# Chapter 6 General Chemistry Molar Conversions, Percent Composition by lfl93601

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```									Chapter 6
General Chemistry
Molar Conversions, Percent Composition, Empirical and Molecular Formulas

The atomic mass of a single atom is so small it cannot be measured in the laboratory. To
make mass easier to use, the gram is substituted for the a.m.u.

Chemists have determined that 6.02 x 10 23 atoms of an element have a mass in grams
equal to the mass of one atom in a.m.u. This number is called Avogadro’s number.

For example, one atom of oxygen is 15.99 a.m.u. So, the mass of 6.02 x 10 23 atoms of
oxygen is 15.99 grams.

MOLECULAR MASS
The molecular mass is the mass of a molecule expressed in grams.

To determine molecular mass:
(1) determine the mass of each element in the compound
(2) multiply this by its subscript.
(3) Add the total masses of each element together.

Example: Ethanol, C2H5OH, is a product of sugar fermentation and is the intoxicating
agent in wine and beer. What is the molecular mass of ethanol?

Element     Number of atoms       Mass from Periodic       Total mass of the element in
table                    the compound

Total Molecular mass of ethanol      _____________________

FORMULA MASS
The formula mass is used to express the mass of compounds that have both positive
and negative ions (ionic compounds).

The formula mass is the sum of the atomic masses of the atoms in a formula of an ionic
compound.

Both formula mass and molecular are calculated in the same way.
The term molar mass may be used to refer to all compounds, molecular or ionic.

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Example: Ammonium sulfate has the formula (NH4)2SO4. What is the formula mass of
ammonium sulfate?

Element     Number of atoms       Mass from Periodic        Total mass of the element in
table                     the compound

Total formula mass of Ammonium sulfate___________________

THE MOLE
 The particles that make up matter (atoms, ions, and molecules) are incredibly small.
 Only extremely large numbers of these particles can be seen or weighed. Chemists
use a quantitative unit to represent a large number of these tiny particles; this
number is called the mole .
 The mole is a counting unit just like a dozen or a ream or a gross.
 1 mole = the molar mass
 1 mole = 6.02 x 10 23
 1 mole of a gas = 22.4 L

These relationships are important in many chemical calculations.
Conversion ratios are used to convert from one unit (such as grams) to a
different unit (such as moles).

Mass                                              Particles

23
Gram formula mass                  6.02 x 10

1 Mole

22.4 L

Volume of a gas

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Examples of Molar Relationships
Substance    Molar mass              Number of              Number of
Particles              moles

C
K+1
CO
N2
NaCl

ONE STEP MOLAR CONVERSIONS
EXAMPLE 1: Calculate the mass in grams of 2.00 moles of sodium metal.
Step1: Write the number you are given
Step 2: Use a conversion factor to change units.

EXAMPLE 2: Calculate the number of moles in 64.0 grams of oxygen molecules.
Remember that the molecule oxygen has the formula O2, so 32 grams Of O2 is equal to
1 mole of O2.

TWO STEP MOLAR CONVERSIONS
To convert from moles to another unit or from another unit to moles requires only one
step, or one conversion factor. To convert between other units requires an intermediary
conversion to moles.

EXAMPLE 1: Find the number of atoms in 16.0 grams of sulfur.
Solving process: This conversion will involve two ratios. Convert from grams to moles,
then from moles to atoms of sulfur.

EXAMPLE 2: What is the mass of 15.5 liters of hydrogen gas at standard temperature
and pressure (STP)?

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PERCENT COMPOSITION CALCULATIONS
The percent composition of a compound gives the relative amount of each element
present.
To calculate percent composition:
(1) Calculate the molar mass of the entire compound.
(2) Calculate the total mass for each element or elements for which the percentage is
desired.
(3) Divide the total mass of each element by the formula mass of the compound and
multiply by 100.

Examples of Percent Composition
EXAMPLE 1: Find the percent of each element in aluminum oxide.

EXAMPLE 2: Copper(II) sulfate pentahydrate is a blue compound used to make colored
pigments, insecticides, and electric batteries. Calculate (1) the percentage of oxygen,
and (2) the percentage of water in this compound.
The percent of oxygen refers to both the oxygen in the copper(II)sulfate and the oxygen
in the attached water molecules.
There are a total of ____ oxygen atoms.

EXAMPLE 3: Calculate the percent composition of sodium sulfide.

EXAMPLE 4: Determine the percent of potassium in potassium phosphate.

EXAMPLE 5: Calculate the amount of strontium in 5.0 grams of SrCl2

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THE MOLE AS VOLUME
One mole of any gas occupies a volume of ________________ under STP.

STP-(Standard Temperature and Pressure): a temperature of 0o C and a pressure of one
atmosphere (1atm).

6.02 x 1023 molecules of a gas occupy 22.4 Liters

1 mole = 6.02 x 10 23 molecules = 22.4 liters

EXAMPLE 1: Under STP, what volume would 2.00 moles of He occupy?

EXAMPLE 2: If 20 L of N2 are present in a container at STP, how many moles of
nitrogen are present in the container?

EXAMPLE 3: A tank contains exactly 100 atoms of Ar gas under STP. What is the
volume of this container?

EXAMPLE 4: What is the mass of 6.00 L of chlorine gas at STP?

EMPIRICAL AND MOLECULAR FORMULAS

The empirical formula of a compound is the lowest whole-number ratio of elements in a
compound.
For example, CH2 is the empirical formula for the series of compounds : C2H4, C3H6,
C4H8, etc.
Ionic compounds are always represented as empirical formulas; however, molecular
formulas represent elements bonded together as well as their ratios in the molecule.

Relationships Between Empirical and Molecular Formulas
Compound                 Empirical Formula           Molecular Formula
sodium chloride          NaCl
water                                                H2O
Hydrogen peroxide                                    H2O2
Dinitrogen tetroxide                                 N2O4
Benzene                                              C6H6
Glucose                  C6H12O6

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You have previously used the formula of a compound to determine its percentage
composition. Now you will reverse the procedure and determine the empirical formula
form the percentage composition.

To determine the empirical formula:
(1) the mass of the each element is converted to moles
(2) a ratio of moles is determined by dividing each answer by the smallest number of
moles
(3) if the ratio is not in whole numbers, multiply all number by a single factor to make it a
whole-number ratio.

EXAMPLE 1: Calcium bromide is a compound used in photography and in the
manufacture of fire extinguishing materials. Analysis reveals that calcium bromide
contains 20.0% calcium and 80.0% bromine. Calculate the empirical formula.
To solve:
Assume a 100 gram sample so that each percentage is numerically equal to the number
of grams of the element. Thus, 20.0 grams Ca and 80.0 grams Br form 100 grams of
compound.
The atomic mass of calcium gives the relationship: 40.1 grams Ca = 1.00 mole Ca.
For bromine, 79.9 grams = 1 mole.

EXAMPLE 2: Find the empirical formula for a compound that contains 36.5% sodium,
25.4% sulfur, and 38.1% oxygen.

EXAMPLE 3: What is the empirical formula of a compound which contains 53.73% Fe
and 46.27% S?

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MOLECULAR FORMULAS
The molecular formula calculation is the same as the empirical formula calculation,
except that the formula mass is used in an additional step.
To calculate a molecular formula, the formula mass must be known.
The molecular formula is always a whole number multiple of the empirical formula.

EXAMPLE 1: An organic compound is found to contain 92.25% carbon and 7.75%
hydrogen. If the molecular mass is 78, what is the molecular formula?
First determine the empirical formula.
(a) Number of moles

(b) Ratio of moles

Second, determine the mass of the empirical formula and divide
it into the mass of the molecular formula.

Third, multiply the empirical formula by this last number.

EXAMPLE 2: If the molecular mass of an oxide of nitrogen is 108, and 4.02 g of N
combine with 11.48 grams of O, what is the molecular formula of this compound?

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PRACTICE PROBLEM SET I
Calculate the formula (or molecular)   mass of the following compounds:
a. H2SO4                               h. C12H22O11                o. MgSO4
b. NaOH                                i. Pb(OH)2                  p. Al(NO3)3
c. NH4NO3                              j. K2SO4                    q. Li3PO4
d. Fe(C2H3O2)3                         k. CaSO3                    r. SO2
e. CuSO4                               l. CuSO4 5H2O               s. MgCO3
f. CaSO4 2H2O                          m. N2O5                     t. Na2CO3
g. MnCl2 4H2O                          n. (NH4)3PO4                u. CHCl2COOH

PRACTICE PROBLEM SET II
1. Calculate the mass in grams for each of the following. Show your work on another
sheet of paper!
a. 3.00 moles Na                             h. 6.00 moles O2
b. 2.50 moles Ca                             i. 4.00 moles Al
c. 5.00 moles Mg                             j. 3.00 moles H
d. 0.500 mole Cl2                            k. 2.00 moles H2SO4
e. 3.50 moles CaCO3                          l. 5.00 moles KI
f. 0.250 moles MgCl2                         m. 1.500 moles Ca(OH)2
g. 3.00 moles Al2O3                          n. 0.500 mole Ca(NO3)3 3H2O

2. Calculate the number of moles for each of the following. Show your work on another
sheet of paper.
a. 200.0 grams F2                    h. 150.0 grams Zn
b. 25.0 grams Li                     i. 160.0 grams Br
c. 60.0 grams Ne                     j. 250.0 grams Fe
d. 180.0 grams Ca                    k. 32.0 grams SO2
e. 200.0 grams NaOH                  l. 10.0 grams Na2S
f. 100.0 grams MgCO3                 m. 60.0 grams K2SO4
g. 50.0 grams ZnO                    n. 80.0 grams H2O2

3. Calculate the number of atoms, molecules, or ions for each of the following. Show
your work on another sheet of paper.
a. 2.00 moles Na to atoms                   f. 25.0 grams S to atoms
b. 1.00 mole N to atoms                     g. 20.0 grams Ca to atoms
c. 46.0 grams Na to atoms                   h. 2.00 moles CO2 to molecules
d. 3.00 moles K+ to ions                    i. 35.0 grams H2O to molecules
e. 68.0 grams H2S to molecules              j. 0.500 mole Mg+2 to ions

4. Calculate the number of grams in each of the following. Show your work on another
sheet of paper.
a. 6.02 x 10 23 atoms of Pb
b. 3.01 x 10 23 formula units of NaOH
c. 1.20 x 10 24 molecules of CO
d. 1.50 x 10 23 ions of Ba+2
e. 3.01 x 10 23 atoms of S
f. 2.41 x 10 24 molecules of H2O

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PRACTICE PROBLEM SET 3
1. Calculate the percent composition of the following compounds:
a. Fe2O3     b. Ag2O       c. HgO          d. Na2S

2. Determine the percent of sodium in sodium sulfate.

3. For the compound sodium sulfate decahydrate, calculate the following:
a. % Na     b. %O        c. %H2O

4. Calculate the percent of nitrogen in each of the following compounds:
a. NH4NO3           b. (NH4)2SO3            c. HNO2

5. Calculate the mass of the metal in each of the following:
a. 50.0 grams MgS                          d. 200.0 kg Al2O3
b. 80.0 kg FeCO3                           e. 150.0 grams SrCl2 2H2O

6. Calculate the amount of the named element in each of the following compounds.
a. iron in 25.0 g of Fe3O4
b. phosphorus in 40.5 g of Ca3(PO4)2
c. carbon in 18.4 g of CaCO3
d. oxygen in 46.45 g of potassium permanganate

PRACTICE PROBLEM SET IV
1. Calculate the empirical formula for the compounds with the following percentages:
a. Fe 46.56%, S 53.44%
b. Fe 63.53%, S 36.47%
c. Mn 63.1%, S 36.9%
d. 26.6%, Cr 35.4%, O 38.0%

2. Calculate the empirical formulas for the following three compounds containing sodium,
sulfur, and oxygen:
a. Na 36.5%, S 25.4%, O 38.1%
b. Na 32.4%, S 22.6%, O 45.0%
c. Na 29.1%, S 22.6%, O 30.4%

3. The formula mass of a compound is 92. Analysis of the compound shows that there
are 0.608 grams of nitrogen and 1.388 grams of oxygen. What is the molecular formula
of this compound?

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4. There are two oxides of phosphorus. Both oxides can exist in different forms
depending on the temperature and the pressure. Calculate the empirical and molecular
formulas from the data:
a. P 56.4%, O 43.7%, molecular mass 220
b. P 43.6%, O 56.4%, molecular mass 284

5. Citric acid, an organic acid found in lemons and other fruits, contains 37.5% carbon,
58.3% oxygen and 4.20% hydrogen. What is the molecular formula of citric acid if it has
the molecular mass of 192?

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