Under mass conversions, connections between **grams, moles **and **molecules** are established.

The **mole** is the chemical unit for the amount of a substance and serves as the bridge that connects grams to molecules, atoms, formula units and ions.

Concept #1: Avogadro’s Number, Moles, Molecules & Atoms

The words **atoms** and **ions** are used when talking about a single element and the words **molecules** and **formula units** are used when talking about more than one element together.

Concept #2: Atoms to Moles to Grams

Example #1: Determine the mass (in grams) found in 7.28 x 10** ^{28}** nitrogen atoms.

Concept #3: Molecules to Moles to Grams

Example #2: Determine the how many molecules of carbon dioxide, CO_{2}, are found in 75.0 g CO_{2}.

Practice: If the density of water is 1.00 g/mL at 25^{o}C. Calculate the number of water molecules found in 1.50 x 10^{3} µL of water.

Practice: Calculate the number of oxygen atoms found in 783.9 g in copper (II) sulfate pentahydrate, CuSO_{4} x 5 H_{2}O.

Practice: The density of the sun is 1.41 g/cm^{3} and its volume is 1.41 x 10^{27} m^{3}. How many hydrogen molecules are in the sun if we assume all the mass is hydrogen gas?

Practice: A cylindrical copper wire is used for the fences around a house. The copper wire has a diameter of 0.0750 in. How many copper atoms are found in 5.160 cm piece? The density of copper is 8.96 g/cm^{3}. ( V = π x r^{2} x h )

How many moles of sodium ions (Na +) are in 56.0 g of sodium phosphate (Na 3PO4)?
A. 0.342 mol Na+
B. 1.03 mol Na+
C. 0.114 mol Na+
D. 3.06 x 103 mol Na+

What is the mass, in grams, of each elemental sample?
b. 0.0355 mol Ba

What is the mass (in kg) of 6.89 × 10 25 molecules of CO2? The molar mass of CO2 is 44.01 g/mol.
A) 3.85 kg
B) 5.04 kg
C) 2.60 kg
D) 3.03 kg
E) 6.39 kg

How many moles of PBr3 are contained in 3.68 × 1025 bromine atoms?
A) 61.1 moles PBr3
B) 20.4 moles PBr3
C) 16.4 moles PBr3
D) 183 moles PBr3
E) 49.1 moles PBr3

How many iron atoms are contained in 354 g of iron?
A) 9.50 × 10 22 Fe atoms
B) 3.82 × 10 24 Fe atoms
C) 2.13 × 10 26 Fe atoms
D) 4.69 × 10 24 Fe atoms
E) 2.62 × 1025 Fe atoms

What is the mass, in grams, of each elemental sample?
c. 43.9 mol Xe

Stearic acid (C18H36O2) is a fatty acid found in beef and butter.
a) What is the molecular mass of stearic acid? Give your answer in units of g/mol.
b) How many oxygen atoms are present in 1.000 g of stearic acid?

What is the mass, in grams, of each elemental sample?
d. 1.3 mol W

What is the mass of 4.91 x 10 21 platinum atoms?

Calculate the mass (in kg) of 4.87 x 10 25 atoms of Zn.
A) 1.09 kg
B) 1.89 kg
C) 5.29 kg
D) 1.24 kg
E) 8.09 kg

How many moles of lithium phosphate are in 85.7 g of this substance?
1. 0.306578
2. 0.341986
3. 0.676199
4. 0.386893
5. 0.265989
6. 0.531978
7. 0.717652
8. 0.60452
9. 0.17272
10. 0.740105

The number of atoms in 9.0 g of aluminum is the same as the number of atoms in _____.
A. 8.1 g of magnesium
B. 9.0 g of magnesium
C. 12.1 g of magnesium
D. 18.0 g of magnesium

Calculate the number of carbon atoms in 4.56 grams of ethanol (CH 3CH2OH).
1. 2.53 × 1026 atoms
2. 1.19 × 1023 atoms
3. 1.79 × 1023 atoms
4. 5.49 × 1024 atoms
5. 5.97 × 1022 atoms

What is the weight of O in 742.0 g of citronella oil that has the chemical formula C10H18O?
a. 19.31
b. 18.52
c. 77.10
d. 115.5
e. 231.3

What is the mass of 1.3 x 10 13 moles of N2 in pg?
a. 3.64 x 1014
b. 1.82 x 1014
c. 1.82 x 1026
d. 3.64 x 1026
e. none of the given answers is even close to being correct

A single atom of a certain element has a mass of 3.352 x 10 -23 g. The element is
a. Ne
b. Co
c. Al
d. Br
e. Ti

Calculate the molar mass for Mg(ClO4)2.
A) 223.21 g/mol
B) 123.76 g/mol
C) 119.52 g/mol
D) 247.52 g/mol
E) 75.76 g/mol

The Freons are a class of compounds containing carbon, chlorine, and fluorine. While they have many valuable uses, they have been shown to be responsible for depletion of the ozone in the upper atmosphere. In 1991, two replacement compounds for Freons went into production: HFC-134a (CH2FCF3) and HCFC-124 (CHClFCF3). Calculate the molar masses of these two compounds.

How many xenon atoms are contained in 2.36 moles of xenon?

How many moles are in 26.7 grams of calcium nitrate?

How many argon atoms are contained in 7.66 x 10 5 mol of argon?
A) 4.61 × 1029 Ar atoms
B) 1.84 × 1028 Ar atoms
C) 1.15 × 1028 Ar atoms
D) 7.86 × 1020 Ar atoms
E) 3.24 × 1026 Ar atoms

Calculate the mass, in kg, of each sample.
a. 7.55 x 1026 cadmium atoms
b. 8.15 x 1027 nickel atoms
c. 1.22 x 1027 manganese atoms
d. 5.48 x 1029 lithium atoms

How many helium atoms are there in a helium blimp containing 536 kg of helium?

If the mass of 2.51 x 10 -3 moles of compound A is 0.452 g, then what is the molar mass?

Calculate the average mass, in grams, of one platinum atom.

Using scanning tunneling microscopy, scientists at IBM wrote the initials of their company with 35 individual xenon atoms (as shown below). Calculate the total mass of these letters in grams.

How many Li atoms are contained in 97.9 g of Li?
A) 5.90 × 1025 Li atoms
B) 7.09 × 1021 Li atoms
C) 8.49 × 1024 Li atoms
D) 4.27 × 1022 Li atoms
E) 4.18 × 1024 Li atoms

How many iron atoms are contained in 354 g of iron?
A) 2.62 × 1025 Fe atoms
B) 2.13 × 1026 Fe atoms
C) 4.69 × 1024 Fe atoms
D) 3.82 × 1024 Fe atoms
E) 9.50 × 1022 Fe atoms

How many formula units are in 0.25 mole of Na 2O?
A) 4.5 x 1023
B) 0.75
C) 1.5 x 1023
D) 4.2 x 10–25
E) 0.25

Phosphorus tribromide is a liquid with a density of 2.852 g/cm3. A beaker contains 0.4875 moles of this compound.
a) What is the chemical formula of phosphorus tribromide?
b) What is the volume of liquid in milliliters (mL)?
c) How many molecules of phosphorus tribromide are in the beaker?
d) How many atoms of bromine are in the beaker?

If 4.05 x 1023 molecules of a substance have a mass of 86.2 g, what is the molar mass of the substance?
A) 128 g/mol
B) 3.49 x 1025 g/mol
C) 2.13 x 1022 g/mol
D) 4.70 x 1021 g/mol
E) 58.0 g/mol

A 1.000-g sample of a metal chloride, MCl 2, is dissolved in water and treated with excess aqueous silver nitrate. After drying, the silver chloride that formed weighed 1.286 g. Calculate the atomic mass of M.
a) 222.8 g
b) 76.00 g
c) 152.0 g
d) 304.0 g
e) none of these

Suppose we have 100 g of each of the following substances. Which sample contains the largest number of moles?
1. MgCO3, formula weight 84.3
2. AgCl, formula weight 143.3
3. Impossible to tell, unless we know what reaction will take place with the substance.
4. HCl, formula weight 36.5
5. H2 O, formula weight 18.0

What mass of the compound CrO3 (M = 100.0) contains 4.5 x 10 23 oxygen atoms?
a) 2.25 g
b) 12.0 g
c) 25.0 g
d) 75.0 g

Identify the correct statement regarding the mole.
a) A mole of oxygen gas contains 6.02 x 10 23 atoms.
b) A mole of chlorine gas contains 2 x 6.02 x 10 23 molecules.
c) A mole of carbon dioxide contains two moles of oxygen atoms.
d) A mole of ammonia gas (NH 3) has a mass of 34.0 g.
e) A mole consists of the number of particles in exactly 12 g of naturally occurring carbon.

How many moles of water contain 2.22 x 10 24 molecules of water?
(A) 3.69 moles
(B) 0.272 moles
(C) 2.72 moles
(D) 36.9 moles
(E) 1.34 x 1048 moles

A pure titanium cube has an edge length of 2.78 in. How many titanium atoms does it contain? Titanium has a density of 4.50 g/ cm3.

Calculate the mass in grams of 1.505 x 10 23 molecules of CH 4.
(A) 4 g
(B) 16 g
(C) 40 g
(D) 64 g
(E) 2.4 x 1024 g

Calculate the molar mass for Mg(ClO4)2.
A) 247.52 g/mol
B) 119.52 g/mol
C) 123.76 g/mol
D) 223.21 g/mol
E) 75.76 g/mol

How many fluorine atoms are present in 19.75 g of the Freon C 2HBrClF3?
(A) 1.81 x 1023
(B) 6.02 x 1023
(C) 6.69 x 1021
(D) 6.03 x 1022
(E) 2.23 x 1023

6.02 x 10 21 molecules of an unknown substance X has a mass of 2.00 grams. What is the molar mass of X in g/mole?
(A) 0.02 g/mol
(B) 0.2 g/mol
(C) 20 g/mol
(D) 200 g/mol
(E) 2000 g/mol

How many bromide ions are in 0.55 g of iron(III) bromide?
HINT: What does the Roman numeral mean?
a. 1.1 x 1021 ions
b. 3.4 x 1021 ions
c. 3.3 x 1023 ions
d. 9.9 x 1023 ions
e. 2.9 x 1026 ions

How many Cl atoms are there in 27.3 grams of magnesium chloride?

A 67.2 g sample of a gold and palladium alloy contains 2.49 x 10 23 atoms. What is the composition (by mass) of the alloy?

How many Cl– ions are there in 15.6 g of MgCl 2?

How many N2O4 molecules are contained in 76.3 g N 2O4? The molar mass of N2O4 is 92.02 g/mol.
A) 4.59 × 10 25 N2O4 molecules
B) 5.54 × 10 25 N2O4 molecules
C) 7.26 × 10 23 N2O4 molecules
D) 1.38 × 10 24 N2O4 molecules
E) 4.99 × 10 23 N2O4 molecules

What is the mass of 4.50 x 1022 atoms of magnesium, Mg?
(A) 0.0748 g
(B) 0.182 g
(C) 0.897 g
(D) 1.82 g
(E) 18.2 g

Calculate the number of moles in 55.0 g of magnesium hydroxide.
(A) 0.943 mol
(B) 1.33 mol
(C) 1.83 mol
(D) 2.89 mol
(E) 5.68 x 1023 mol

How many C2H4 molecules are contained in 45.8 mg of C 2H4 ? The molar mass of C2H4 is 28.05 g/mol.
A) 2.71× 10 20 C2H4 molecules
B) 9.83 × 10 20 C2H4 molecules
C) 7.74 × 10 26 C2H4 molecules
D) 4.69 × 10 23 C2H4 molecules
E) 3.69 × 10 23 C2H4 molecules

What is the molecular weight of glucose, C6H12O6

32.0 grams of the element oxygen:
(A) contain 6.02 x 1023 atoms of oxygen
(B) contain 1.204 x 1024 molecules of oxygen
(C) contain the same number of oxygen atoms as 18.0 g of water
(D) contain the same number of oxygen atoms as 72.0 g of water
(E) contain the same number of oxygen atoms as 90.0 g of water

Calculate the number of nitrogen atoms in 240. g of ammonium nitrate.
(A) 2.01 x 1023 nitrogen atoms
(B) 6.02 x 1023 nitrogen atoms
(C) 1.20 x 1024 nitrogen atoms
(D) 1.81 x 1024 nitrogen atoms
(E) 3.61 x 1024 nitrogen atoms

6.02 x 1021 molecules of an unknown substance X has a mass of 11.0 grams. What is the molar mass of X in g/mole?
(A) 110 g/mol
(B) 220 g/mol
(C) 1100 g/mol
(D) 2200 g/mol
(E) cannot be determined without the formula of X

How many oxygen atoms are in a 125 mg sample of aspirin? The molar mass of aspirin is 180.15 g/mol and its molecular formula is C9H8O4.
a) 4.18 × 1023
b) 4.18 × 1020
c) 1.67 × 1021
d) 1.36 × 1025
e) 8.68 × 1023

How many moles are in 42.6 g of water?
1. 767 mol
2. 3.04 mol
3. 2.66 mol
4. 2.37 mol

Of the following: one atom of uranium (U), one molecule of benzene (C6 H6), one mole of hydrogen atoms, or 6.02 × 1020 oxygen molecules, which one weighs the most?
1. one mole of hydrogen atoms
2. 6.02 × 1020 oxygen molecules
3. one molecule of C6 H6
4. one atom of U

What is the mass (in kg) of 6.89 × 10 25 molecules of CO2? The molar mass of CO2 is 44.01 g/mol.
A) 5.04 kg
B) 3.85 kg
C) 3.03 kg
D) 2.60 kg
E) 6.39 kg

What is the mass of 9.44 × 10 24 molecules of NO2? The molar mass of NO2 is 46.01 g/mol.
A) 294 g
B) 341 g
C) 205 g
D) 685 g
E) 721 g

How many moles of N2O3 contain 2.55 × 1024 oxygen atoms?
A) 7.87 moles N2O3
B) 1.41 moles N2O3
C) 4.23 moles N2O3
D) 12.7 moles N2O3
E) 2.82 moles N2O3

How many moles of C3H8 contain 4.95 × 10 24 hydrogen atoms?
A) 3.09 moles C3H8
B) 6.58 moles C3H8
C) 1.03 moles C3H8
D) 9.73 moles C3H8
E) 8.22 moles C3H8

What is the molar mass of calcium permanganate?
A) 199 g/mol
B) 278 g/mol
C) 216 g/mol
D) 159 g/mol

How many sulfur atoms are present in 256 mg of Al 2(S2O3)3?
a. 3.95 x 1022
b. 6
c. 7.90 x 1022
d. 0.393
e. 2.37 x 1021

What is the identity of substance X if 0.380 mol of X weighs 17.5 g?
A) NO2
B) N2O
C) N2O4
D) NO3

How many sodium atoms are in 6.0 g of Na 3N?
a. 1.3 x 1023 atoms
b. 3.6 x 1024 atoms
c. 1.217 atoms
d. 4.6 x 1022 atoms
e. 0.072 atoms

A 2.000 g sample of an unknown metal, M, was completely burned in excess O 2 to yield 0.02224 mol of the metal oxide, M2O3. What is the metal?
A. Y
B. Ca
C. Al
D. Sc

How many atoms of carbon are there in 0.80 moles of C 6H4Cl2?
a. 3.9 x 1024
b. 3.6 x 1024
c. 2.9 x 1024
d. 6.0 x 1023
e. 4.8 x 1023

How many sulfur atoms are there in 3.8 mol of sulfur?

Which of the following samples contains the largest number of atoms?
a. 1 g Li
b. 1 g F2
c. 1 g C
d. 1 g P4
e. 1 g N2

How many moles of aluminum do 5.8 X 1024 aluminum atoms represent?

What is the average mass in grams of one atom of iron?
a. 55.85 g
b. 6.02 x 10-23 g
c. 9.28 x 10-23 g
d. 1.66 x 10-24 g
e. 55.85 x 10-25 g

Determine the number of moles of silicon in 5.00 mg Si.
a. 1.78 x 10-4 mol
b. 2.40 x 10-4 mol
c. 0.140 mol
d. 5.62 mol
e. 5.62 x 103 mol

What mass of carbon is present in 0.500 mol of sucrose (C12H22O11)?
Molar mass: C12H22O11 = 342 g/mol
A. 60.0 g
B. 72.0 g
C. 90.0 g
D. 120 g

What mass of carbon is present in 0.500 mol of sucrose (C 12H22O11)?
a) 60.0 g
b) 72.0 g
c) 90.0 g
d) 120.0 g

How many atoms are in 1.50 g of Al?
a) 0.0556
b) 18.0
c) 3.35 x 1022
d) 2.44 x 1025

A 7.36-g sample of copper is contaminated with an additional 0.51 g of zinc. Suppose an atomic mass measurement was performed on this sample. What would be the measured atomic mass?

How many grams of gold contain 1.39 x 10 23 atoms of gold?
a. 0.220 g
b. 0.231 g
c. 4.33 g
d. 45.5 g
e. 853 g

What mass of carbon is present in 1.4 x 10 20 molecules of sucrose (C12H22O11)?
a) 1.7 x 1021 g
b) 2.0 x 1022 g
c) 3.3 x 10 -2 g
d) 2.8 x 10-3 g

A 0.370 mol sample of a metal oxide (M 2O3) weighs 55.4 g. How many grams of M are in the sample, and what element is represented by the symbol M?
a) 75.28 g/mol; Arsenic
b) 101.7 g; Ruthenium
c) 37.6 g; Vanadium
d) 17.8 g; Metalium
e) 41.3 g; Iron

How many atoms of oxygen are there in 53.2 g Al 2(SO4)3?
a. 9.36 x 1022
b. 3.75 x 1023
c. 1.12 x 1024
d. 2.81 x 1023

What mass (in kg) does 0.0822 moles of lead (Pb) have?
a. 0.397 kg
b. 17.0 kg
c. 2.52 kg
d. 0.0170 kg
e. 0.632 kg

Which of the following amounts would contain the least atoms?
a) 10.0 g Sr
b) 10.0 g Br
c) 10.0 g Mg
d) 10.0 g Li

A 1.000-g sample of a metal chloride, MCl 2, is dissolved in water and treated with excess aqueous silver nitrate. After drying, the silver chloride that formed weighed 1.286 g. Calculate the mass of M.
a) 222.8 g b) 76.00g c) 152.0 g d) 304.0 g e) none of these

Phenylenediamine (pictured below) is mainly used as a component of engineering polymers and composites. It is also an ingredient in hair dyes and is occasionally used as a substitute for henna.
What mass of phenylenediamine contains 45.0 g carbon?
a. 67.6 g
b. 45.0 g
c. 72.0 g
d. 100 g

Phenylenediamine (pictured below) is mainly used as a component of engineering polymers and composites. It is also an ingredient in hair dyes and is occasionally used as a substitute for henna.
How many molecules are in a 2.00 g of phenylenediamine?
a. 1.30 x 1028
b. 1.11 x 1022
c. 3.59 x 10-20
d. 3.07 x 10-24

A sample of a compound of xenon and fluorine contains molecules of a single type; XeFn , where n is a whole number. If 9.03 x 10 20 of these XeFn molecules have a mass of 0.311 g, what is the value of n?
a) 2
b) 3
c) 4
d) 6

Which of the following amounts have the most molecules?
a) 15.0 g N2
b) 15.0 g Br2
c) 15.0 g O2
d) 15.0 g l2

If 2.50 grams of an unknown compound contains 6.25 x 10 19 molecules, what is its molecular mass?

How many Cl atoms are there in 27.3 grams of magnesium chloride?

A 3.41 x 10–6 g sample of a compound is known to contain 4.67 x 10 16 molecules. This compound is
a) CO2
b) CH4
c) NH3
d) H2O

What is the molar mass of aspartic acid, C 4O4H7N?
A) 43.03 g/mol
B) 70.02 g/mol
C) 86.91 g/mol
D) 133.11 g/mol
E) 197.98 g/mol

The number of atoms in 9.0 g of aluminum is the same as the number of atoms in
a) 8.1 g of magnesium.
b) 9.0 g of magnesium.
c) 12.1 g of magnesium.
d) 18.0 g of magnesium.

A single molecule of a certain compound has a mass of 3.4 x 10 –22 g. Which value comes closest to the mass of a mole of this compound?
a) 50 g•mol–1
b) 100 g•mol–1
c) 150 g•mol–1
d) 200 g•mol–1

What mass of KClO3 will produce 48.0 g of oxygen gas, O2, if the decomposition of KClO3 is complete?
a) 61.3 g
b) 74.5 g
c) 122.5 g
d) 245.0 g