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Math of Formulas
Chapter 10
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Macro vs. Micro
• Chemistry has two worlds:
– The macroscopic world = what a scien>st can see and weigh
– The microscopic world = the atomic level, filled with >ny molecules
• Chemists need a way to convert from the molecular level to one that is usable in the laboratory
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Enter the Mole…
• Mole (mol) -‐ SI unit for measuring the amount of a substance
• Avogadro’s Number
• 1 mole = 6.02x1023 representa>ve par>cles
• Just as 1 dozen = 12 …
• A mole is 602,000,000,000,000,000,000,000 par>cles
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Avogadro’s Analogies
• The popula>on of the earth is six billion (6 x 109 people). It would take about 100 trillion Earth popula>ons to sum up to Avogadro's number.
• One mole of high school textbooks would cover the USA to a depth of about 320 km (200 miles).
• Water flows over Niagara Falls at about 650,000 kL (172,500,000 gallons) per minute. At this rate it would take 134,000 years for one mole of water drops (6.02 x 1023 drops) to flow over Niagara Falls.
• Avogadro's number (6.02 x 1023 ) is the approximate number of milliliters of water in the Pacific Ocean (7 x 108 km3 or 7 x 1023 mL).
• If one mole of par>cles the size of sand grains were released by the erup>on of Mount St. Helens, they would cover the en>re state of Washington to the depth of a ten-‐story building.
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How Do I Weigh a Mole?
• Molar Mass – mass, in grams, of one mole of a substance (g/mol)
• Molar Mass of elements = atomic mass in grams
• ex: molar mass of Carbon is 12 g/mol • Molar Mass of compounds = sum of the par>al masses of the elements within a compound
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What is the Molar Mass of Water?
• H2O
• Symbol: # of atoms x atomic mass = par>al mass H 2 1 2 O 1 16 16
• Add up par>al masses to get molar mass: • 2 + 16= 18 g/mol
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Examples
• Br2
• H2SO4
• Al(NO3)3
Br 2 x 80 = 160 g/mol
H 2 x 1 = 2 S 1 x 32 = 32 O 4 x 16 = 64 98 g/mol
Al 1 x 27 = 27 N 3 x 14 = 42 O 9 x 16 = 144 213 g/mol
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What is the molar mass of (NH4)2CO3?
A.) 144 g/mol
B.) 138 g/mol
C.) 96 g/mol
D.) 78 g/mol
N 2 x 14 = 28 H 8 x 1 = 8 C 1 x 12 = 12 O 3 x 16 = 48
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What is the molar mass of (NH4)3PO4
N 3 x 14 = 42 H 12 x 1 = 12 P 1 x 31 = 31 O 4 x 16 = 64 149 g/mol
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Percent ComposiLon
• % composiLon = part x 100
whole • Of an element in a compound…
% composiLon = parLal mass of element x 100
molar mass of compound
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Examples
• What is the percent by mass of oxygen in the compound P2O5? Phosphorus?
P 2 x 31 = 62 O 5 x 16 = 80 142 g/mol
%O = 80 x 100 = 56.3% 142
%P = 62 x100 = 43.7% 142
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What is the percent composiLon of chromium in BaCrO4?
A.) 4.87 %
B.) 9.47 %
C.) 20.5 %
D.) 25.2 %
Ba 1 x 137 = 137 Cr 1 x 52 = 52 O 4 x 16 = 64 253 g/mol
%Cr = 52 x 100 = 253
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What is the percent composiLon of nitrogen in the compound (NH4)2SO4?
N 2 x 14 = 28 %N = 28 x 100 = 21.2% H 8 x 1 = 8 132 S 1 x 32 = 32 O 4 x 16 = 64 132 g/mol
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Mole-‐Mass Conversions
• Write down the given amount
• Mul6ply by a frac6on – Units to cancel must be on bo=om – Desired units on top
• Plug in values for substance’s molar mass – X grams in 1 mole
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Examples
• How many moles are contained in 34.0 g of NH3?
• What is the mass (in grams) of 3 moles of NH3?
34.0g x g mol
17
1 = 2.0 mol N 1 x 14 = 14 H 3 x 1 = 3 17 g/mol
3 mol X mol g 17
1 = 51 g
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What is the mass in grams of 5.90 moles of C8H18?
A.) 0.0512 g
B.) 19.4 g
C.) 389 g
D.) 673 g
5.90 mol x 114 g = 673 g 1mol
C 8 x 12 = 96 H 1 x 18 = 18 114 g/mol
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What is the number of moles in 432 grams of Ba(NO3)2?
A.) 0.237 mol
B.) 0.605 mol
C.) 1.65 mol
D.) 3.66 mol
432 g x 1mol = 1.65 mol 261 g
Ba 1 x 137 = 137 N 2 x 14 = 28 O 6 x 16 = 96 261 g/mol
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Mole Triangle
• The mole has three values
– Mass: one mole is equal to the molar mass – Par6cles: one mole is 6.02x1023 par6cles – Volume: one mole is 22.4 L (gases only) at STP
1 Mole
Molar Mass
6.02x1023 par6cles 22.4 L (gas)
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How many atoms are in 3.5 moles of arsenic atoms?
A.) 5.8 x 10-‐24 atoms
B.) 7.5 x 101 atoms
C.) 2.1 x 1024 atoms
D.) 1.7 x 1023 atoms
3.5 mol x 6.02x1023 atom = 1 mol
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How many moles of silver atoms are in 1.8 x 1020 atoms of silver?
A.) 3.0 x 10-‐4
B.) 3.3 x 10-‐3
C.) 3.0 x 102
D.) 1.1 x 1044
1.8x1020 atom x 1 mol = 6.02x1023 atom
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What is the number of moles in 500 Liters of Helium gas at STP?
A.) 0.05 mol
B.) 0.2 mol
C.) 22 mol
D.) 90 mol
500L x 1 mol = 22.4 L
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MulPstep Conversions • Convert to moles and then to desired
• How many molecules of water are present in a 30 gram sample?
• What is the mass of a sample that contains 3.12 x 1024 carbon atoms?
30g x g
mol 1
18 x
mol
molecules
1
6.02x1023
3.12x1024atom x 1mol x 12g = 6.22 g 6.02x1023atom 1mol
= 1x1024 molecules
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Empirical Vs. Molecular Formulas
• Empirical Formula – shows the smallest whole-‐number ra9o of the atoms in the compound
• ex: NO2 (1:2)
• Molecular Formula – exactly how many atoms are present in the molecule (may be the empirical formula or not)
• ex: NO2 or N2O4
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Empirical or Molecular?
If molecular give its corresponding empirical formula
• H2O • H2O2
• N2O5
• C6H12O6
• C2H4
• PI3
Press:
A for empirical
B for molecular
E M
E
M
M E
HO
CH2O CH2
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Which of the following is NOT an empirical formula?
A.) Sb2S3
B.) C2H8O
C.) C2N2H8
D.) BeCr2O7
CNH4
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Which of the following have the same empirical formula?
A.) CO2 and SO2
B.) C7H14 and C10H20
C.) C4H10 and C10H4
D.) C6H12 and C6H14
CO2 and SO2
CH2 and CH2
C2H5 and C5H2
CH2 and C3H7
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Chemical Formulas and Moles
Al2O3 Subscripts tell you the number of moles of atoms in a formula
2 moles Al and 3 moles O
PI3? 1 mol Phosphorous and 3 moles Iodine
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Determining Empirical Formulas From Percent Composi9on
• Empirical formulas have a simple whole number ra9o of atoms
1) Assume that you have 100 grams of substance (replace percent with grams)
2) Change grams to moles 3) Find lowest whole number ra9o (divide all numbers by
the lowest value for moles) 4) Use value from step 3 as your subscripts for the
respec9ve elements (if all values are not within 0.1 of a whole number, alter by mul9plying by a whole number)
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Examples
• A compound is analyzed and found to contain 50% sulfur and 50% oxygen. What is its empirical formula?
O 50g
S 50g x 1mol 32g
x 1mol 16g
= 1.5625mol
= 3.125mol
1.5625
1.5625 = 2
= 1
SO2
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A compound is analyzed and found to contain 25.9% nitrogen and 74.1% oxygen. What is its empirical formula?
N 25.9g x 1mol = 1.85mol 14g
O 74.1g x 1mol = 4.63mol 16g
1.85
1.85
= 1
= 2.5
x 2 = 2
x 2 = 5
N2O5
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What is the empirical formula of a compound that is 40% sulfur and 60% oxygen by weight?
A.) SO
B.) SO2
C.) SO3
D.) S6O4
S 40g x 1mol = 1.25mol = 1 32g 1.25
O 60g x 1mol = 3.75mol = 3 16g 1.25
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Combined Problem • A compound contain 64.9% C, 13.5% H, and 21.6% O. Its molecular mass is 74 g/mol. Find the molecular formula.
C 64.9g x 1mol = 5.408mol = 4 12g 1.35
H 13.5g x 1mol = 13.5mol = 10 1g 1.35
O 21.6g x 1mol = 1.35mol = 1 16g 1.35
C4H10O
C 4 x 12 = 48 H 10 x 1 = 10 O 1 x 16 = 16 74 g/mol
74 = 1 74
C4H10O
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• Zeanxanthin is one of the compounds found to cause the colors in maple leaves in the fall.
• It has a molecular weight of 544 and is 83.82% carbon, 10.29% hydrogen, and 5.88% oxygen.
• Find the molecular formula of zeanxanthin.
C 83.82g x 1mol = 6.985 = 19 12g 0.3675
H 10.29g x 1mol = 10.29 = 28 1g 0.3675
O 5.88g x 1mol = 0.3675 = 1 16g 0.3675
C19H28O
C 19 x 12 = 228 H 28 x 1 = 28 O 1 x 16 = 16 272g/mol
544 = 2 272
C38H56O2
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Chapter 5/6 Test To do well on this test you should be able to comfortably do the following:
• Name compounds if given formula • Give formula of a compound if given its name • Mole concept and relaUonships (molar mass = 1 mol = 6.02x1023
parUcles) • Determine the molar masses of elements and compounds • Determine percent composiUon of elements within a compound • Molar conversions (mass ↔ mole & mass ↔ parUcles) • IdenUfy empirical and molecular formulas • Determine the empirical formula of a compound from percent
composiUon or lab data • Determine the molecular formula of a compound from percent
composiUon (or enough informaUon to determine it) and molar mass
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Hydrates
• A crystalline form of an ionic substance that contains a definite number of water molecules (loosely bound by intermolecular forces).
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Anhydrous vs. Hydrated Salts
• Anhydrous (no water) is a term used to describe the ionic compound once water has been removed
• Heat can be used to remove the water from the hydrated salt – CuSO4 ● 5H2O + heat CuSO4 + 5H2O
Hydrate Lab