AuCl3

%Au = 100 x 196.967 / 303.325 = 64.94% Au
%Cl = 100 x 106.358 / 303.325 = 35.06% Cl

    Check your Understanding:  Take the Quiz!
    "Do you know me yet?" says the Mole