Chapter 7 - Chemical
Quantities
Chapter 7 – Chemical Quantities
Part 1 – Notes: Mole Calculations
Objectives:
Identify, define, and explain: mole, Avogadro’s
number, representative particle, gram atomic mass, gram molecular mass,
gram
formula mass, molar mass, standard temperature and pressure, and molar
volume.
Describe how Avogadro’s
number is related
to a mole of any substance.
Calculate the
mass of a mole of any
substance.
Convert
between various units: mass, volume at STP, molecules, atoms of a
specific element in a compound, and mole, using unit analysis.
Text Reference:
Section 7.1 (pages 171-181) and Section
7.2 (pages 182-186)
Start-up Problem: We go
to the store to buy apples. We know that
the medium-sized apples we wish to buy have a mass of 2.0-kg per dozen
apples.
What would be the mass of the 90 apples we wish to purchase? We
need
to use unit analysis!!!
Previously you learned that matter is composed of different component
particles.
One method of measuring a substance is to count the number of component
particles
in the substance but since atoms, ion, and molecules are very small,
counting
them is very impractical. So we introduce a unit that allows us
to
count large quantities of component particles. Due to the size of
atoms,
ions, and molecules, this unit will need to account for a LARGE number
of
component particles. Let’s begin exploring the MOLE.
The MOLE
is unit used to count large numbers of representative particles
in compounds. The number associated with the mole was
experimentally
determined.
The experimentally determined number is 6.02x1023.
This number is known as Avogadro’s number.
Officially, the number of particle present in 1 mole of a substance is equal
to the number of carbon-12 atoms in exactly 12 grams of a sample of
carbon-12.
Since it is a number, it can also be applied to other substances with
various
representative particles.
Representative particle:
the smallest unit into which a substance may
be broken down without a change in composition; it refers to the
component
particles of various types of substance: atoms, ions, or molecules.
The representative particle of an element is an atom. Remember
that
there are seven elements which
exist as diatomic elements in
their free (uncombined)
state. These elements are:
Let’s solve some problems using our new-found mole knowledge:
TYPE I:
You know that the mole relationship can be
used to determine the number of atoms or molecules in a given number of
moles
and vice versa:
MOLES
<---> ATOMS of an element
MOLES <--->
MOLECULES or FORMULA UNITS of a compound
Example 1:
How many atoms of calcium are present in 5.376
moles of calcium?
TYPE II:
You know that since a mole is a specified
number of objects and you can take the mass of a specified number of
things,
then a mole of things has a certain mass. You use the PERIODIC
TABLE
to determine the mass of a given element. You can use the
relationship
between mole and mass from the periodic table to perform the following
calculations:
MOLE
<---> MASS (grams) OF AN ELEMENT
Example 2:
How many moles of copper are present in a sample
of copper that has a mass of 213.025 g?
Note every substance you encounter will be an element. You will
have
to be able to determine the mass of a compound. How do you
accomplish
this? And what do we call this?
Gram Atomic Mass:
Gram Molecular Mass:
Gram Formula Mass:
TYPE III:
Since you can determine the mass of a single
element and you can correctly write formulas of compounds, then you can
determine
the molar mass of various compounds and use the determined molar mass
in
the following calculations:
MOLE
<---> MASS (grams) OF A COMPOUND
Example 3:
What is the mass of a 2.7654 mol sample of copper
(I) oxalate?
Example 4:
How many moles are present in a sample of copper
(II) acetate that has a mass of 213.564?
TYPE IV:
You know you can relate various quantities
to the mole. You may relate mass to moles and we may relate
number
of particles to the mole. But can you relate mass directly to the
number
of particles? NO!!! WE MUST GO THROUGH THE MOLE. It
is
a two-step process.
MOLECULES
<--->
MOLES <---> MASS
Example 5:
How many molecules of CO2 are present in a sample
with a mass of 187.564 g?
TYPE V:
You must also be able to use the formula
of a compound to determine information about the elements that make up
the
element. For example, water is made up of hydrogen and
oxygen.
If you have 1 mole of water molecules, you have two moles of hydrogen
atoms
and 1 mole of oxygen atoms. Be sure to write the correct formula of the
compound
to receive full credit.
Example 6:
How many atoms of hydrogen are present in a
4.25 mol sample of lithium acetate?
Example 7:
How many moles of carbon dioxide could be made
by using 5.46 x 1024 atoms of
oxygen?
You may also have mass in these problems. Remember – to get out
of
mass – you need to go through moles. Show the formula and molar mass to
receive
full credit.
Example 8:
How many atoms of hydrogen are in 164.987 g
aluminum acetate?
Example 9:
Calculate the mass of carbon in 82.0 g of propane
(C3H8)?
TYPE VI:
Frequently you will encounter a problem
with a gas. It is not very helpful to refer to the mass of a gas
since
a sample of a gas can expand to fill its container. It is more
helpful
to work with the VOLUME
of a gas. Since the volume of a gas varies
with temperature and pressure, it is useful to have a set of standard
conditions
with which to work; we will work with STP.
STP – Standard temperature and Pressure
– the condition where the pressure
= 1 atmosphere and the temperature = 273 K
Standard Molar Volume – the
volume of one mole of a gas at STP
One mole of any gas at
STP conditions has a volume of
22.4 L. This information may be used in mole problems.
Example 10:
Assuming conditions of STP, what is the volume
(in Liters) of 145.0 g of chlorine gas?
Chapter 7 – Chemical
Quantities
Part 1 –
Assignment: Mole Calculations
Solve the following problems. Use unit analysis and show
all work and
set-ups.
1. You have one mole of each of the following
substances:
cobalt (II)
chloride gold (III) chloride
potassium
dichromate ammonium acetate
(a) Which
sample contains the greatest
number of formula units?
(b) Which sample has
the greatest mass?
(c) Which sample
contains the greatest
number of atoms?
2. You have 11.78 g of lithium. How many moles
of
lithium do you have?
3. You have 2.75 moles of calcium acetate. What
is
the mass of your sample?
4. How many moles are present in a sample that
contains
8.25x1024 molecules of sulfur
trioxide?
5. You have a 147.35-g sample of potassium
sulfate.
How many moles if this sample?
6. What is the mass of 0.001254 moles of tin (IV)
carbonate?
7. How many moles are present in a sample of 5.743 x
1024
molecules of water?
8. How many formula units are in 0.0236 moles of
barium
phosphate?
9. How many formula units are in a 13.098 g sample of
tungsten
(V) oxide?
10. What is the mass of 5.468 x 1023
“molecules” of iron
(III) oxide?
11. How many formula units are in 225.0 g of calcium
permanganate?
12. How many atoms of calcium are present in a sample
that
has a mass of 64.25 g calcium?
13. What is the mass of a sample containing 8.756 x 1022
formula units of ammonium oxide?
14. How many atoms of hydrogen are present in 1.9083
moles
of aluminum bicarbonate?
15. What mass of tin (II) hydroxide may be formed
using
4.738 x 1022 atoms of oxygen?
16. How many atoms of hydrogen are found in a 14.576
g
sample of ammonium acetate?
17. How many atoms of nitrogen are in a 2.39 mole
sample
of aluminum nitrate?
18. Calculate the mass of nitrogen in 125 g of CO(NH2)2.
19. Which contains more molecules: 1.00 mol H2O2,
1.00 mol C2H6,
or 1.00 mol CO?
20. Which contains more atoms: 1.00 mol H2O2,
1.00 mol
C2H6,
or 1.00 mol CO?
21. Calculate the volume of 7.6 mol of argon gas at
STP.
22. Calculate the volume of 135.25 g carbon dioxide
at
STP.
23. What is the density of helium gas at STP?
24. What is the density of fluorine gas at STP?
25. The densities of gases A, B, and C are 1.25 g/L,
2.86
g/L, and 0.714 g/L, respectively. Calculate the molar mass of
each
substance. Then identify each substance as ammonia (NH3),
sulfur dioxide,
chlorine, nitrogen, or methane (CH4).
26. What is the total mass of a mixture of 3.50x1022
formula
units of sodium sulfate, 0.500 mole of water, and 7.23 g of AgCl?
27. A typical virus is 5.00x10-6 cm in
diameter.
If Avogadro’s number of these virus particles were laid in a row, how
many
kilometers long would the line be?
28. An imaginary “atomic balance” is shown to the
right.
Fifteen atoms of boron on the left side are balanced by six atoms of an
unknown
element E on the right side.
a. What is the atomic mass of
element
E?
b. What is the identity of element
E?
Chapter 7 –
Chemical Quantities
Part 2 – Notes: Percent
Composition and Molarity
Objectives:
Identify, define, and explain: percent composition,
molarity, and concentration.
Calculate the
percentage by mass of a specific component in a compound.
Calculate the molar
concentration of
a solution. Calculate other components of a solution using
molarity.
Text Reference:
Section 7.2 (Pages 188-191)
Percent
Composition by Mass
A whole compound is made of two or more elements. Each
element is a
part of the whole compound. You can determine the percentage of a
whole
compound that is a specific element part. This is the percent
composition
by mass of a compound.
Example 1:
What is the percent composition by mass of each
element in aluminum oxalate?
Molarity
Concentration
refers to. . .
Molarity is
a unit of concentration. The MOLARITY of a
solution is
the number of moles of solute in every 1 liter of solution. A 1
molar
(1 M) solution of a pure substance may be prepared by adding enough
water
to one mole of substance to make a total of one liter of
solution.
Note: the volume is the volume of the total solution, not the
volume of the
solvent (water added).
So the Molarity is expressed in the formula:
Molarity = M
= moles of solute / liters of solution
Example 1:
What is the concentration in molarity of a solution
prepared by dissolving 35.45 g calcium chloride in enough water to make
1.75
liters of solution?
Example 2:
What is the mass of sodium hydroxide needed
to make 3.25 liters of a 1.75M solution
Example 3:
What is the volume of a 0.825M solution that
may be made with 123.45 g calcium chloride
Example 4:
How many moles of tin (II) hydroxide are required
to make 0.875 L of a 2.50M solution?
Chapter 7 – Chemical
Quantities
Part 2 –
Assignment: Percent Composition and Molarity
Solve the following. You must show all work, set-ups,
formulas, units,
etc.
1. What is the percent composition by mass of each
element
in ammonium carbonate?
2. An organic compound is decomposed into its
elements
and it produces 8.20 g C and 1.44 g H from the original sample whose
mass
was 32.80 g. The remainder of the sample escapes as oxygen gas
during
the decomposition. What is the mass of the oxygen gas? What
is
the percent composition, by mass, of each element in this compound?
3. Consider separate 100.0-g samples of each of the
following:
H2O
N2O
C3H6O2
CO2
Rank them from highest to lowest percent oxygen by
mass.
Be sure to show your work.
4. What mass of NaCl is contained in 806 mL of a
2.48M
solution?
5. Calculate the mass of sulfuric acid in 2.00 L of a
0.100M
solution?
6. The density of nickel is 8.91 g/cm3.
How large
a cube, in cm3, would contain
2.00x1024 atoms of nickel?
7. In your own words, describe how to make a 1.00M
solution
of NaCl.
8. Calculate the percent composition by mass of
hydrogen
in (a) calcium acetate and (b) hydrocyanic acid.
9. Use the results from question 8, calculate the
amount
of hydrogen in 124 g calcium acetate.
10. Dry air is about 20.95% oxygen by volume.
Assuming
STP, how many oxygen molecules are in a 75.0-g sample of air? The
density
of air is 1.19 g/L?
Chapter
7 – Chemical Quantities
Part 3 – Notes:
Empirical and Molecular Formulas
Objectives:
Identify, define, explain, and differentiate
between: empirical formula, molecular formula.
Determine empirical formulas
from lab
data or percentage by mass data.
Determine molecular formulas
from an
empirical formula and the molar mass.
List the common fractions that
will
be used in empirical formulas to determine the smallest whole number
ratio.
Text Reference:
Section 7.3 (Pages 192-195)
Molecular formulas indicate the
actual number of atoms present in a molecule
or ionic unit of a substance.
A molecule of
glucose has _______ atoms of C, _______ atoms of H, and _______
atoms of O.
Empirical formulas represent
the elements present in a substance in the simplest
whole number ratio of the atoms of these elements.
The formula of
glucose shows the actual number of atoms in the molecule.
But the empirical formula of glucose shows the atoms in a ratio of
_______
atoms of C to _______ atoms of H to _______ atoms of O.
The empirical formula and the molecular formula are related in the
following
way:
(empirical
formula)n = molecular formula
n
= (molar mass of molecular formula) / (molar mass of
empirical formula)
In other words, an empirical formula times some whole number is equal
to
the molecular formula.
DETERMINING
EMPIRICAL FORMULAS
When scientists analyze an unknown substance to determine of what it is
composed,
they determine the empirical formula of the substance. They use
the
“SMMRF”
method.
Substances:
determine the substances present
Mass:
determine the mass of each substance
Moles:
determine the moles of each substance
Ratio:
determine the ration of moles of each substance
with the smallest whole numbers
Formula: use
the numbers from the ratio as the subscripts
in the empirical formula
Example 1:
A sample of a compound with a mass of 8.66 g
is decomposed and found to be 0.17 g hydrogen, 2.82 g sulfur, and 5.67
g
oxygen. Determine the empirical formula.
Example 2:
Analysis of 100.0 g of a compound shows that
it is composed of carbon, hydrogen, and oxygen. The sample is
40.7
g carbon and 5.0 g hydrogen. Determine the empirical formula.
NOTE: In
this example, the ratio is not close to
a whole number. This will occur from time to time and you must
round
the decimal to one of the following places: 0.25, 0.33, 0.50, 0.66, or
0.75.
Always round to the closest decimal. Once you have rounded,
convert
the decimal to a fraction.
0.25 = 1/4 0.33 =
1/3 0.50 = 1/2
0.66 = 2/3 0.75 = 3/4
It is not possible to have a
fraction of an atom in a chemical formula.
You must multiply all of the atoms by the denominator of the fraction
to
cancel the denominator and give the smallest whole number ratio.
Example 3:
100.0 g of an unknown compound is analyzed and
found to be composed of carbon, hydrogen, and oxygen. 51.5 g are
carbon
and 8.7 g are hydrogen. Determine the empirical formula.
Some examples will give you
percentages instead of masses of a compound.
When this occurs, assume you have 100.0 g of the sample and use the
percentages
as masses in grams.
Example 4:
A compound is found to consist of 46.0% carbon
and 53.9% nitrogen. What is the empirical formula?
DETERMINING
MOLECULAR FORMULAS
Calculating the molecular formula is a rather easy one once you have
determined
the empirical formula. You will be given the same type of
information
as in an empirical formula question but you will also be given the
molar
mass of the molecular formula. This allows you to determine “n”.
Remember: (empirical
formula mass)n = molecular formula
mass then
(empirical formula)n = molecular
formula
When the problem states that the “molar mass is,” it is referring to
the
molar mass of the molecular formula.
Example 5:
Determine the molecular formula of the compound
is Example 4 given the fact that the molar mass is 52.04 g/mol.
Example 6:
A compound has an empirical formula of CH2O
and a molar mass of 240.24 g/mol. Determine the molecular formula
of
the compound.
Chapter 7 – Chemical
Quantities
Part 3A –
Assignment: Empirical and Molecular Formulas – 1
Determine the empirical and/or molecular formula for each
substance represented
below. Show all steps, set-ups, and work, etc.
1. Which of the following molecular formulas are also
empirical
formulas?
(a)
ribose (C5H10O5)
(b) ethyl butyrate (C6H12O2)
(c)
chorophyll (C55H72MgN4O5)
(d) DEET
(C12H17ON)
2. A compound is 9.93% carbon, 58.64% chlorine, and
31.34%
fluorine. What is its empirical formula?
3. A compound is 35.00% nitrogen, 5.05% hydrogen, and
59.95%
oxygen. What is its empirical formula?
4. Analysis of an organic compound shows that it is
40.7%
C, 5.00% H, and 54.3% O. The molar mass of the compound is 118.10
g.
What is its molecular formula?
5. An unknown compound has a composition of 51.8% C,
8.72%
H, and 39.5% O. The molar mass of the compound is 324.42 g.
What
is its molecular formula?
6. You find that 7.36 g of a compound has decomposed
to
give 6.93 g of oxygen. The only other element in this compound is
hydrogen.
If the molar mass of the compound is 34.0 g/mol, what is the molecular
formula?
Chapter 7 – Chemical
Quantities
Part 3B –
Assignment: Empirical and Molecular Formulas – 2
Determine the empirical and/or molecular formula for each
substance represented
below. Show all steps, set-ups, and work, etc.
1. A sample of an organic compound has a mass of
5.678
g. It is analyzed and found to contain 3.780 g C, 0.318 g H,
0.840
g O, and 0.736 g N. The molar mass of the compound is 108.13
g.
What is the molecular formula of the compound?
2. A sample of an unknown compound has a mass of 3.58
g;
it is analyzed and found to contain 3.18 g carbon and 0.40 g
hydrogen.
The molar mass of the compound is 135.25 g. What is the molecular
formula
of the compound?
3. Analysis of a gaseous compound shows that it
consists
of 89.92% carbon and 10.08% hydrogen. The molar mass of the
compound
is 120.21 g. What is the molecular formula of this substance?
4. A sample of unidentified compound has a mass of
8.366
g; it is analyzed and found to contain 2.180 g carbon, 0.366 g
hydrogen,
and 5.820 g sulphur. The molar mass of the substance is 230.45
g?
What is the molecular formula?
5. Calculate the empirical formula for a compound
consisting
of 0.40 mol Cu per 0.80 mol Br.
6. Textbook – page 199 – Question 68. Complete
the
question and show your work here.
a.
b.
c.
Chapter
7 – Chemical Quantities
Part 4 – Notes:
Hydrates
Objectives:
Identify, define, and explain: water of hydration,
hydrate, anhydrous salt, hydration, and dehydration.
Determine the empirical formula
of
a hydrated salt using lab data.
Name and
write formula for hydrated
salts.
Calculate the molar mass of a hydrate and the percent of water in a
hydrate.
Text Reference:
Section 17.3 (Pages 485-488)
A HYDRATE is . . .
The loosely attached water molecules are called
________________________________________________________.
A hydrate is formed when . . .
When writing formulas for hydrates, a dot is used to separate the ionic
salt
from the water of hydration. A prefix is used to indicate how
many
water molecules are loosely attached. This number of water
molecules
comes after the regular name of the ionic salt.
Na2B4O7
· 10 H2O
|
sodium
tetraborate decahydrate
|
Borax
|
CaCl2
·
2 H2O
|
???
|
Rock
Salt
|
MgSO4
·
7 H2O
|
???
|
Epsom
Salts
|
Na2SO4
·
10 H2O
|
???
|
----
|
???
|
iron
(II) sulfate heptahydrate
|
green
vitriol
|
???
|
barium
hydroxide octahydrate
|
----
|
Waters of hydration may be removed by
__________________________________.
This process is called dehydration and is due to a
________________________________
in energy, making it an ______________thermic process.
The compound without the attached water molecules is called . . .
The water molecules may be re-introduced into the anhydrous compound by
adding
water. This re-hydration process would cause a
_______________________________
in energy, making it an _____________thermic process.
To calculate the molar mass of a hydrated salt, you must also take into
account
the amount of water attached to the compound.
For example:
Calcium chloride dihydrate = CaCl2
· 2H2O
= 40.08 g + 2(35.45 g) + 2{ 2(1.01 g) + 16.00 g}
= 40.08 g + 70.90 g +
2(18.02
g) = 147.02 g/mol
What is the percent by mass of water in calcium chloride dihydrate?
The molar mass of iron (II) sulfate heptahydrate is
________________________________________.
The percent of water in barium hydroxide octahydrate is
_________________________________________.
***We will be performing a lab where the empirical formula of a hydrate
will
be determined. We will be heating the hydrate to drive off the water.
The
substances
are ________________________ & _________________________.
Once the water is driven off, we can determine the mass of the
water and
the moles
of the water and salt. Then we can determine the ratio of moles,
from the ratio of moles we can determine the empirical formula.
Let's look at some lab data:
Mass
of beaker
|
52.25
g
|
Mass
of beaker + hydrate
|
65.50
g
|
Mass
of hydrate
|
???
|
Mass
of beaker + anhydrous salt
|
58.72
g
|
Mass
of anhydrous salt
|
???
|
Mass
of water (driven off)
|
???
|
Moles
of water (driven off)
|
???
|
Molar
mass of anhydrous salt
|
120.27
g
|
Moles
of anhydrous salt
|
???
|
If I wanted to find the formula of the hydrate, I need to know how many
moles
of water are attached to 1 mole of the anhydrous salt. I need to set up
the
ratio - with the smallest whole numbers.
The ratio of anhydrous salt to water
The formula of the hydrate
Chapter 7 – Chemical
Quantities
Part 4 –
Assignment: Hydrates
Solve the following problems. Show all your work, set-ups, units,
etc.
Be complete.
1. One of the new superconducting materials
discovered
in 1987 has the following composition by mass: 41.23% barium, 28.62%
copper,
13.35% yttrium, and 16.81% oxygen. What is its empirical formula?
2. Find the percent composition by mass of each
element
in cobalt (II) arsenate.
3. A student in Ms. Anderson’s chemistry class
performed
an experiment and obtained the following results:
mass of hydrate + evaporating
dish
37.69
g (before
heating)
mass of anhydrous compound +
evaporating
dish 37.21 g (after
heating)
mass of evaporating dish
34.11 g
Identity of the anhydrous
salt
barium
sulfate
(a) Calculate the empirical
formula
of the hydrate.
(b) What is the percentage of
water
in the hydrated salt?