The Mole Concept g of Carbon-12 contains x atoms (1 mole) Moles - How chemists count atoms

Chemist’s Definition of a Mole particles (atoms, molecules, ions, formula units) of a substance x 10 23

The Mole is a Number The mole represents a # of particles. The mole represents a # of particles. A pair = 2A dozen = 12 A pair = 2A dozen = 12 A mole = x A mole = x This number is often referred This number is often referred to as “Avogadro’s Number”

The Mole is a BIG number x represents an incomprehensively large number! x represents an incomprehensively large number! If a mole of marbles were laid on the surface of the earth, how much of the earth would be covered? If a mole of marbles were laid on the surface of the earth, how much of the earth would be covered? Cover entire earth to a height of 50 miles! Cover entire earth to a height of 50 miles!

1 mole (6.022 x atoms) of different elements g g g g g g Note 1 mole of elements takes up relatively little space – each individual atom is incredibly tiny. We need an a hugh number of atoms to be able to see them with our eyes.

How many particles are present? In chemistry, it is important to know the # of atoms (or molecules) that you have. In chemistry, it is important to know the # of atoms (or molecules) that you have. Chemical formulas, like H 2 O, give us ratios of atoms: 2 H atoms bonded to 1 O atom. Chemical formulas, like H 2 O, give us ratios of atoms: 2 H atoms bonded to 1 O atom.

How many particles are present? Chemical equations: 2 H 2 + O 2  2 H 2 O give us ratios of reacting particles. Chemical equations: 2 H 2 + O 2  2 H 2 O give us ratios of reacting particles. Both formulas and equations are needed to calculate recipes for reactions. Both formulas and equations are needed to calculate recipes for reactions.

BIG Problem Atoms are too small to see with the naked eye! Atoms are too small to see with the naked eye! STM image of Si on 0.09 nm scale. (0.09 x m) (0.09 x m) = 9 x m = 9 x m Counting would take a lifetime! Counting would take a lifetime!

Chemist’s Solution to Problem Counting of Atoms or Molecules The Mole Concept The mole connects the # of particles present with a property we can measure in the lab: mass. (Counting by grouping and counting by weighing) Can’t see Can measure Work HW 5-1 #1, p. 103

COUNTING BY WEIGHING How could you determine the number of marbles in the bag using a scale? Bag of marbles Bag of marbles Scale Scale How can you account for small variations in the masses of individual marbles? Problem: Marbles are similar, but not exactly the same mass

Determining the Average Mass of a Marble (or an atom) Marbles (like atoms) will have similar but not necessarily identical masses. Marbles (like atoms) will have similar but not necessarily identical masses. Recall mass on periodic table represents average mass taking into account all of the isotopes of an atom. Recall mass on periodic table represents average mass taking into account all of the isotopes of an atom. Determination average mass of 10 marbles: Determination average mass of 10 marbles: ÷ 10 = 5.00 g Average atomic mass

Counting by Weighing Determine total mass of all marbles in the bag: g Determine total mass of all marbles in the bag: g Let N = number of marbles Let N = number of marbles Average mass of 1 marble x N = total mass of all marbles Average mass of 1 marble x N = total mass of all marbles N = total mass ÷ average mass N = total mass ÷ average mass 2000 / 5.00 = 400. marbles 2000 / 5.00 = 400. marbles Work HW 5-1 #2, p. 103 A) 10.8 amu B) 1.08 x amu/ 10.8 amu/atom= 1 x 10 9

Developing the Definition of a Mole The definition of a mole (the # of atoms in 12 g of Carbon) was chosen to make it easy to determine the mass of a mole of atoms using the periodic table. The definition of a mole (the # of atoms in 12 g of Carbon) was chosen to make it easy to determine the mass of a mole of atoms using the periodic table.

Connecting Atomic Mass with the Number of Atoms Masses on periodic table represent the average mass on 1 atom measured in amu. Masses on periodic table represent the average mass on 1 atom measured in amu. For example, the average mass of 1 carbon atom is amu. For example, the average mass of 1 carbon atom is amu.

Counting by weighing – Connecting Mass in Grams with the Number of Atoms However, In the lab we can’t see single atoms so we have to work with very large numbers of atoms by measuring masses in grams. We Need to work in grams (large #’s we can see, not amu (tiny numbers – can’t see)

What is the pattern in the following data? Element (atomic #) # of atoms present # of moles present Mass in grams He (#2)6.022 x g Li (#3)6.022 x g B (#5)6.022 x g C (#6)6.022 x g Cu (#29)6.022 x g Au (#79)6.022 x g

Understanding the Mole Concept Fill in the missing information Fill in the missing information Mass of 1 mole ____________________ of an element = atomic _________ in _______ (6.022 x atoms ) mass grams

Connecting Mass in Grams with Number of Atoms How many carbon atoms (N) are present in g C? How many carbon atoms (N) are present in g C? Work HW 5-1 #3, p. 103

Connecting Mass in Grams with Number of Atoms What is the average mass of 1 carbon atom ? ( Hint: Look at the periodic table) We need to connect mass in amu from the periodic (convenient unit for 1 atom) with a mass in grams (convenient unit for large numbers of atoms we can actually see): We need to connect mass in amu from the periodic (convenient unit for 1 atom) with a mass in grams (convenient unit for large numbers of atoms we can actually see): 1 amu = 1.66 x g 1 amu = 1.66 x g Calculate the Mass of 1 carbon atom in grams: Calculate the Mass of 1 carbon atom in grams: Mass of 1 carbon atom = Mass of 1 carbon atom = amu x 1.66 x g amu x 1.66 x g = 1 amu 1 amu 1.99 x g

Connecting Mass in Grams with Number of Atoms How many carbon atoms (N) are present in g C? How many carbon atoms (N) are present in g C? N = Total Mass (12.01 g) ÷ Average Mass of 1 Carbon (Where N = # of Carbon Atoms) Work HW 5-1 #3, p. 103

How many C atoms are present in g of C? N = g ÷ 1.99 x g = N = Total Mass (12 g) ÷ Average Mass of 1 Carbon (Where N = # of Carbon Atoms) 6.02 x Work HW 5-1 #4 & 5, p. 104

HW 5-1, #5 ElementNumber of AtomsMass in Grams Beryllium (#4)6.022 x Magnesium (#12)6.022 x Aluminum (#13)6.022 x Copper (#29) Carbon (#6)6.022 x Carbon (#6)6.022 x Carbon (#6)1.204 x g g g g x 10 23

Examples of counting by grouping

Could you go to the store and ask for 8,563 Rice Krispies please? NO! THEY SELL RICE KRISPIES BY THE BOX BECAUSE BOXES ARE EASIER TO COUNT!

To avoid working with extremely large numbers, we count by grouping in units of x – called 1 mole. To avoid working with extremely large numbers, we count by grouping in units of x – called 1 mole x = 1 mole x = 1 mole ½ mole = ½ (6.022 x ) = x ½ mole = ½ (6.022 x ) = x mole = 2 (6.022 x ) = x mole = 2 (6.022 x ) = x mole = 3 (6.022 x ) = 1.81 x mole = 3 (6.022 x ) = 1.81 x 10 24

Relationship between # of particles,“packing boxes” and mass If eachHas a mass of 10 mass units, (Ignore mass of “packing box”) 12 particles 1 “PACKING BOX” ? MASS UNITS WEIGHES ? MASS UNITS Ignoring the container mass, how much would 1 box weigh? ANS: 120 mass units (12 particles per box x 10 mass units per particles) Work HW 5-1 #6, p. 104

HW 5-1, #6 Count the atoms by drawing a box around each set of 12 atoms. How total sets are present? How many total atoms? Ans: 3 boxes; 36 atoms

HW 5-1, #7 GroupNumber of objects 1 Pair of Aces 2 2 Pairs of Aces 1 Dozen Doughnuts 12 3 Dozen Doughnuts Dozen Doughnuts Doughnuts 1 Mole of B atoms x atoms 2 ( x ) atoms 3(6.022 x ) atoms 4 ( x ) atoms ½ ( x ) atoms Moles of B atoms 3 Moles of B atoms 4 Moles of B atoms 1/2 Moles of B atoms

HW 5-1, # x atoms B ÷ x10 23 atom/mole = moles B

HW 5-1, #10 ElementNumber of AtomsNumber of Moles He6.022 x Li6.022 x Ne6.022 x Ar1.00 Cu3.01 x Cu1.20 x Cu1.81 x Zn3.01 x Zn3.00 Zn1.20 x x x10 23

HW 5-1, #10 ElementNumber of AtomsNumber of Moles Ag0.500 Ag2.00 Ag1.81 x x x

HW 5-1, #11, p A) 12 x 10 = 120 amu 11B) 60 ÷ 12 = 5 boxes 5 boxes x 120 amu/box = 600 amu 11C) 10 boxes x 12 atom/box = 120 atom ½ box x 12 atom/box = 6 Total atoms = 126 Total mass = 126 x10 = 1260 units

Link to mole review Link to mole review Link to mole review Link to mole review

HW 5-1, #12 moles Number of atoms Element Mass in grams x Fe x Zn x S Al x Ar

HW 5-1 #13 Which of the following contains the same # of atoms as g of C? Which of the following contains the same # of atoms as g of C? Equal masses does NOT mean equal # of atoms because each type of atom has a different mass. Equal masses does NOT mean equal # of atoms because each type of atom has a different mass. Need to compare # of particles – chemists unit for # of particles = mole Need to compare # of particles – chemists unit for # of particles = mole How many moles are present in g? How many moles are present in g? Ans: 1 mole Ans: 1 mole C = 12 amu He = 4 amu

HW 5-1 #13 Question now becomes which of the following also represents 1 mole? Question now becomes which of the following also represents 1 mole? A) (1 mole = 6.94 g); g Li ≈ 2 moles A) (1 mole = 6.94 g); g Li ≈ 2 moles B) (1 mole = 4.00 g); 12.0 g He ≈ 3 moles B) (1 mole = 4.00 g); 12.0 g He ≈ 3 moles C) (1 mole = 10.8 g); 5.4 g of B ≈ 1/2 moles C) (1 mole = 10.8 g); 5.4 g of B ≈ 1/2 moles D) g Ne = mass on periodic table = 1 mole D) g Ne = mass on periodic table = 1 mole

HW 5-3 #1 1 mole 12 g 0.25 moles 0.50 moles 0.33 moles 0.75 moles 3.0 g4.0 g 6.0 g 9.0 g

HW 5-3 # moles 2.50 moles 3.00 moles 24 g 30 g 36 g

HW 5-1, #15 moles Number of atoms Element Mass in grams x He x He x He x He Ne Ne Ne Ne g 4.00 g 8.00 g g g g g g x x x x 10 24