Examples on Stoichiometry
What is the number of atoms and mass of 1.00-mole samples of each of the following. (a) H,
(b) He, (c) C, (d) Ne
(a) The mass of 6.02 x 1023 atoms H is 1.01 g.
(b) The mass of 6.02 x 1023 atoms He is 4.00 g.
(c) The mass of 6.02 x 1023 atoms C is 12.0 g.
(d) The mass of 6.02 x 1023 atoms Ne is 20.2 g.
(e) The mass of 6.02 x 1023 atoms Fe is 55.8 g.
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How many moles of Cr atoms are found in a 1.00-g sample of Cr?
Beside the mass, which is given in the problem, the molar mass of Cr, 52.0 g Cr/mol Cr, obtained
from the periodic table, is needed. Use the molar mass to cancel g Cr, yielding mol Cr.
1.0
g Cr x 1 mol Cr/52.0 g Cr = 0.0190 mol Cr
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What is the mass in grams of 2.5 mol Al?
The molar mass of Al is 27.0 g Al/mol. Use this conversion factor to convert mol Al to g Al.
2.5 mol Al x 27.0 g Al/1 mol Al = 67.5 g Al = 68 g Al
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Calcium is a silvery white metal. Calcium ions, Ca2+, are a major component of the skeletal
systems of animals. (a) How many Ca atoms are found in 1.200-mol sample of Ca? (b) Why
is the molar mass of Ca not needed in this problem?
(a) The conversion factors needed to solve this problem is 1 mol Ca/6.022 x 1023 atoms Ca. Use it
to convert mol Ca to atoms.
1.200 mol Ca x 6.022 x 1023 atoms Ca/1 mol Ca = 7.226 x 1023 atoms Ca
(b) The molar mass is not needed in this problem; no mass is specified, just the number of moles.
Any element could be substituted for Ca, and the answer would be the same: 1.200 mol of any
element has exactly the same number of atoms.
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sample of Au is found to contain 9.7 x 1023 atoms Au. How many moles of Au atoms are in
the sample?
The only conversion factor needed for this problem is 6.022 x 1023 atoms Au/1 mol Au. Use it to
convert atoms to mol
9.7 x 1023 atoms Au x 1 mol Au/6.022 x 1023 atoms Au = 1.6 mol Au
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How many Pb atoms are found in a 100.0-g sample of pure Pb?
Two conversion factors are needed to solve this problem: 1 mol Pb/207.2 g Pb, and 6.022 x 1023
atoms Pb/1 mol Pb. First, convert g to mol and then convert mol to atoms.
100.0 g Pb x 1 mol Pb/207.2 g Pb x 6.022 x 1023 atoms Pb/1 mol Pb = 2.906 x 1023 atoms Pb
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What is the mass of 5.64 x 1023 atoms of uranium?
Two conversion factors are needed to solve this problem: 1 mol U/6.022 x 1023 atoms U, and 238
g U/1 mol U. First, convert atoms to mol and then mol to g.
5.64 x 1023 atoms U x mol U/6.022 x 1023 atoms U x 238 g U/1 mol U = 223 g U
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What mass of C atoms have the same number of atoms as are in a 10.0-g sample of Si?
If the number of Si and C atoms are the same, then the moles of Si and C atoms are also the same,
mol C/mol Si. Thus, start this problem by converting the mass of Si to moles using the molar mass
of Si, 28.1 g Si/mol Si. Finally, convert the moles of C to grams using 12.0 g C/mol C.
10.0 g Si x 1 mol Si/28.1 g Si x 1 mol C/1 mol Si x 12.0 g C/mol C = 4.27 g C
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Calculate the molecular and molar masses of each of the following. (a) CH4, (b) HNO3, (c)
B10H16
(a) Molecular mass of CH4
1 atom C x 12.0 = 12.0
4 atoms H x 1.0 = +4.0
= 16.0
The molar mass of CH4 is 16.0 g CH4/mol.
(b) Molecular mass of HNO3
1 atom H x 1.0 = 1.0
1 atom N x 14.0 = 14.0
3 atoms O x 16.0 = +48.0
= 63.0
The molar mass of HNO3 is 63.0 g HNO3/mol.
(c) Molecular mass of B10H16:
10 atoms x 10.81 = 108.1
16 atoms x 1.01 = +16.1
= 124.2
The molar mass of B10H16 is 124.2 g B10H16/mol
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(a) What is the molar mass of carbon dioxide, CO2? (b) How many particles are contained in
that mass?
(a) Calculate the molecular mass of CO2; one C atom, 12, and two O atoms, each 16, gives a
molecular mass of 44. Adding grams as the unit gives 44 g CO2/mol, the molar mass of CO2.
(b) A 44-g sample of CO2 contains 6.0 x 1023 molecules of CO2.
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Nitrous oxide, N2O, is a colorless gas with a pleasant odor. It has been used as a general
anesthetic for medical and dental operations for over 50 years. What is the mass of a 4.05mol sample of N2O?
First, calculate the molar mass of N2O.
2 mol N x 14.0 g N/mol N = 28.0 g N
1 mol O x 16.0 g O/mol O = +16.0 g O
= 44.0 g/1 mol N2O
Then, convert from mol N2O to g N2O as follows.
4.05 mol N2O x 44.0 g N2O/1 mol N2O = 178 g N2O
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Sulfuric acid, H2SO4, is the industrial chemical produced in greatest amount in the United
States. How many sulfuric acid molecules are in a 0.100-g sample of H2SO4?
First, calculate the molar mass of sulfuric acid.
2 mol H x 1.0 g H/mol H = 2.0 g H
1 mol S x 32.1 g S/mol S = 32.1 g S
4 mol O x 16.0 g O/1 mol O = +64.0 g O
= 98.1 g/1 mol H2SO4
Convert the mass of H2SO4 to moles, using the molar mass, and then to molecules, using
Avogadro's number.
0.100 g H2SO4 x 1 mol H2SO4/98.1 g H2SO4 x
6.022 x 1023 H2SO4 molecules/1 mol H2SO4 = 6.14 x 1020 molecules H2SO4
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2
Glucose, C6H12O6, is also known as blood sugar because it circulates in the blood. It is also
found in grapes, honey, and various fruits. What is the mass of 3.39 x 1022 molecules of
glucose?
First, calculate the mass of C6H12O6.
6 mol C x 12.0 g C/mol C = 72.0 g C
12 mol H x 1.0 g H/mol H = 12.0 g H
6 mol O x 16.0 g O/mol O = +96.0 g O
= 180.0 g C6H12O6
Then, convert molecules of C6H12O6 to moles using Avogadro's number, and then convert to
grams of C6H12O6, using the molar mass.
3.39 x 1022 molecules C6H12O6 x 1 mol C6H12O6/6.02 x 1023 molecules C6H12O6 x
180.0 g C6H12O6/1 mol C6H12O6 = 10.1 g C6H12O6
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How many moles of C and H atoms are in 9.25 g C5H10?
First, calculate the molar mass of C5H10.
5 moles C x 12.0 g C/mol C = 60.0 g C
10 moles H x 1.01 g H/mol H = +10.1 g H
= 70.1 g C5H10
Convert the mass of C5H10 to moles, using the molar. Then, convert to moles of C by knowing that
one mole of C5H10 has five moles of C.
9.25 g C5H10 x 1 mol C5H10/70.1 g C5H10 x 5 mol C/1 mol C5H10 = 0.660 mol C
It is not necessary to write the full set-up to find the number of moles of H. The ratio of H to C in
C5H10 is 10 to 5 or 2 to 1: 2 mol H/1 mol C.
0.660 mol C x 2 moles H/1 mol C = 1.32 mole H
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Nitrogen(V) oxide, N2O5, is a gas that combines with water to produce nitric acid, HNO3, one
of the most important industrial acids. What is the percent composition of N2O5?
First, calculate the molar mass of N2O5.
2 mol N x 14.0 g N/mol N = 28.0 g N
5 mol O x 16.0 g O/mol O = +80.0 g O
= 108.0 g N2O5/mol N2O5
Then, calculate the mass percent of N and O in one mole N2O5 by dividing the masses of N and O
by the molar mass and then multiply times 100.
% N = (g N/g N2O5) x 100 = (28.0 g N/108.0 g N2O5) x 100 = 25.9% N
% O = (g O/g N2O5) x 100 = (80.0 g O/108.0 g N2O5) x 100 = 74.1% O
The percent composition of N2O5 is 25.9% N and 74.1% O.
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Ethanol, C2H6O, is produced when grains or fruits are fermented by yeast. Calculate the
percent composition of ethanol.
First, calculate the molar mass of ethanol.
2 mol C x 12.0 g C/mol C = 24.0 g C
6 mol H x 1.01 g H/mol H = 6.06 g H
1 mol O x 16.0 g O/mol O = +16.0 g
= 46.1 g C2H6O/mol
Divide the masses of each element by the molar mass of ethanol and multiply by 100 to convert to
mass percents.
% C = (g C/g C2H6O) x 100 = (24.0 g C/46.1 g) x 100 = 52.1%
% H = (g H/g C2H6O) x 100 = (6.06 g H/46.1 g) x 100 = 13.1%
% O = (g O/g C2H6O) x 100 = (16.0 g O/46.1 g) x 100 = 34.7%
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