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The Mole and Stoichiometry: Using Moles
Class Notes:
Objective —Use factor-labeling to convert between moles, masses and number of particles.
Units you already know…
A dozen is ______ objects.
An hour is ______ seconds.
New Unit:
Ex:
A ream of paper is __________ sheets.
A decade is _______ years.
A mole is ________________________ particles.
A mole of beans are ________________________ beans.
A mole of pencils are ________________________ pencils.
A mole of _____________ is _____________________ ___________.
The Mole (Avogadro’s Constant)
Where did the mole come from? The mole is a quantity of a substance such that the actual mass in grams
has the same value as the average atomic mass listed on the periodic table. It was discovered by Amadeo
Avogadro in 1811 and is known as Avogadro’s rule. Avogadro's rule says that a mole of any substance always
contains the same number of molecules. A mole of oxygen has as many molecules as a mole of hydrogen,
which has as many molecules as a mole of water.
Huh? In other words, the mole is the number of carbon-12 atoms needed to make 12.0 grams of carbon-12. Or
the number of oxygen-16 atoms needed to make 16.0 grams of oxygen-16.
In addition, you should remember that the mass of __________ mole has the _________ value as
the ______________________ listed in the ______________________. So…
1 mole of any element = average atomic mass of that element in grams
(found on the periodic table)
1 mole of Carbon =
_____________
grams of Carbon
1 mole of Nitrogen =
_____________
grams of Nitrogen
1 mole of Hydrogen =
_____________
grams of Hydrogen
1 mole of Copper =
_____________
grams of Copper
Got it? Let’s practice and see
Solve the following problems using factor-labeling….
1) What is the mass of one mole of nitrogen? _______________________
2) What is the mass of five moles of nitrogen? _______________________
3) How many atoms are in one mole of nitrogen? _____________________
4) How many atoms are in five moles of nitrogen? ____________________
5) What is the mass of one mole of iron? ____________________
6) What is the mass of three moles of iron? ____________________
Part II.
Molar Mass for Compounds
Like individual atoms, each molecule or ion has a characteristic average mass. For example, we
know from the chemical formula H2O that a single molecule of water is composed of exactly _____
hydrogen atoms and _____ oxygen atom. The molar mass of a water molecule is found by
_____________ the masses of the three atoms in the molecule.
One mol of Hydrogen = _________ gram
One mol of Oxygen = __________ grams
2 H mol
x
1.008 g
1 H mol
= 2.016 g
1 O mol
x
16.00 g
1 O mol
= 16.00 g
2.016 g + 16.00 g = 18.016 g = mass of one mole H2O
1) What is the molar mass of magnesium chloride, MgCl2?
2) What is the molar mass of a phosphate ion, PO4?
3) What is the molar mass of dinitrogen trioxide, N2O3?
Name: ____________________
Practice – Molar Mass
Block: _____
________________
Instructions: Show your work for the following problems. Circle your final answer with the label.
Part A.
Answers should be in grams.
1.
What is the mass of one mole of lithium?
__________________
2.
What is the mass of one mole of calcium?
__________________
3.
What is the mass of one mole of silver?
__________________
4.
What is the molar mass of one mole of fluorine, F2?
__________________
5.
What is the molar mass of one mole of KBr?
__________________
6.
What is the mass of 4 moles of lithium?
7.
What is the mass of 7 moles of strontium?
8.
What is the mass of 2 moles of KBr?
9.
What is the mass of 3 moles of NaCl?
10.
What is the mass of 4 moles of AgO?
11.
What is the mass of 3 moles of water?
12.
What is the mass of 7 moles of beryllium sulfide (BeS)?
13.
What is the mass of 5 moles of hydrochloric acid (HCl)?
Part. B
Calculate the moles present in:
(Leave answers in decimal form)
1) 2.00 grams of H2O
2) 75.57 grams of KBr
3) 100. grams of KClO4
4) 8.76 grams of NaOH
5) 26.0 gram CaCl
6) 5.08 gram XeF4
7) 32.0 gram O2
10.08)gram
10.0Algram
2(SOV
4)23O5
Practical Application:
1) If pencil weighs 3.80 grams, how much would a mole of pencils weigh?
2) If a peron eats 200 beans a week, how many weeks would it take for a person to eat a mole
of beans?
3) If the cafeteria serves 1,600 lunches a day, how many days would it take the cafeteria to serve a
mole of lunches? If the school year is 180 days, how many years would it take to serve?
Additional Problems:
Calculate the mass in grams of each of the following quantities.
9) 0.200 moles of H2S
14) 2.55 mole Cu2CrO4
10) 0.100 moles of KI
15) 1.95 mole HNO3
11) 1.500 moles of KClO
16) 2.00 mole HC2H3O2
12) 0.750 moles of NaOH
17) 10.0 mole NaCl
13) 3.40 x 10-5 moles of Na2CO3
18) 2.20 mole SnCl2
Practice Problems
Complete all work on separate paper.
1) How many moles of compound are there in the following?
a. 4500 g calcium hydroxide, Ca(OH)2
b. 25.0 g sulfuric acid, H2SO4
c. 125 g of sugar, C12H22O11
2) What is the mass of each of the following?
a. 1.00 mol of beryllium chloride, BeCl2
b. 3.50 mol of dinitrogen tetroxide, N2O4
c. 0.625 mol of barium nitrate, Ba(NO3)2
3) What is the mass in grams of 6.25 mol of copper (II) nitrate?
4) How many moles are in 123 g of KCl?
The Mole and Stoichiometry: Molar Math Practice
Objective 8-3—Use dimensional analysis to convert between moles, masses and number of particles.
Molar Math Practice
Complete all work on separate paper and write your final answers on this page.
Be prepared to show your work.
Calculate the moles present in:
19) 2.00 grams of H2O
24) 5.08 gram XeF4
20) 75.57 grams of KBr
25) 10.0 gram Al2(SO4)3
21) 100. grams of KClO4
26) 32.0 gram O2
22) 8.76 grams of NaOH
27) 10.0 gram V2O5
23) 26.0 gram Ca(ClO4)2
28) 2.50 gram CoSO4 . 6H2O
Calculate the mass in grams of each of the following quantities.
29) 0.200 moles of H2S
34) 2.55 mole Cu2CrO4
30) 0.100 moles of KI
35) 1.95 mole HNO3
31) 1.500 moles of KClO
36) 2.00 mole HC2H3O2
32) 0.750 moles of NaOH
37) 10.0 mole NaCl
33) 3.40 x 10-5 moles of Na2CO3
38) 2.20 mole SnCl2
Calculate the number of molecules in each of the following quantities.
39) 3.00 mole H2
40) 3.27 mole O2
41) 0.000300 mole AuCl3
42) 1.55 mole KrF2
43) 0.100 mole NH3
Objective 8-3 Review
Complete all work on separate paper and write your final answers on this page.
Be prepared to show your work.
1) What is the mass of one mole of arsenic? ____________________
2) How many atoms are in one mole of arsenic? ____________________
3) How many moles are contained in 2.005 x 1023 atoms of arsenic? _______________
4) How many moles are in 200.5 grams of arsenic? ________________
5) What is the formula mass of zinc fluoride, ZnF2? _______________
6) What is the formula mass of a sulfate ion, SO42-? _______________
7) What is the molar mass of hydrogen peroxide, H2O2? _______________
8) What is the molar mass of iron (III) hydroxide, Fe(OH)3? _______________
9) How many moles of compound are there in the following?
a. 1.023 g copper (II) nitrate, Cu(NO3)2 _______________
b. 17 g of fructose, C6H12O5 _______________
10) What is the mass of each of the following?
a. 2.30 mol of phosphorus trifluoride, PF3 _______________
b. 0.034 mol of selenium sulfide, SeS _______________
11) What is the mass in grams of 0.52 mol potassium chloride? _______________
12) How many moles are in 123 g of salt? _______________
13) What is the difference between formula mass and molar mass?
14) Compare the size of a mole of salt with a mole of beans—how many particles are in each? What
is the mass of each?
15) What is a conversion factor? How are they useful when converting?
Objective 8-3 Review (Part II)
Complete all work on separate paper and write your final answers on this page.
Be prepared to show your work.
Calculate the number of molecules in each of the following quantities.
1) 3.00 mole Zr
6) 0.00550 mole C
2) 3.27 mole Zn
7) 0.100 mole W
3) 0.000300 mole Au
8) 0.500 mole Ca
4) 1.55 mole Kr
9) 0.300 mole P
5) 0.100 mole Ni
10) 1.500 mole K
Calculate the moles present in:
11) 2.00 grams of Ca
16) 5.08 gram Xe
12) 75.57 grams of Fe
17) 10.0 gram Al
13) 100. grams of K
18) 32.0 gram P
14) 8.76 grams of Na
19) 10.0 gram V
15) 26.0 gram Ca
20) 2.50 gram Co
Calculate the mass in grams of each of the following quantities.
21) 0.100 moles of K
26) 1.95 mole Ba
22) 1.500 moles of Cr
27) 2.00 mole Ag
23) 0.750 moles of Na
28) 10.0 mole Os
24) 3.40 x 10¯5 moles of C
29) 2.20 mole
25) 2.55 mole Cu
30) 0.200 moles of Sn
The Mole and Stoichiometry: Stoichiometry
Objective 8-4—Use mole ratios to solve stoichiometry problems.
STOICHIOMETRY PROBLEM-SOLVING
When solving stoichiometry problems, you should always follow the 5-step method below.
1 balance equation
2 identify given
3 identify want
4 set up equation
5 solve the equation
1)
__ LiOH + __ HBr  __ LiBr + __ H2O
If you start with ten grams of lithium hydroxide, how many grams of lithium bromide will be
produced?
2)
__ C2H4 + __ O2  __ CO2 + __ H2O
If you start with 45 grams of ethylene (C2H4), how many grams of carbon dioxide will be
produced?
3)
__ Mg + __ NaF  __ MgF2 + __ Na
If you start with 5.5 grams of lithium chloride, how many grams of calcium chloride will be
produced?
4)
__ HCl + __ Na2SO4  __ NaCl + __ H2SO4
If you start with 20 grams of hydrochloric acid, how many grams of sulfuric acid will be
produced?
Stoichiometry Problems with a Limiting Reactant
Using your knowledge of stoichiometry and limiting reactants, answer the following questions:
1)
Write the balanced equation for the reaction of lead (II) nitrate with sodium iodide to form
sodium nitrate and lead (II) iodide:
2)
If I start with 25.0 grams of lead (II) nitrate and 15.0 grams of sodium iodide, how many grams
of sodium nitrate can be formed? SHOW YOUR WORK.
3)
What is the limiting reagent in the reaction described in the above problem?
4)
How much of the non-limiting reagent will be left over from the reaction in the above problem?
5)
Write the balanced equation for the reaction of hydrogen gas and oxygen gas to form water:
6)
If I start with 20 g of hydrogen gas and 20 g of oxygen gas, how many grams of water can be
formed? SHOW YOUR WORK.
7)
What is the limiting reagent in the reaction described in the above problem?
8)
How much of the non-limiting reagent will be left over from the reaction in the above problem?
More Stoichiometry Problems
__ C6H12O6 + __ O2  __ CO2 + __ H2O + energy
1. Use the above equation to determine how many grams of CO2 are produced from 3.00 moles
of C6H12O6.
__ NO2 + __ O2 
__ NO3
2. Use the above equation to determine how many grams of nitrogen dioxide are needed to
produce 1.55 X 1040 molecules of nitrogen trioxide.
__ CaCO3  __ CO2 + __ CaO
3. Use the above equation to determine if 1,212 g calcium carbonate are consumed, how many
grams of calcium oxide are produced.
Zinc reacts with excess sulfuric acid to produce zinc sulfate and hydrogen gas
4. In the above reaction, how many atoms of zinc are needed to produce 7 moles of hydrogen
gas?
Barium hydroxide plus sulfuric acid produces barium sulfate and water.
5. In the above reaction, what mass of barium sulfate is formed when 75.0 g of barium hydroxide
is missed with an excess of sulfuric acid?
__ Fe + __ CuSO4  __ FeSO4 + __ Cu
5. In the above reaction, if 48.2 grams of iron react with 5.62 moles cupric sulfate, how many
moles of copper can be produced?
6. What is the limiting reagent in the reaction described in the above problem? Explain.
7. How much of the non-limiting reagent will be left over from the reaction in the above problem?
__ Zn + __ H2SO4  __ H2 + __ ZnSO4
8. A student reacts 8.32 grams zinc with excess sulfuric acid and produces hydrogen gas and
zinc sulfate. How many moles of zinc sulfate will be produced?
The Mole and Stoichiometry: Percent Composition
Objective 8-5—Calculate the percent composition of a certain element in a compound.
Calculating Percent
What is a percent? A percent is a ratio given in terms of parts per hundred (remember: there are 100
cents in a dollar). These ratios are usually expressed in percents and we can use the cross-product
method to find our percentage.
For example, let’s say there are five pieces of cake and Doris eats 4 of them. What percentage of the
cake did she eat?
To solve this, we set up a proportion and then cross multiply to find the missing value.
4
=
x
First, multiply the cross: (4)(100) = (5) (x)
5
100
Then divide to isolate the variable: (4)100
=
5x
5
5
80 = x
Doris ate 80% of the cake
Now another way to look at the equations we just solved is to see that we are taking the fraction and
multiplying it by 100
4
x 100 = 80
5
And it is this equation which is more applicable when looking at percent composition.
Part x
Whole
100 = the percent
Second example: Central High School must hold classes 180 days a year. If there are 365 days in a
year, what percentage of the year is spent in school?
180 x
100 = 49.3%
365
Practice Problems (show all work on separate paper):
1) At a basketball game, Sarah shoots 12 times and scores 9 of those times. What is her shooting
percentage?
2) Joe just got his nine weeks tests back and wants to find out which test he did best on. He got a
84/95 on his history exam, a 48/50 on his English exam and a 94/120 on his math exam. What
were his percentages on each of those tests? Which exam did he perform the best on?
3) There are 50 states in the United States and 11 of them border the Mississippi River. What
percentage of states are along the Mississippi?
4) Calculate the percentage of students wearing khakis in this class
5) Calculate the percentage of girls in this class.
Calculating Percent Composition
A chemical formula can tell us the ratio of atoms in a compound. For example, the formula for
potassium chlorate tells us that there is 1 potassium atom, 1 chlorine atom, and three oxygen atoms
bonded together in one molecule of KClO3.
However, it is also useful for scientists to know what percentage by mass of a particular
element in a chemical compound. Suppose we wanted to use potassium chlorate as a source for
oxygen—we would want to know how much oxygen is in a sample of KClO3. How can we figure this
out? Well we use the basic formula for percents and take the part divided by the whole:
Mass of element in 1 mol of compound x 100 = % element in compound
Molar Mass of Compound
The percentage by mass of each element in a compound is known as the percentage composition
of the compound
Example What is the percent composition of potassium chlorate, KClO3?
1)
First, find the molar mass:
39.098 + 35.45 + 3(16.00) = 122.55 g/mol
2)
Next, find the masses of each element by multiplying the molar mass of the element by the
number of atoms of that element in the compound:
K = 1(39.098 g) = 39.098 g
Cl = 1 (35.45 g) = 35.45 g
O = 3(16.00) = 48.00 g
3)
Now, take the mass of each element divided by the mass of the compound to find the percent
of each element:
K: 39.098 x 100 = 31.9%
122.55
4)
Cl: 35.45 x 100 = 28.9%
122.55
O: 48.00 x 100 = 39.2%
122.55
Check your answer to see if your percents add up to 100%.
31.9% + 28.9% + 39.2% = 100%
Potassium chlorate is 31.9% K, 28.9% Cl and 39.2% O.
Practice Problems (show all work on this paper. If you run out of room you may show some work on
separate paper):
1) Find the percent composition of copper (I) sulfide, Cu2S.
2) What is the percent composition of barium nitrate, Ba(NO3)2?
3) Calculate the percent composition of ammonium carbonate, (NH4)2CO3.
4) Determine the percent composition of sodium chloride, NaCl.
5) Find the percent composition of silver nitrate AgNO3.
6) What is the percent composition of sulfurous acid, H2SO3?
7) Calculate the percent composition of beryllium chloride, BeCl2.
8) Determine the percent composition of diarsenic pentoxide, As2O5.
9) Which has a greater percent composition of oxygen—iron (II) oxide (FeO) or iron (III) oxide
(Fe2O3)? Explain.
10) Magnesium hydroxide is 54.87% oxygen by mass. How many grams of oxygen are in 175g of the
compound? How many mole of oxygen is this?
Practice Problems (Calculate the percentage of EACH element in the following compounds. Show all
work on separate paper and write answers on this paper. Be prepared to show your work.):
1) KNO3
2) H2SO4
3) C2H5OH
4) C6H5NH2
5) lithium bromide, LiBr
6) anthracene, C14H10
7) ammonium nitrate, NH4NO3
8) nitrous acid, HNO2
9) silver sulfide, Ag2S
10) iron(II) cyanide, Fe(CN)2
11) lithium acetate LiCH3COO
12) nickel(II) fluoride NiF2
Practice Problems (Calculate the percentage of THE GIVEN element in the following compounds.
Show all work on THIS paper and write answers on this paper.):
13) nitrogen in urea, NH2CONH2
14) sulfur in sulfuryl chloride, SO2Cl2
15) thallium in thallium(III) oxide, Tl2O3
16) oxygen in potassium chlorate, KClO3
17) bromine in calcium bromide, CaBr2
18) tin in tin(IV) oxide, SnO2
19) oxygen in chromium permanganate, CrMnO4
20) nitrogen in calcium nitrate, Ca(NO3) 2
Working Backwards
Some Chemistry problems are tough because you cannot always just plug numbers into the formula
as you have learned them. The important part of algebra is that it teaches that we can rearrange
equations to solve for whatever we’re missing.
Magnesium hydroxide is 54.87% oxygen by mass. How many grams of oxygen are in 175g of the
compound? How many mole of oxygen is this?
The equation we learned taught us that:
Mass of element in 1 mol of compound x 100 = % element in compound
Molar Mass of Compound
So here we need to work backwards—instead of knowing the mass of one element and the molar
mass, we know the mass of a sample and the percentage.
Mass of oxygen
175 g
x 100 = 54.87%
OR Mass of oxygen = 54.87% x 175 g
100
Therefore the mass of oxygen is 96.0 g
As we learned in Obj 3, we can use the molar mass to convert to moles:
96.0 g O x 1 mole O
= 6.0 moles O
16.00 g O
Let’s try that technique on another similar problem:
Methane is 75% carbon and 25% hydrogen. You have 16.05 g of methane –how many grams of
carbon do you have? How many grams of hydrogen? How many moles of carbon do you have? How
many moles of hydrogen?
Mass of carbon
16.05 g
x 100 = 75% OR Mass of carbon = 75% x
100
16.05 g
Therefore the mass of carbon is 12.01 g = 1 mol C
Mass of hydrogen
16.05 g
x 100 = 25% OR Mass of hydrogen = 25% x 16.05 g
100
Therefore the mass of hydrogen is 4.04 g = 4 mol H
How does the relationship between carbon and hydrogen in this problem relate to the chemical
formula for methane?
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The Mole and Stoichiometry: Empirical and Molecular Formulas
Objective 8-6— Predict the empirical formula and calculate the molecular formula of a compound using the
masses of each element.
Determining Empirical Formula
The methane problem on the last page was easy because our amount of sample was exactly equal to
the molar mass of methane (16.05g). However, our lives are not always that convenient. Frequently,
we will have a larger amount that is a nice round number (like 100g). In these cases, the moles do not
appear in nice round numbers. Therefore we have to divide the moles to find an easy mole ratio.
Example 1: Let’s say we have 100g of the gas diborane. It is 78.1% boron and 21.9% hydrogen.
What is the empirical formula for diborane?
First we use the percentage composition formula to find the mass
Mass boron = 78.1% x 100 = 78.1g
100
(Percent Mass)
Mass of hydrogen = 21.9% x 100 = 21.9g
100
Next, convert the masses to moles by using molar mass as a conversion factor
(MassMole)
B: 78.1 g B x
1 mol B
= 7.22 mol B
10.81 g B
H: 21.9 g H
x
1 mol H = 21.7 mol H
1.008g H
Then, we need to figure out the mole ratios. Right now we have 7.22 mol B to 21.7 mol H. How can
we simplify this? Just like we do with fractions, divide by the smaller number (in this case 7.22 mol )
7.22 mol B = 1 mol B
7.22 mol B
Now figure out what the formula will be:
21.7 mol H = 3.01 mol H
7.22 mol B
1 boron and 3 hydrogens OR BH3.
Example 2: Analysis tells us that a compound is 32.38% sodium, 22.65% sulfur, and 44.99%
oxygen. Find the empirical formula for this compound.
First, find the masses of each element.
(Percent  Mass)
We don’t have a given mass so let’s pretend that we had 100g. It doesn’t much matter because the
ratio will be the same no matter what. We like 100g because then the percentage is the same as the
mass. (32.38 g Na, 22.65g S, and 44.99 g O)
Next, find the moles of each element
Na: 32.38 g Na x 1 mol Na = 1.408 mol Na
22.99 g Na
O: 44.99 g O x 1 mol O = 2.812 mol O
16.00 g O
(Mass  Moles)
S: 22.65 g S x 1 mol S = 0.7063 mol S
32.07g S
Then divide by the smallest (in this case, 0.7063 mol S)
Na: 1.408 mol Na = 1.993 mol Na
0.7063 mol
S: 0.7063 mol S = 1 mol S
0.7063 mol
O: 2.812 mol O = 3.981 mol O
0.7063 mol
Although the numbers aren’t exact, because we are within .01 of a whole number, we can round to
make our answers complete
2 mol Na: 1 mol S: 4 mol O  Na2SO4 (sodium sulfate)
But what is the numbers aren’t exact and are not within 0.01 of a whole number?
Then we have to multiply both numbers until they are whole.
If the decimal is close to 0.50, multiply by 2
0.25, 0.75 multiply by 4
0.33, 0.66 multiply by 3
Example 3: Analysis of a 10.150 g sample of a compound known to contain only phosphorus
and oxygen indicates a phosphorus content of 4.433 g. What is the empirical formula for this
compound?
Here we have a given mass so we do not need to worry about the percent composition instead we
can start with step 2 (mass mole)
Total Mass: 10.150 g
Mass P: 4.433 g
Mass O: 10.150 g – 4.433 g = 5.717 g
P: 4.433 g P x 1 mol P
30.97 g P
= 0.1431 mol P
O: 5.717 g O x 1 mol O
16.00 g O
= 0.3573 mol O
Now divide by the smallest (in this case 0.1431 mol)
P: 0.1431 mol P = 1 mol P
0.1431 mol
O: 0.3573 mol O = 2.497 mol O
0.1431 mol
2.497 is not close to a whole number but it is close to 0.50 so we will multiply by numbers by 2
1 mol P x 2 = 2 mol P
2.497 mol O x 2 = 4.994 mol O
Since 4.994 is within 0.01 of a whole number we can round it up to 5
The formula is 2 mol P to 5 mol O or P2O5 (Diphosphorus Pentoxide)
Want an easy way to remember these steps? Just learn this poem!
Percent to mass
Mass to mole
Divide by the small
Multiply ‘til whole
Practice Problems ( Show all work on THIS paper and circle your final answers.):
1) A compound is found to contain 63.52% iron and 36.48% sulfur. Find its empirical formula.
2) Find the empirical formula of a compound found to contain 26.56% potassium, 35.41% chromium,
and the remainder oxygen.
3) Analysis of a 20.0 g of a compound containing only calcium and bromine indicates that 4.00 g of
calcium are present. What is the empirical formula of the compound?
4) Determine the empirical formula of a compound containing 63.50% silver, 8.25% nitrogen and the
remainder oxygen.
5) Determine the empirical formula of a compound found to contain 52.11% carbon, 13.14%
hydrogen and 34.75% oxygen.
6) A compound is found to contain 36.48% Naa, 25.41% S and 38.11% O. Find its empirical formula.
7) Find the empirical formula of a compound that contains 53.70% iron and 46.30% sulfur.
8) Analysis of a compound indicates that it contains 1.04 g K, 0.70 g Cr, and 0.86 g O. Find its
empirical formula.
9) Chemical analysis of citric acid shows that it contains 37.51% C, 4.20% H, and 58.29% O. What is
its empirical formula?
10) A 175.0 g sample of a compound contains 56.15 g C, 9.43 g H, 74.81 g O, 13.11 g N, and 21.49 g
Na. What is its empirical formula?
Empirical Practice and Molecular Formulas
An empirical formula contains the smallest possible whole numbers that describe the atomic ratio.
However, many molecular compounds have the same empirical formula but have unique molecular
formulas—which are the actual formulas of a molecular compound.
For example, diborane’s empirical formula is BH3. Any multiple of BH3, such as B2H6, B3H9, B4H12 and
so on represents the same ratio of B: H so will have the same empirical formula. However, each of
these is a unique substance. How can we distinguish between them? By looking at their molecular
formula.
We can find molecular formula by multiplying the empirical formula by a whole number
x (empirical formula) = molecular formula
1 (BH3) = BH3
2 (BH3) = B2H6
3 (BH3) = B3H9
4 (BH3) = B4H12
Formula masses have a similar relationship:
x (empirical formula mass) = molecular formula mass
We rearrange our equation to solve for our variable and get x = molecular formula mass
empirical formula mass
Example 1: Experimentation shows that the formula mass of diborane is 27.67 amu. What is
the molecular formula for diborane?
First, follow the steps to find the empirical formula
(see 5-2)
BH3
Second, calculate the formula mass of the empirical formula
(see 3-2)
10.81 amu + 3 (1.008 amu) =13.84 amu
Third, divide molecular formula mass by empirical formula mass to solve for x
x=
27.67 amu
13.84 amu
= 2.00
Fourth, multiply the empirical formula by x to find the molecular formula
2 (BH3) = B2H6
Which of course makes sense because di- means two
Example 2: The compound studied in Example 3 on 5-2 (between phosphorus and oxygen)
has been found to have a molar mass of 283.89 g/mol. What is the compound’s molecular
formula?
First, find the empirical formula
P2O5
Second, calculate the formula mass of the empirical formula
(see 3-2)
2(30.97 amu) + 5 (16.00 amu) =141.94 amu
Third, divide molecular formula mass by empirical formula mass to solve for x
x=
283.89 amu = 2.00
141.94 amu
Fourth, multiply the empirical formula by x to find the molecular formula
2 (P2O5) = P4O10
Tetraphosphorus Decoxide
Practice Problems ( Show all work on THIS paper and circle your final answers.):
1) Determine the molecular formula of the compound with an empirical formula of CH and a formula
mass of 78.110 amu.
2) A sample of a compound with a formula mass of 34.000 amu is found to consist of 0.44 g H and
6.92 g O. Find its molecular formula.
3) If 4.04 g N combine with 11.46 g O to produce a compound with a formula mass of 108.0 amu,
what is the molecular formula of this compound?
4) The molar mass of a compound is 92 g/mol. Analysis of a sample of the compound indicates that
it contains 0.606 g N and 1.390 g O. Find its molecular formula.
5) What is the molecular formula of the molecule that has an empirical formula of CH 2O and a molar
mass of 120.12 g/mol?
6) A compound with a formula mass of 42.08 amu is found to be 85.64% carbon and 14.16%
hydrogen by mass. Find its molecular formula.
The Mole and Stoichiometry: Empirical and Molecular Formulas ACTIVITY
Objective 8-6— Predict the empirical formula and calculate the molecular formula of a compound
using the masses of each element.
The Strange Case of Mole Airlines Flight 1023
You and your team of medical examiners are called to the scene of a plane crash that has no
survivors. The plane shows evidence of a pre-crash explosion. The site of the explosion has a
compound with the following analysis: 37.01% C, 2.22% H, 18.5% nitrogen, and 42.27% oxygen. The
victims are found and in and around the crash and must be identified by the substance found in their
belongings or in their bodies as dental records are not available. One passenger was murdered with
the time of death established as 1 hour before the crash.
Your job as the forensic scientist on duty is to:
1. Use the percent compositions to determine the chemical formulas and identities for the compounds
found on the victims. (Use a separate sheet of paper and show all work)
2. Use personal data to make a probable identification of each victim.
3. Determine who was murdered and who is the most probable murderer.
4. Determine who caused the plane to explode.
Victim #
1
2
3
4
5
6
7
8
67.31% C
63.15% C
46.66 % C
72.20 % C
15.87% C
75.42 % C
37.01 % C
57.14% C
80.48% C
81.58 % C
60.00 % C
63.56 % C
75.42 % C
Analysis
of
6.96% H
5.30% H
4.48% H
7.08 % H
2.22 % H
6.63 % H
2.22 % H
6.16 % H
7.45 % H
8.90 % H
4.48 % H
6.00 % H
6.63 % H
Compound
4.62% N
31.10% N
4.68 % N
18.51 % N
8.38 % N
18.50 % N
9.52 % N
9.39 % N
9.52 % N
9.27 % N
8.38 % N
21.10 % O
31.55% O
17.76 % O
16.03 % O
63.41 % O
9.57 % O
42.27 % O
27.18 % O
2.68 % O
35.53 % O
21.17 % O
9.57 % O
Where found
Blood &Luggage
Briefcase
Stomach
Pockets
Blood & Pockets
Blood
Luggage
Briefcase
Briefcase
Luggage
Pockets &
Briefcase
Pockets &
Briefcase
Briefcase
List of substances and their common uses
Acetaminophen
Aspartame
Aspirin
Codeine
Cocaine
Curare
Dimetacrine
Nitroglycerine
Strychnine
Thriobromine
Trinitrotoluene (TNT)
Vanilla
C8H9NO2
C14H18N2O5
C9H8O4
C18H21NO3
C17H21NO4
C40H44N4O
C40H52N4
C3H5N3O9
C21H22N2O2
C7H8N4O2
C7H5N3O6
C8H8O3
Tylenol, non-prescription painkiller
artificial sweetener
painkiller, over the counter
prescription painkiller, often used in dentistry
narcotic, illegal substance
poison
antidepressant, prescription
explosive; heart medication
rat poison
chocolate flavoring used in frosting on pastries
TNT, explosive
flavoring, used in baking
List of Passengers and Crew
Amadeo Aviator - a pilot with a heart condition
Curie Drugs - a sales representative of Advil company
Bohr Diet - Chemistry teacher "addicted" to sugar-free drinks
Kelvin Doughnut - baker, specializes in pastries shaped like the famous scientist
Democritus "D" Victory - professional athlete suspended for drug violations
Ruthy Ford-Recycle - electrical engineer, had been severely depressed lately due to a canceled
project
Dalton Molar - high school student who recently underwent dental surgery
Norm Einstein - leader of group called the Mighty Order of Lavoisier Enthusiasts, a suspected
terrorist organization more commonly know as MOLE. According to Mole-der and Skulley, the groups'
goal is to make everyone aware of the power of Chemistry.
1 What compound was found at the crash site?
2 Who is victim #1? What compound(s) did he/she have on them?
3 Who is victim #2? What compound(s) did he/she have on them?
4 Who is victim #3? What compound(s) did he/she have on them?
5 Who is victim #4? What compound(s) did he/she have on them?
6 Who is victim #5? What compound(s) did he/she have on them?
7 Who is victim #6? What compound(s) did he/she have on them?
8 Who is victim #7? What compound(s) did he/she have on them?
9 Who is victim #8? What compound(s) did he/she have on them?
10 Who was the murdered victim?
11 Who was the murderer?
12 Who caused the plane to explode? Why?
The Mole and Stoichiometry: Empirical and Molecular Formulas LAB
Objective 8-6— Predict the empirical formula and calculate the molecular formula of a compound
using the masses of each element.
By knowing the relative weights of the elements in a compound, the empirical formula (or simplest
chemical formula) can be deduced. This is a common practice in forensic science. In this experiment
the percentage of the carbon in a carbonate salt will be calculated. As the carbonates are
decomposed by their reaction with hydrochloric acid, carbon dioxide is released as a gas. The
decrease in mass of the salt will correspond to the amount of gas liberated. By knowing the mass of
gas, carbon dioxide, released we can calculate the mass of the carbon in the salt sample originally
and calculate the percentage of carbon in the salt.
Safety Note: Chemical goggles and laboratory apron should be worn. Use extreme care when
obtaining, transporting, dispensing, and discarding hydrochloric acid and its solutions. It is extremely
corrosive.
Materials:



Unknown Carbonate salt
hydrochloric acid, 6M
pipet


spot plate
balance
Procedure:
1.
Place a spot plate on a balance and record the mass to the nearest 0.01 g.
2.
Obtain a small sample (<0.7 g) of the carbonate salt to be tested. However, do not use the
tiniest sample imaginable!
3.
Place the sample into one of the central wells on the plate. All of the sample should be placed in
just one well. Note the mass of the microplate and sample.
4.
Obtain a pipet and fill it with approximately 4 mL of hydrochloric acid solution. WARNING!
Hydrochloric acid is corrosive to eyes and skin.
5.
Place the filled pipet into a well near the carbonate salt, e.g. well C3. Note the total mass of the
microplate, sample, pipet, and hydrochloric acid solution.
6. Slowly add the hydrochloric acid dropwise to the sample. Allow the bubbles of CO 2 to dissipate
before adding each additional drop. Continue to add the acid until the carbonate salt has
dissolved and the solution fails to react. The bubbles may be small so look carefully.
7.
Weigh the tray, its contents, and the pipet containing unused acid. Record this figure. This
system should have less mass than originally. Discuss why with your lab group?
8.
Rinse the microplate with water and dry with a paper towel. Repeat the experiment with a
second sample of the same substance. Average your results and record the date in the data
table below.
Sample Identity ________
Dat
a
T
a
b
l
e
1.
___ ___
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ga
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a _ _
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3. ___ ___
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of
the
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4.
___ ___
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5.
___ ___
M _ _
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s g
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6.
___ ___
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7.
___ ___
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2
8. %C in sample
_____ %
9. Average
_____ %
_____ %
Analysis (complete all work on separate paper):
1.
Calculate the mass of CO2 released.
2.
Calculate the mass of carbon (in the carbon dioxide) that was released. Use the five step
method.
3. Calculate the percentage of carbon in the original unknown sample. Use the five step method.
4. Using the following list of possible compounds, identify your unknown sample by using the
percent of carbon present. SHOW ALL WORK!
potassium carbonate
calcium carbonate
Student ID #: ________
Pre-Test
sodium carbonate
cupric carbonate
sodium bicarbonate
magnesium carbonate
Score: _____/ 60
= _______%
Unit 8: The Mole and Stoichiometry
You may write directly on this exam. All questions are worth 2.5 points each unless noted otherwise.
You may use a calculator (non-graphing) on this test. DO YOUR BEST!! 
1
(8-1)
How many significant digits are in the number 0.000400?
2
(8-1)
How many significant digits are in the number 4.58 x 109?
3
(8-1)
Perform the following calculation. Write your answer with the correct number of significant figures.
2.561 + 15.2 =
4
(8-1)
Perform the following calculation. Write your answer with the correct number of significant figures.
223 / 2 =
Objective 8-1 score: ______/10
5
(8-2)
Write the number 52,500 in scientific notation.
6
(8-2)
Write the number 4.58 x 10-9 in standard notation.
7
(8-2)
Perform the following calculation and write your answer in scientific notation with the correct number of
significant digits:
1.50 x 102 + 6.29 x 104 =
8
(8-2)
Perform the following calculation and write your answer in scientific notation with the correct number of
significant digits:
4.590 x 10-8 x 1.2x 10-6 =
Objective 8-2 score: ______/10
9
(8-3)
What is the formula mass of dinitrogen trioxide, N2O3? (5 points)
10 (8-3)
How many moles are present in 10.0 gram Al2(SO4)3? (5 points)
11 (8-4)
__ C2H4 + __ O2  __ CO2 + __ H2O
Objective 8-3 score: ______/10
In the above reaction, if you start with 45 grams of ethylene (C 2H4), how many grams of carbon dioxide
will be produced? SHOW YOUR WORK. (5 points)
12 (8-4)
Lead (II) nitrate reacts with sodium iodide to form sodium nitrate and lead (II) iodide. If I start with 25.0
grams of lead (II) nitrate and 15.0 grams of sodium iodide, how many grams of sodium nitrate can be
formed? SHOW YOUR WORK. (5 points)
Objective 8-4 score: ______/10
13 (8-5)
What is the percent composition of each element in barium nitrate, Ba(NO 3)2? SHOW YOUR WORK. (5
points)
14 (8-5)
What is the percent composition of nitrogen in urea, NH2CONH2? SHOW YOUR WORK. (5 points)
Objective 8-5 score: ______/10
15 (8-6)
Chemical analysis of citric acid shows that it contains 37.51% C, 4.20% H, and 58.29% O. What is its
empirical formula? SHOW YOUR WORK. (5 points)
16 (8-6)
A compound with a formula mass of 42.08 amu is found to be 85.64% carbon and 14.16% hydrogen by
mass. Find its molecular formula. SHOW YOUR WORK. (5 points)
Objective 8-6 score: ______/10
BONUS: A 175.0 g sample of a compound contains 56.15 g C, 9.43 g H, 74.81 g O, 13.11 g N, and 21.49 g Na.
What is its empirical formula?