The Mole

1
The Mole

• OBJECTIVES
• Describe the mole concept
• Calculate the mass of a mole of any substance.
• Convert between moles, grams, liters, and
  particle number

2
What is a Mole?

• We measure mass in grams.
• We measure volume in liters.
• We count pieces in MOLES.

3
The Mole Concept

• A Carbon-12 atom
• has a mass of 12amu

C
12amu
4
The Mole Concept

• Mole of atoms

Atomic Mass in grams
5
The Mole Concept
27.0g

• A mole of aluminum
• A mole of gold
• A mole of silver
• A mole of boron

197g
108g
10.8g
6
The Mole Concept

• So,
• How many atoms are in a mole?
• Does a mole of H have the same number of atoms as
  a mole of He?

7
If a Helium atom is 4 times heavier than a
Hydrogen atom,
He
H
then a dozen Helium atoms is 4 times heavier than
a dozen Hydrogen atoms.
8
And a mole of Helium atoms is 4 times heavier
than a mole of Hydrogen atoms.
9
So, the number of atoms in a mole is always the
same
The number of atoms in a mole is
called, Avogadro's Number
Avogadro's Number 6.022 x 1023
10
Technically, The mole is based on the exact
number of atoms in 12.0g of Carbon-12.
Because 1amu 1/12th the mass of 126C
11
Gram Atomic Mass

• Equals the mass of 1 mole of an element
• 12.01 grams of C has the same number of pieces as
  1.008 grams of H and 55.85 grams of iron.
• We can write this as 12.01 g C 1 mole C
• We can count things by weighing them.

12
Conversions
How many moles of Na atoms are there in 46.0g of
Na?
Na has a mass of 23.0
46.0g Na
2 mol Na
23.0
Step 2 Look up the atomic mass on the periodic
table and find out how many grams 1mole
Step 3 Place the units you need to cancel on the
bottom, and multiply by the top and divide by the
bottom
Step 1 Write a grid and place the given number
into the upper left hand part of the grid
13
Examples

• How much would 2.34 moles of carbon weigh?
• How many moles of magnesium is 24.31 g of Mg?
• How many atoms of lithium is 1.00 g of Li?
• How much would 3.45 x 1022 atoms of U weigh?

14
What about compounds?

• in 1 mole of H2O molecules there are two moles of
  H atoms and 1 mole of O atoms
• To find the mass of one mole of a compound
• determine the moles of the elements they have
• Find out how much they would weigh
• add them up

15
What about compounds?

• What is the mass of one mole of CH4?
• 1 mole of C 12.01 g
• 4 mole of H x 1.01 g 4.04g
• 1 mole CH4 12.01 4.04 16.05g
• The Gram Molecular Mass (gmm) of CH4 is 16.05g
• this is the mass of one mole of a molecular
  compound.

16
Gram Formula Mass (gfm)

• The mass of one mole of an ionic compound.
• Calculated the same way as gmm.
• What is the GFM of Fe2O3?
• 2 moles of Fe x 55.85 g 111.70 g
• 3 moles of O x 16.00 g 48.00 g
• The GFM 111.70 g 48.00 g 159.70 g

17
Molar Mass

• Molar mass is the generic term for the mass of
  one mole of any substance (in grams)
• The same as 1) gram molecular mass, 2) gram
  formula mass, and 3) gram atomic mass- just a
  much broader term.

18
Examples

• Calculate the molar mass of the following and
  tell what type it is
• Na2S
• N2O4
• C
• Ca(NO3)2
• C6H12O6
• (NH4)3PO4

19
Molar Mass

• The number of grams of 1 mole of atoms, ions, or
  molecules.
• We can make conversion factors from these.
• To change grams of a compound to moles of a
  compound.

20
For example

• How many moles is 5.69 g of NaOH?

21
For example

• How many moles is 5.69 g of NaOH?

22
For example

• How many moles is 5.69 g of NaOH?

• need to change grams to moles

23
For example

• How many moles is 5.69 g of NaOH?

• need to change grams to moles
• for NaOH

24
For example

• How many moles is 5.69 g of NaOH?

• need to change grams to moles
• for NaOH
• 1mole Na 22.99g 1 mol O 16.00 g 1 mole of
  H 1.01 g

25
For example

• How many moles is 5.69 g of NaOH?

• need to change grams to moles
• for NaOH
• 1mole Na 22.99g 1 mol O 16.00 g 1 mole of
  H 1.01 g
• 1 mole NaOH 40.00 g

26
For example

• How many moles is 5.69 g of NaOH?

• need to change grams to moles
• for NaOH
• 1mole Na 22.99g 1 mol O 16.00 g 1 mole of
  H 1.01 g
• 1 mole NaOH 40.00 g

27
For example

• How many moles is 5.69 g of NaOH?

• need to change grams to moles
• for NaOH
• 1mole Na 22.99g 1 mol O 16.00 g 1 mole of
  H 1.01 g
• 1 mole NaOH 40.00 g

28
Examples

• How many moles is 4.56 g of CO2?
• How many grams is 9.87 moles of H2O?
• How many molecules is 6.8 g of CH4?
• 49 molecules of C6H12O6 weighs how much?

29
Gases

• Many of the chemicals we deal with are gases.
• They are difficult to weigh.
• Need to know how many moles of gas we have.
• Two things effect the volume of a gas
• Temperature and pressure
• We need to compare them at the same temperature
  and pressure.

30
Standard Temperature and Pressure

• 0ºC and 1 atm pressure
• abbreviated STP
• At STP 1 mole of gas occupies 22.4 L
• Called the molar volume
• 1 mole 22.4 L of any gas at STP

31
Examples

• What is the volume of 4.59 mole of CO2 gas at
  STP?
• How many moles is 5.67 L of O2 at STP?
• What is the volume of 8.8 g of CH4 gas at STP?

32
Summary

• These four items are all equal
• a) 1 mole
• b) molar mass (in grams)
• c) 6.02 x 1023 representative particles
• d) 22.4 L at STP
• Thus, we can make conversion factors from them.

33
Practice Problems

• How many atoms in 2 mol Na?
• How many grams of potassium is in 3.5mol of
  potassium?
• How many moles are in 11.2L of methane?
• How much ammonium nitrate is needed to have
  .050mol of it?
• How many grams of nitrogen gas would fit in a
  1.0x105 L room?

34
Homework

• Read and take Cornell Notes on
• Pages198-203
• Do problems on
• Page 203 s 34-41
• Page 217 s 89-94

35
Section 7.3Percent Composition and Chemical
Formulas

• OBJECTIVES
• Calculate the percent composition of a substance
  from its chemical formula or experimental data.

36
Section 7.3Percent Composition and Chemical
Formulas

• OBJECTIVES
• Derive the empirical formula and the molecular
  formula of a compound from experimental data.

37
Calculating Percent Composition of a Compound

• Like all percent problems
• Part whole
• Find the mass of each component,
• then divide by the total mass.

x 100
38
Example

• Calculate the percent composition of a compound
  that is 29.0 g of Ag with 4.30 g of S.

39
Getting it from the formula

• If we know the formula, assume you have 1 mole.
• Then you know the mass of the pieces and the
  whole.

40
Examples

• Calculate the percent composittion of C2H4?
• How about Aluminum carbonate?
• Sample Problem 7-11, p.191
• We can also use the percent as a conversion
  factor
• Sample Problem 7-12, p.191

41
The Empirical Formula

• The lowest whole number ratio of elements in a
  compound.
• The molecular formula the actual ratio of
  elements in a compound.
• The two can be the same.
• CH2 is an empirical formula
• C2H4 is a molecular formula
• C3H6 is a molecular formula
• H2O is both empirical molecular

42
Calculating Empirical

• Just find the lowest whole number ratio
• C6H12O6
• CH4N
• It is not just the ratio of atoms, it is also the
  ratio of moles of atoms.
• In 1 mole of CO2 there is 1 mole of carbon and 2
  moles of oxygen.
• In one molecule of CO2 there is 1 atom of C and 2
  atoms of O.

43
Calculating Empirical

• We can get a ratio from the percent composition.
• Assume you have a 100 g.
• The percentages become grams.
• Convert grams to moles.
• Find lowest whole number ratio by dividing by the
  smallest.

44
Example

• Calculate the empirical formula of a compound
  composed of 38.67 C, 16.22 H, and 45.11 N.
• Assume 100 g so
• 38.67 g C x 1mol C 3.220 mole C
  12.01 gC
• 16.22 g H x 1mol H 16.09 mole H 1.01
  gH
• 45.11 g N x 1mol N 3.219 mole N 14.01
  gN

45
Example

• The ratio is 3.220 mol C 1 mol C
  3.219 molN 1 mol N
• The ratio is 16.09 mol H 5 mol H
  3.219 molN 1 mol N
• C1H5N1
• A compound is 43.64 P and 56.36 O. What is
  the empirical formula?
• Caffeine is 49.48 C, 5.15 H, 28.87 N and
  16.49 O. What is its empirical formula?

46
Empirical to molecular

• Since the empirical formula is the lowest ratio,
  the actual molecule would weigh more.
• By a whole number multiple.
• Divide the actual molar mass by the empirical
  formula mass.
• Caffeine has a molar mass of 194 g. what is its
  molecular formula?

47
Example

• A compound is known to be composed of 71.65 Cl,
  24.27 C and 4.07 H. Its molar mass is known
  (from gas density) to be 98.96 g. What is its
  molecular formula?
• Sample Problem 7-14, p.194