3.1 Formula Mass and the Mole Concept
Because the definition of both the mole and the atomic mass unit are based on the same reference substance, _____, the molar mass of any substance is numerically equivalent to its atomic or formula weight in amu.
¹²C
The word "mole" translates as:
"large mass or bulk"
25. Determine which one of the following contains the greatest mass of aluminum: 122 g AlPO₄ 266 g Al₂Cl₆ 225 g Al₂S₃ Step 1: calculate the relative percent composition of aluminum in each compound
%Al in AlPO₄= 26.98 g mol⁻¹ Al/121.95 g mol⁻¹ AlPO₄ = 0.2212 %Al in Al₂Cl₆ = 53.96 g mol⁻¹ Al/266.66 g mol⁻¹ Al₂Cl₆= 0.2024 %Al in Al₂S₃ = 53.96 g mol⁻¹ Al/150.7 g mol⁻¹ Al₂S₃ = 0.3593
A single ¹²C atom weighs 12 amu (its atomic mass is 12 amu). How many grams of ¹²C are there in a mole of ¹²C?
12 grams
25. Determine which one of the following contains the greatest mass of aluminum: 122 g AlPO₄ (0.2212 Al) 266 g Al₂Cl₆ (0.2024 Al) 225 g Al₂S₃ (0.3593 Al) Step 2: multiply the relative percent composition of aluminum in each compound by the mass of the compound
122 g AlPO₄ x (0.2212 Al) = 26.99 g Al 266 g Al₂Cl₆ x (0.2024 Al) = 43.83 g Al 225 g Al₂S₃ x (0.3593 Al) = 80.85 g Al Al₂S₃ has the greatest mass of aluminum
15b. Calculate the molar mass of the herbicide paraquat, C₁₂H₁₄N₂Cl₂
12C x 12.011 = 144.132 g/mol 14H x 1.008 = 14.112 g/mol 2N x 14.007 = 28.014 g/mol 2Cl x 35.45 = 70.90 g/mol molar mass = 257.2 g/mol
15e. Calculate the molar mass of a typical soap, C₁₇H₃₅CO₂Na
18C x 12.011 = 216.198 g/mol 35H x 1.008 = 35.28 g/mol 2O x 15.999 = 31.998 g/mol 1Na x 22.990 = 22.990 g/mol molar mass = 306.5 g/mol
15d. Calculate the molar mass of urea, CO(NH₂)₂
1C x 12.011 = 12.011 g/mol 1O x 15.999 = 15.999 g/mol 2N x 14.007 = 28.014 g/mol 4H x 1.008 = 4.032 g/mol molar mass = 60.06 g/mol
15a. Calculate the molar mass of the anesthetic halothane, C₂HBrClF₃
2C x 12.011 = 24.022 g/mol 1H x1.008 = 1.008 g/mol 1Br x 79.904 = 79.904 g/mol 1Cl x 35.45 = 35.45 g/mol 3F x 18.998 = 56.994 g/mol molar mass = 197.4 g/mol
13c. Calculate the molar mass of: Sc₂(SO₄)₃
2Sc x 44.956 = 89.912 g/mol 3S x 32.06 = 96.18 g/mol 12O x 15.999 = 191.988 g/mol molar mass = 378.1 g/mole
13d. Calculate the molar mass of: CH₃COCH₃ (acetone)
3C x 12.011 = 36.033 g/mol 6H x 1.008 = 6.048 g/mol 1O x 15.999 = 15.999 g/mol molar mass = 58.08 g/mol
CCl₂O 1C x 12.011 = 12.011 amu 2Cl x 35.45 = 70.90 amu 1O x 15.999 = 15.999 amu Molecular mass = 98.91 amu
4a. Determine the molecular mass
C₂H₂ 2C x 12.011 = 24.022 amu 2H x 1.008 = 2.016 amu Molecular mass = 26.04 amu
4b. Determine the molecular mass
C₂H₂Br₂ 2C x 12.011 = 24.022 amu 2H x 1.008 = 2.016 amu 2Br x 79.904 = 159.808 amu Molecular mass = 185.8 amu
4c. Determine the molecular mass
H₂SO₄ 2H x 1.008 = 2.016 amu 1S x 32.06 = 32.06 amu 4O x 15.999 = 63.996 amu Molecular mass = 98.07 amu
4d. Determine the molecular mass
13b. Calculate the molar mass of: C₅H₁₂
5C x 12.011 = 60.005 g/mol 12H x 1.008 = 12.096 g/mol molar mass = 72.101 g/mol
C₄H₈ 4C x 12.011 = 48.044 amu 8H x 1.008 = 8.064 amu Molecular mass = 56.11 amu
5a. Determine the molecular mass
C₂H₆ 2C x 12.011 = 48.044 amu 6H x 1.008 = 6.048 amu Molecular mass = 54.09 amu
5b. Determine the molecular mass
H₂Si₂Cl₄ 2H x 1.008 = 2.016 amu 2Si x 28.085 = 56.17 amu 4Cl x 35.45 = 141.8 amu Molecular mass = 200.0 amu
5c. Determine the molecular mass
H₃PO₄ 3H x 1.008 = 3.024 amu 1P x 30.974 = 30.974 amu 4O x 15.999 = 63.996 amu Molecular mass = 97.99 amu
5d. Determine the molecular mass
13e. Calculate the molar mass of: C₆H₁₂O₆ (glucose)
6C x 12.011 = 72.066 g/mol 12H x 1.008 = 12.096 g/mol 6O x 15.999 = 95.994 g/mol molar mass = 180.16 g/mol
C₂H₂ 2C x 12.011 = 24.022 amu 2H x 1.008 = 2.016 amu Molecular mass = 26.04 amu No, this molecule does not have the molecular mass of 28.05
6a. Does this molecule have a molecular mass of 28.05?
C₂H₄ 2C x 12.011 = 24.022 amu 4H x 1.008 = 4.032 amu Molecular mass = 28.05 amu Yes, this molecule has a molecular mass of 28.05
6b. Does this molecule have a molecular mass of 28.05?
C₂H₆ 2C x 12.011 = 24.022 amu 6H x 1.008 = 6.048 amu Molecular mass = 30.07 amu No, this molecule does not have a molecular mass of 28.05
6c. Does this molecule have a molecular mass of 28.05?
15c. Calculate the molar mass of caffeine, C₈H₁₀N₄O₂
8C x 12.011 = 96.088 g/mol 10H x 1.008 = 10.08 g/mol 4N x 14.007 = 56.028 g/mol 2O x 15.999 = 31.998 g/mol molar mass = 194.2 g/mol
13a. Calculate the molar mass of: S₈
8S x 32.06 = 256.5 g/mol
Vitamin C is a covalent compound with the molecular formula C₆H₈O₆. The recommended daily dietary allowance of vitamin C for children aged 4-8 years is 1.42 x 10⁻⁴ mol. What is the formula mass of vitamin C?
C 6 atoms x 12.01 amu = 72.06 amu H 8 atoms x 1.008 amu = 8.064 amu O 6 atoms x 16.00 amu = 96.00 amu Formula mass of vitamin C C₆H₈O₆ = 176.1 amu
Calculate the molecular mass of chloroform (CHCl₃): Average atomic mass of C = 12.01 Average atomic mass of H = 1.008 Average atomic mass of Cl = 35.45
C x 1 atom = 12.01 H x 1 atom = 1.008 Cl x 3 atoms = 106.35 Molecular mass = 119.37
Calculate the molecular mass of ibuprofen (C₁₃H₁₈O₂): Average atomic mass of C = 12.01 Average atomic mass of H = 1.008 Average atomic mass of O = 16.00
C x 13 = 156.13 H x 18 = 18.114 O x 2 = 32.00 Molecular mass = 206.27
Calculate the molecular mass of acetaminophen (C₈H₉NO₂): Average atomic mass of C = 12.01 Average atomic mass of H = 1.008 Average atomic mass of O = 16.00 Average atomic mass of N = 14.01
C x 8 = 96.08 H x 9 = 9.072 O x 2 = 32.00 N x 1 = 14.01 Molecular mass = 151.16
Calculate the molecular mass of aspirin (C₉H₈O₄): Average atomic mass of C = 12.01 Average atomic mass of H = 1.008 Average atomic mass of O = 16.00
C x 9 = 108.9 H x 8 = 8.064 O x 4 = 64.00 Molecular mass =180.15
3c. Calculate the molecular or formula mass of the following molecule: Ca(NO₃)₂.
Ca 1 atom x 40.08 amu = 40.08 amu N 2 atoms x 14.01 amu = 28.02 amu O 6 atoms x 16.00 amu = 96.00 amu formula mass Ca(NO₃)₂ is 164.10 amu
Calcium phosphate Ca₃(PO₄)₂ is an ionic compound and a common anti-caking agent added to food products. What is the formula mass (amu) of calcium phosphate? Ca (40.08 amu) P (30.97 amu) O (16.00 amu)
Ca 3 atoms x (40.08 amu) = 120.24 amu P 2 atoms x (30.97 amu) = 61.94 amu O 8 atoms x (16.00 amu) = 128.00 amu Formula mass of Ca₃(PO₄)₂ = 310.18 amu
For covalent substances, the formula represents the numbers and types of atoms composing a single molecule of the substance; therefore, the formula mass may be correctly referred to as a ________ mass.
Molecular
For covalent substances the formula mass can be called the:
Molecular mass
What is the formula mass of hydrazine, N₂H₄?
N 2 atoms x 14.01 amu = 28.02 amu H 4 atoms x 1.008 amu = 4.032 amu Formula mass of hydrazine N₂H₄ = 32.05 amu
Calculate the formula mass of table salt. Na (22.99 amu) Cl (35.45 amu)
Na 1 atom x 22.99 amu = 22.99 amu Cl 1 atom x 35.45 amu = 35.45 amu Formula mass of NaCl = 58.44 amu
How many carbon atoms are in a sample containing 1.31 x 10²⁰ saccharin molecules (C₇H₅NO₃S)?
Number of carbon atoms = 7 carbon atoms per saccharin molecule x 1.31 x 10²⁰ saccharin molecules Number of carbon atoms = 9.19 x 10²⁰
3a. Calculate the molecular or formula mass of the following molecule: P₄.
P 4 atoms x 30.97 amu = 123.88 amu
27. The Cullinan diamond was the largest natural diamond ever found (January 25, 1905). It weighed 3104 carats (1 carat = 200 mg). How many atoms are present in the diamond? Outline the steps required to solve this problem.
Step 1: convert 3104 carats into grams Step 2: calculate moles of carbon in diamond Step 3: multiply moles of carbon by Avogadro's number to determine number of atoms in diamond
25. Determine which one of the following contains the greatest mass of aluminum: 122 g AlPO₄ 266 g Al₂Cl₆ 225 g Al₂S₃ Outline the steps necessary to answer this question.
Step 1: determine the relative percentage of aluminum in each compound by dividing the average atomic mass of aluminum by the molecular mass of the compound Step 2: multiply the mass of each compound by the relative percentage of aluminum. The result with the highest number is the compound with the greatest mass of aluminum.
The average molecular mass of a covalent molecule is equal to the _______ of the average atomic masses of the atoms therein.
Sum
Vitamin C is a covalent compound with the molecular formula C₆H₈O₆. The recommended daily dietary allowance of vitamin C for children aged 4-8 years is 1.42 x 10⁻⁴ mol. What is the mass of this allowance in grams? (Formula mass of vitamin C is 176.1 g/mol)
grams = moles x formula mass = 1.42 x 10⁻⁴ mol x 176.1 g/mol = 0.0250 g of vitamin C
What is the mass of 0.443 mol of hydrazine, N₂H₄? (formula mass of hydrazine is 32.05 amu)
mass g = 0.443 mol x 32.05 g/mole mass g = 14.2 g of Hydrazine
17a. Determine the mass of 0.0146 mol KOH
mol = g/formula weight g = mol x formula weight g=0.0146 mol x (39.098 K + 15.999 O + 1.008 H) g= 0.819 grams
17e. Determine the mass of 2.86 mol Co(NH₃)₆Cl₃
mol = g/formula weight g = mol x formula weight g=2.86 mol x (58.933 x 1Co + 14.007 x 6N + 1.008 x 18H + 35.45 x 3Cl) g=765 grams
17c. Determine the mass of 1.6 x 10⁻³ mol Na₂SO₄
mol = g/formula weight g=mol x formula weight g=1.6 x 10⁻³ mol x (22.990 x 2Na + 32.06 x 1S + 15.999 x 4O) g=0.23 grams
17b. Determine the mass of 10.2 mol ethane, C₂H₆
mol = g/molecular weight g=mol x molecular weight g=10.2 mol x (12.011 x 2C + 1.008 x 6H) g=307 grams
17d. Determine the mass of 6.854 x 10³ mol glucose, C₆H₁₂O₆
mol = g/molecular weight g=mol x molecular weight g=6.854 x10³ mol x(12.011 x 6C + 1.008 x 12H + 15.999 x 6O) g=1.285 x10⁶ grams
A packet of an artificial sweetener contains 40.0 mg of saccharin (C₇H₅NO₃S). Given that saccharin has the molar mass of 183.18 g/mole, how many saccharin molecules are there in a 40.0 mg (0.0400 g) sample of saccharin?
moles = grams/molecular mass moles = 0.0400 g/183.18 g per mole moles = 2.18 x 10⁻⁴ moles of saccharin number of saccharin molecules = 2.18 x 10⁻⁴ moles x 6.022 x 10²³ atoms per mole number of saccharin molecules = 1.31 x 10²⁰
How many C₄H₁₀ molecules are contained in 9.213 g of this compound (molecular mass is 58.12 amu)?
moles = grams/molecular mass moles = 9.213 g/58.12 g per mole moles = 0.1585 number of molecules = moles x 6.022 x 10²³ molecules per mole number of molecules = 0.1585 mol x 6.022 x 10²³ molecules per mole number of molecules = 9.545 x 10²² molecules
How many hydrogen atoms are contained within 9.545 x 10²² molecules of C₄H₁₀?
number of H atoms in sample = number H atoms per C₄H₁₀ molecule x number of molecules of C₄H₁₀ number of H atoms in sample = 10 atoms H per molecule x 9.545 x 10²² molecules of C₄H₁₀ number of H atoms in sample = 9.545 x 10²³
How many moles of sucrose, C₁₂H₂₂o₁₁, are in a 25-g sample of sucrose? (Formula mass of sucrose is 342.30 g/mol)
number of moles = 25 g x 1 mole/ 342.30 g number of moles = 0.073 moles sucrose
Our bodies synthesize protein from amino acids. One of these amino acids is glycine, which has the molecular formula C₂H₅O₂N. Given the formula mass of glycine is 75.07 g/mol, how many moles of glycine molecules are contained in 28.35 g?
number of moles = 28.35 g x 1 mol/75.07 g number of moles = 0.3776 moles of glycine
Aluminum sulfate Al₂(SO₄)₃ is an ionic compound that is used in the manufacture of paper and in various water purification processes. What is the formula mass (amu) of this compound? Al (26.98 amu) S (32.06 amu) O (16.00 amu)
Al 2 atoms x 26.98 amu = 53.96 amu S 3 atoms x 32.06 amu = 96.18 amu O 7 atoms x 16.00 amu = 192.00 amu Formula mass of Al₂(SO₄)₃ = 342.14 amu
A liter of air contains 9.2 x 10⁻⁴ mol argon. What is the mass of Ar in a liter of air?
Atomic mass of Ar is 39.95 amu 1 mole of Ar is 39.95 g mass = 9.2 x 10⁻⁴ mol x 39.95 g/mol mass =0.037 g of Ar
What is the mass of 2.561 mol of gold?
Atomic mass of Au is 196.97 amu 1 mole of Au is 196.97 g mass = 2.561 mol x 196.97 g/mol mass = 504.4 g
A prospector panning for gold in a river collects 15.00 g of pure gold. How many Au atoms are in this quantity of gold?
Atomic mass of Au is 196.97 amu 1 mole of Au is 196.97 g number of moles = 15.00 g x 1 mol/196.97 g number of moles = 0.07615 mol number of Au atoms = 0.07615 mol x 6.022 x10²³ atoms/mol number of Au atoms = 4.586 x 10²²
Beryllium is a light metal used to fabricate transparent X-ray windows for medical imaging instruments. How many moles of Be are in a thin-foil window weighing 3.24 g?
Atomic mass of Be is 9.01 amu 1 mole Be is 9.01 g Number of moles = 3.24 g Be x 1 mole/9.01 g Be Number of moles = 0.360 Be
Copper is commonly used to fabricate electrical wire. How many copper atoms are in 5.00 g of copper wire?
Atomic mass of Cu is 63.55 amu 1 mole of Cu is 63.55 g number of moles = 5.00 g x 1 mol/63.55 g number of moles = 0.0787 moles number of atoms in a mole = 6.022 x 10²³ number of atoms in 0.0787 moles Cu = 0.0787 mol x 6.022 x 10²³ atoms/mole number of Cu atoms=4.74 x 10²² atoms
According to nutritional guidelines from the USDA, the estimated average requirement for dietary potassium is 4.7 g. What is the average requirement of potassium in moles?
Atomic mass of K is 39.10 amu 1 mole of K is 39.10 g Number of moles = 4.7 g K x 1 mole/39.10 g K Number of moles = 0.12 K
The molar mass of any substance is numerically equivalent to its _______ weight in amu.
Atomic or formula
One mole of any element contains the same number of ______ as one mole of any other element.
Atoms
Formula mass is the sum of the ______ of all the atoms represented in a substance's formula.
Average atomic masses
Avogadro's number is also known as the:
Avogadro constant
The number of entities in a mole is 6.022 x 10²³. This fundamental constant is named:
Avogadro's number
1a. What is the total mass (amu) of carbon in the following molecule: CH₄?
C 1 atom x 12.01 amu = 12.01 amu
1b. What is the total mass (amu) of carbon in the following molecule: CHCl₃?
C 1 atom x 12.01 amu = 12.01 amu
1c. What is the total mass (amu) of carbon in the following molecule: C₁₂H₁₀O₆?
C 12 atoms x 12.01 amu = 144.1 amu
3e. Calculate the molecular or formula mass of the following molecule: C₁₂H₂₂O₁₁ (sucrose, cane sugar)
C 12 atoms x 12.01 amu = 144.12 amu H 22 atoms x 1.008 amu = 22.176 amu O 11 atoms x 16.00 amu = 176.00 amu formula mass C₁₂H₂₂O₁₁ is 342.3 amu
What is the formula mass of sucrose, C₁₂H₂₂O₁₁?
C 12 atoms x 12.01 amu =144.12 amu H 22 atoms x 1.008 amu = 22.176 amu O 11 atoms x 16.00 amu = 176 amu Formula mass of sucrose C₁₂H₂₂O₁₁ = 342.30
Our bodies synthesize protein from amino acids. One of these amino acids is glycine, which has the molecular formula C₂H₅O₂N. What is the formula mass of glycine?
C 2 atoms x 12.01 amu = 24.02 H 5 atoms x 1.008 amu = 5.040 O 2 atoms x 16.00 amu = 32.00 N 1 atom x 14.007 amu = 14.007 Formula mass (g/mol) = 75.07
3d. Calculate the molecular or formula mass of the following molecule: CH₃CO₂H (acetic acid)
C 2 atoms x 12.01 amu = 24.02 amu H 4 atoms x 1.008 amu = 4.032 amu O 2 atoms x 16.00 amu = 32.00 amu formula mass CH₃CO₂H is 60.05 amu
What is the molecular mass of C₄H₁₀?
C 4 atoms x 12.01 amu = 48.04 H 10 atoms x 1.008 amu = 10.08 Molecular mass of C₄H₁₀ = 58.12 amu
1d. What is the total mass (amu) of carbon in the following molecule: CH₃CH₂CH₂CH₂CH₃?
C 5 atoms x 12.01 amu = 60.05 amu
7. Write a sentence that describe how to determine the number of moles of a compound in a known mass of the compound if we know its molecular formula.
First we find the formula mass of the compound by multiplying the number of atoms of each element by the atomic mass of each element then summing the products. This gives us the mass of one mole of compound. Then we divide the known mass by the formula mass to determine the number of moles in the sample of compound.
9. Which contains the greatest mass of oxygen: 0.75 mol of ethanol (C₂H₅OH), 0.60 mol of formic acid (HCO₂H), or 1.0 mol of water (H₂O)? Explain why.
Formic acid. Its formula has twice as many oxygen atoms as the other two compounds (one each). Therefore, 0.60 mol of formic acid would be equivalent to 1.20 mol of a compound containing a single oxygen atom.
The sum of the average atomic masses of all the atoms represented in a substance's formula is called the:
Formula mass
8b. Compare 1 mole of H₂, 1 mole of O₂, and 1 mole of F₂. Which has the greatest mass? Explain why?
F₂ has the greatest mass. The mass of a mole of a molecule is the sum of the atomic masses in grams. The atomic mass of F₂ is greater than H₂ or O₂.
2b. What is the total mass of hydrogen in the following molecule: CHCl₃?
H 1 atom x 1.008 amu = 1.008 amu
2c. What is the total mass of hydrogen in the following molecule: C₁₂H₁₀O₆?
H 10 atoms x 1.008 amu = 10.08 amu
2d. What is the total mass of hydrogen in the following molecule: CH₃CH₂CH₂CH₂CH₃?
H 12 atoms x 1.008 amu = 12.10 amu
3b. Calculate the molecular or formula mass of the following molecule: H₂O.
H 2 atoms x 1.008 amu = 2.016 amu O 1 atom x 16.00 amu = 16.00 amu formula mass H₂O is 18.02 amu
2a. What is the total mass of hydrogen in the following molecule: CH₄?
H 4 atoms x 1.008 amu = 4.032 amu
The masses of 1 mole of different elements are different because the ______ of individual atoms are drastically different.
Masses
The ______ of an element (or compound) is the mass in grams of 1 mole of that substance, a property expressed in units of grams per mole (g/mol).
Molar mass
A ____ is defined as the amount of substance containing the same number of discrete entities (such as atoms, molecules, and ions) as the number of atoms in a sample of pure ¹²C weighing exactly 12 g.
Mole
The number of entities composing a _____ has been experimentally determined 6.02214179 x 10²³.
Mole
What unit provides a link between an easily measured macroscopic property, bulk mass, and an extremely important fundamental property, number of atoms, molecules, and so forth?
Mole
What unit provides a specific measure of the number of atoms or molecules in a bulk sample of matter?
Mole
11. How are the molecular mass and molar mass of compound similar and how are they different?
The two masses have the same numerical value,but the units are different: The molecular mass is the mass of 1 molecule while the molar mass is the mass of 6.022 × 10²³ molecules.
8a. Compare 1 mole of H₂, 1 mole of O₂, and 1 mole of F₂. Which has the largest number of molecules? Explain why.
They all have an equal number of molecules. A mole is defined as having 6.022 x 10²³ molecules.
If we know the mass and chemical composition of a substance, we can determine the number of moles and calculate the number of atoms or molecules in the sample. True or False?
True
If we know the number of moles of a substance, we can derive the number of atoms of molecules and calculate the substance's mass. True or False?
True
Since the electrons weigh so little, the loss or gain of electrons will make little difference in formula mass. True or False?
True
The atomic masses of Ca and Ca²⁺ are indistinguishable. True or False?
True
The formula mass for ionic compounds is calculated the same as covalent compounds. However, since the formula for an ionic compound does not represent the composition of a discrete molecule, it is incorrect to refer to the formula mass as the molecular mass. True or False?
True
The molar mass is a measure of the atomic mass in grams. True or False?
True
The units of molar mass are grams per mole. True or False?
True
