Moles
Chemistry/Hart
Moles
How can we count how many atoms or molecules are in a piece of matter if we can’t see them?
How can we count how many atoms or molecules are in a piece of matter if they have different
masses?
What can we measure in the laboratory that will help us?
What is the “common currency”?
MOLES!
1 mole = the amount of pure substance that contains as many particles (atoms, molecules,
or fundamental units) as there are atoms in exactly 12 grams of carbon-12
(agreed upon by chemists and physicists in 1960/61)
= 6.02 x 1023 particles = Avogadro’s number
Mole comes from molekül (German) = molecule
Molecule comes from molecula (New Latin), meaning very small specimen
Background:
Lorenzo Romano Amedeo Carlo Avogadro (1776-1856) - Italian physics professor
1811 - Avogadro's hypothesis - now a law
"Equal volumes of gases under the same conditions have equal numbers of molecules."
 “universal container”
Late 1800s – chemists – developed scale of relative atomic masses of gases, based on 1/16
of the average atomic mass of oxygen
1920s – physicists – developed relative atomic masses based on 1/16 of the oxygen-16
atom
1959-1961 – chemists and physicists - agreed to switch to carbon-12 as the standard,
setting its atomic mass at 12 (pragmatic reasons – carbon-12 was the standard in mass
spectroscopy, and close to chemistry’s oxygen standards)
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Moles
Chemistry/Hart
Moles in conversion factors
number of “particles” moles
6.02 x 1023 particles
1 mole
mass (g)  moles
average atomic mass in g
1 mole
number of “particles”  mass (g)
both of the above conversion factors
number of atoms in a compound
# atoms
1 compound
Math and the Mole
(# particles/mole)
1.
How many fingers are there on 1 person?
2.
How many fingers are there on 1 dozen people?
3.
How many fingers are there on 3 dozen people?
4.
How many fingers are there on 1 mole of people?
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Moles
Chemistry/Hart
5.
How many fingers are there on 3.12 moles of people?
6.
How many F atoms in 3.12 moles of F?
7.
How many moles of F do you have if you have 2.45 x 1022 atoms of F?
(mass/mole)
Hint: if problem includes numbers of atoms or other representative particles and moles, use
Avogadro’s number: 6.02 x 1023 particles
If problem includes grams and moles use the periodic table to find molar mass.
8.
How many grams of F are in 3.89 moles of F?
9.
How many moles of F atoms are in 45.6 g of F?
(# particles/mass)
10.
How many F atoms are in 65.8 g F?
11.
What is the mass, in grams, of 7.62 x 1024 F atoms?
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Moles
Chemistry/Hart
(# atoms/compound)
12.
How many F atoms are in 3.84 moles of MoF6 molecules?
Molar Mass
Molar mass = mass, in grams, of 1 mole of a substance (6.02 x 1023 particles)
expressed in g/mol
Molar mass is numerically equal to average atomic mass in amus (atomic mass units).
So, molar mass of oxygen (O) = mass of 1 mole of O atoms
= mass of 6.02 x 1023 atoms
= 16.00 g/mol
molar mass of lead (Pb)
= mass of 1 mole of Pb atoms
= mass of 6.02 x 1023 atoms
= 207.2 g/mol
How do we determine the molar mass of compounds?
Add up the molar masses of all elements in the compound, taking into account the number of
moles of each element.
e.g. What is the molar mass of Na3PO4?
3 moles of Na @ 22.99 g/mol = 3 mol x 22.99 g
mol
1 mole of P @ 30.97 g/mol
= 1 mol x 30.97 g
mol
4 moles of O @ 16.00 g/mol
= 4 mol x 16.00 g
mol
Add these together = 163.94 g = molar mass of Na3PO4
How do we use molar mass of a compound in a conversion problem?
The same way we use molar mass of an atom…
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Moles
Chemistry/Hart
(#atoms/compound and molar mass of compounds)
13.
How many Na atoms are in 252 g of Na3PO4?
Moles Warmups
1.
How many moles of Cu are in 4.95 g of Cu?
A: 0.0779 mol Cu
2.
How many atoms of Cu are in 5.00 mol of Cu?
A: 3.01 x 1024 Cu atoms
3.
How many grams of Na are in 5.29 moles Na?
A: 122 g Na
4.
How many moles of Ba are in 5.25 x 1039 atoms of Ba? A: 8.72 x 1015 mol Ba
5.
What is the mass (in g) of 7.5 x 1015 atoms of Ni? (hint: 2 conversion factors)
A: 7.3 x 10-7 g Ni
6.
How many atoms of Na are in 25 g of Na? (hint: 2 conversion factors)
A: 6.5 x 1023 Na atoms
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Moles
Chemistry/Hart
7.
What is the molar mass of calcium chloride (CaCl2)? A: 110.98 g/mol
8.
How many O atoms are in 2.9 moles of SO3?
9.
How many Ca atoms are in 532 g of Ca? A: 7.99 x 1024 Ca atoms
10.
How many grams of Pb are in 4.20 x 1022 atoms of Pb? A: 14.5 g Pb
11.
How many K atoms are in 16.2 g of K2S?
12.
What is the molar mass of barium nitrate (Ba(NO3)2?
13.
What is the mass of 5.26 mol of NaOH?
14.
What is the mass of 5.62 x 1019 formula units of CuSO4?
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A: 5.2 x 1024 O atoms
A: 1.77 x 1023 K atoms
A: 261.35 g/mol
A: 210. g NaOH
A: 1.49 x 10-2 g
Moles
15.
Chemistry/Hart
How many hydrogen atoms are in 562 g of ethanol (C2H6O)?
A: 4.41 x 1025 H atoms
Molar Calculations relating to Chemical Formulas
Warmup: What is the molar mass of Pb3(PO4)2?
1.
Determine percent composition (by mass) of all elements present in a compound:
Find the molar masses of each element in the compound.
Find the total molar mass.
Calculate:
% composition = molar mass of element
x 100%
total molar mass of compound
e.g. What is the % composition (by mass) of NaCl? CaCl2?
Apply % composition:
e.g. What mass of Na is present in 200.0 g NaCl?
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Moles
Chemistry/Hart
Mass Percent Warmups
1. Copper (I) sulfide is found in nature as the mineral chalcocite, a copper ore.
What is the mass percent of copper in chalcocite?
A: 79.85% Cu
2. Chalcopyrite has the formula CuFeS2.
What is the mass percent of copper in chalcopyrite?
A: 34.6% Cu
3. Will you get more copper from the same mass of pure chalcopyrite or pure chalcocite?
Explain your answer.
2. Convert % composition (mass percent) empirical formula
a.
Assume a 100 g sample – use same numbers as grams rather than % .
b.
Perform mass  mole conversions.
c.
Divide each result (mole) by the smallest result present (mole ratio).
d.
Look for whole number ratio.
Rhyme to remember order of steps to convert % composition  empirical formula:
Percent to mass
Mass to mole
Divide by small
Times till whole
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Moles
Chemistry/Hart
Practice:
1. One of the components of fresh alkaline batteries is a black powdery compound, made
of 63% manganese and 37% oxygen. What is the compound’s empirical formula?
2. While analyzing a dead alkaline battery, Antonio found a compound that is made of 70.0%
manganese and 30.0% oxygen. What is its empirical formula?
Empirical Formula Warmups
1.
During a winter vacation, you work at a ski resort covering icy sidewalks with a
substance containing 26.2% N, 7.5% H, and 66.3% Cl.
What is the formula for this compound?
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A: NH4Cl
Moles
2.
Chemistry/Hart
Phosphorus forms two oxides. One has 56.34% P and 43.66% O. The other has
43.64% P and 56.36% O. What are the empirical formulas for these compounds?
A: P2O3 and P2O5
3.
What is the empirical formula for a compound that contains 26.56% potassium,
35.41% chromium, and 38.03% oxygen?
4.
A: K2CrO7
What is the empirical formula for a compound that contains 111.16 g of iron and 63.84
g of sulfur?
A: FeS
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Moles
Chemistry/Hart
3. How to determine molecular formula
Empirical vs. Molecular Formula
Compound
Empirical
formula
Empirical
molar mass
Molecular
molar mass
Molecular
formula
Formaldehyde
CH2O
30.03 g
30.03 g
CH2O
Acetic acid
CH2O
30.03 g
60.06 g
C2H4O2
Glucose
CH2O
30.03 g
180.18 g
C6H12O6
To find the molecular formula of glucose,
divide the molecular molar mass by the empirical molar mass, round to the nearest whole
number.
(molecular) molar mass = 180.18 g = ~ 6
empirical molar mass
30.03 g
then multiply subscripts by 6 => C6H12O6 to get the molecular formula
Practice Problem – Determining molecular formula
Hydrazine is 87.42% N and 12.58% H.
The (molecular) molar mass of hydrazine is 32.0 g/mol.
a) What is its empirical formula?
b) What is its molecular formula?
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Moles
Chemistry/Hart
Solution Concentration
Percent by Mass
Mass % of component = mass of component in solution x 100%
total mass of solution
e.g. In order to maintain a sodium chloride (NaCl) concentration
similar to ocean water, an aquarium must contain 3.6 g
NaCl per 100.0 g of water. What is the percent by mass of
NaCl in the solution?
3.6 g NaCl
x 100% = 3.6 g NaCl x 100%
100.0 g H2O + 3.6 g NaCl
103.6 g total
= 3.5%
e.g. A solution contains 2.7 g of CuSO4 in 75 mL of solution.
Assume the density of the solution is 1.0 g/mL.
What is the mass percent of the solution?
2.7 g (1 mL) x 100% = 3.6%
75 mL 1.0 g
Molarity
Molarity = the # moles solute dissolved in 1 L of solution
Molarity: the concentration of solution in moles solute
L solution
not solvent
See Moles WS 6 for notes and practice problems related to molarity.
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