Problem solving: Chemical Quantities/Stoichiometry (CHM130) (PDF)

Chemical Quantities
Definition of mole
Conversion factors
1 mole = 6.022 x 10 23 items
(Example)
1 mole of carbon atoms = 6.022 x 10 23 carbon atoms
(number to mole)
1mole C atoms
23
6.022 x 10
or
C atoms
(mole to number)
23
6.022 x 10
C atoms
1mole C atoms
1 mole of NaCl formula units = 6.022 x 10 23 NaCl
formula units
1mole NaCl
23
6.022 x 10
or
NaCl
23
6.022 x 10
1mole
NaCl
NaCl
Sample Problems
1. How many sodium atoms are in 3.45 moles of sodium?
i) given: 3.45 moles of Na
wanted: # Na
ii)
iii)
plan: mole of Na # Na
problem solving:
3.45 moles Na
x
6.022 x 10 23 #Na
1 mole Na
= 2.08 x 10 24 #Na
definition of mole
2. How many moles of CO 2 are contained in 2.45 x 10 25 CO 2 molecules?
i) given: 2.45 x 10 25 CO 2
wanted: moles CO 2
ii) plan: #CO 2 molecules mole CO 2
iii)
problem solving:
2.45 x 10 25 CO 2 x
1 mole CO 2
6.022 x 10 23 #CO 2
= 40.7 moles CO 2
definition of mole
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Molar mass of atoms
(= mass of 1 mole of atoms)
1 mole of atoms = mass (in grams) of atoms of an
element
(Example)
In the periodic table
element of carbon is shown as below.
6
C
12.01
This indicates one mole of carbon has a mass of 12.01
g of carbon atoms.
Therefore, 1 mole of C atoms = 12.01 g of C atoms
(mass to mole) (mole to mass)
1mole C 12.01g C
or
12.01g C 1mole C
Sample problems
A jewelry contains 0.0450 moles of silver metal. How many grams of silver metal does the
jewelry contain?
i) given: 0.0450 moles Ag
wanted: g Ag
ii) plan: mole Ag g Ag
iii)
problem solving:
0.0450 moles Ag
x
107.87 g Ag
1 mole Ag
=
4.85 g Ag
molar mass of Ag
2

Mole ratio and molar mass of compounds
(Example 1)
1 mole of CO 2 = 1 mole (C + 2O) = 1 mole C + 2 moles O
Molar mass of CO 2 can be calculated as
1 mole C = 12.01 g
+ 2 moles of O = 2 x 16.00 g = 32.00 g
44.01 g CO 2
Therefore, 1 mole of CO 2 = 44.01 g CO 2
(Molar ratio)
1mole CO
2 1mole C
or
1mole C 1mole CO
2
1mole CO
2
2 moles O
1mole CO
2
44.01g CO
2
2 moles O
or
1mole CO
2
(Molar mass)
44.01g CO
or
2
1mole CO
2
(Example 2)
1mole Ca(NO
3
)
2
1mole Ca
(Molar ratio)
1mole Ca
or
1mole Ca(NO
3
)
2
1 mole of Ca(NO 3 ) 2 = 1 mole (Ca + 2N + 6O)
= 1 mole Ca + 2 moles N + 6 moles O
1mole Ca(NO
3
)
2
2 moles N
2 moles N
or
1mole Ca(NO
3
)
2
Molar mass of Ca(NO 3 ) 2 can be calculated as
1 mole of Ca = 40.08 g
2 moles of N = 2 x 14.01 g = 28.02 g
+ 6 moles of O = 6 x 16.00 = 96.00 g
164.10 g Ca(NO 3 ) 2
1mole Ca(NO
3
)
2
6 moles O
6 moles O
or
1mole Ca(NO
3
)
2
(Molar mass)
1mole Ca(NO
3
)
2
164.10 g Ca(NO
3
)
or
2
164.10 g Ca(NO
3
)
2
1mole Ca(NO
3
)
2
3

Sample Problems
1. How many moles oxygen atoms are contained in 0.125 moles of Al 2 (SO 4 ) 3 ?
i) given: 0.125 moles Al 2 (SO 4 ) 3
wanted: moles O
ii) plan: mole Al 2 (SO 4 ) 3 mole O
iii)
Problem solving:
0.125 mole Al 2 (SO 4 ) 3
x
12 moles O
= 1.50 moles O
1 mole Al 2 (SO 4 ) 3
mole ratio
2. What is the mass (in grams) of 0.018 mole of Mg(OH) 2 ?
i) given: 0.018 mole Mg(OH) 2
wanted: g Mg(OH) 2
ii) plan: mole Mg(OH) 2 g Mg(OH) 2
iii)
problem solving:
0.018 mole Mg(OH) 2
x
58.33 g Mg(OH) 2 = 1.05 g Mg(OH) 2
1 mole Mg(OH) 2
molar mass*
*molar mass of Mg(OH) 2 :
+
1 mole of Mg = 24.31 g
2 moles of O = 2 x 16.00 = 32.00 g
2 moles of H = 2 x 1.01 g = 2.02 g
58.33 g
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Chemical equations for reactions
2H 2 + O 2 →
2H 2 O
(Mole ratio)
2 moles H 2 : 1 mole O 2 : 2 moles H 2 O
(Mole ratio)
1mole H
2
1mole O
or
2
1mole O
2
1mole H
2
1mole O
2
1mole H
2
O
1mole H O
or
2
1mole O
2
1mole H
2
1mole H
2
O
1mole H O
or
2
1mole H
2
Sample Problems
1. How many moles of carbon dioxide will be produced if 3.48 moles of propane gas (C 3 H 8 )
reacted with oxygen gas (=combustion of propane gas)?
C 3 H 8 +
5O 2 3CO 2 + 4H 2 O
i) given: 3.48 moles C 3 H 8
wanted: moles CO 2
ii) plan: mole C 3 H 8 mole CO 2
iii)
problem solving:
3.48 moles C 3 H 8
x
3 moles CO 2
= 10.4 moles CO 2
1 mole C 3 H 8
mole ratio
(from coefficients in reaction equation)
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Exercises
1. How many moles of NaCl are in 4.43 x 10 26 formula units of NaCl?
2. Calculate the molar mass of calcium hydroxide, Ca(OH) 2 .
3. What is the mass (in grams) of 4.55 moles of oxygen gas (O 2 )?
4. How many moles of copper (Cu) are present in 0.0250 grams of copper?
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5. How many moles of oxygen atoms are in 0.300 g of Mg(OH) 2 (antiacid, laxative)?
6. How many sulfur atoms are in 0.215 mole of Al 2 (SO 4 ) 3 (antiperspirant)?
7. How many sulfur atoms are present in 5.50 g of carbon disulfide (CS 2 )?
8. Iron metal reacts with oxygen gas to produce nitrogen iron(III) oxide.
a) Write a balanced chemical equation.
b) Write the mole-mole conversion factors (or mole ratio) between the pairs below.
Iron and oxygen gas:
7

Iron and iron(III) oxide:
Oxygen and iron(III) oxide:
9. Complete combustion of propane gas (C 3 H 8 ) produces carbon dioxide and water.
a) Write a balanced chemical equation.
b) How many moles of carbon dioxide will be produced if 12.0 g of propane gas reacted
with excess amount of oxygen gas?
10. How many moles of HCl gas can be obtained by reacting 11.5 g of hydrogen gas with 45.8
g of chlorine gas? Which substance is the limiting reactant?
H 2(g) + Cl 2(g) 2HCl (g)
First, the amount of product (in moles) that can be produced from each reactant.
Then, identify the limiting reactant. Reactant that gives the least amount of product is the
limiting reactant.
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Answer key to Exercises
1. How many moles of NaCl are in 4.43 x 10 26 formula units of NaCl?
i) given: 4.43 x 10 26 # NaCl
wanted: mole NaCl
ii) plan: # NaCl mole NaCl
iii)
problem solving:
4.43 x 10 26 # NaCl x
1 mole NaCl
= 736 moles NaCl
6.022 x 10 23 # NaCl
definition of mole
2. Calculate the molar mass of calcium hydroxide, Ca(OH) 2 .
1 mole Ca(OH) 2 contains 1 mole Ca, 2 moles O, and 2 moles H. Therefore,
1 mole Ca = 1 x 40.08 g = 40.08 g
+
2 moles O = 2 x 16.00 g = 32.00 g
2 moles H = 2 x 1.01 = 2.02 g
74.10 g = molar mass of Ca(OH) 2
3. What is the mass (in grams) of 4.55 moles of oxygen gas (O 2 )?
i) given: mole O 2
wanted: g O 2
ii) plan: mole O 2 g O 2
iii)
problem solving:
4.55 moles O 2
x
32.00 g O 2
= 146 g O 2 (or 1.46 x 10 2 g O 2 )
1 mole O 2
molar mass of O2
9

4. How many moles of copper (Cu) are present in 0.0250 grams of copper?
i) given: grams Cu
wanted: mole Cu
ii)
iii)
plan: g Cu mole Cu
problem solving:
0.0250 g Cu
x
1 mole Cu
63.55 g Cu
= 3.93 x 10-4 mole Cu (or 0.000393 mole Cu)
molar mass of Cu
5. How many moles of oxygen atoms are in 0.300 g of Mg(OH) 2 (antiacid, laxative)?
i) given: 0.300 g Mg(OH) 2
wanted: moles O
ii) plan: g Mg(OH) 2 moles Mg(OH) 2 moles O
iii)
problem solving:
0.300 g Mg(OH) 2 1 mole Mg(OH) x 2 x
58.33 g Mg(OH) 2
molar mass of Mg(OH) 2
2 mole O
1 mole Mg(OH) 2
= 0.0103 mole O
mole ratio
6. How many sulfur atoms are in 0.215 mole of Al 2 (SO 4 ) 3 (antiperspirant)?
i) given: 0.215 mole Al 2 (SO 4 ) 3
wanted: # of S atoms
ii) plan: mole Al 2 (SO 4 ) 3 mole S # S
iii)
problem solving:
0.215 mole Al 2 (SO 4 ) 3
3 mole S
x
1 mole Al 2 (SO 4 ) 3
x
6.022 x 10 23 # S
1 mole S
= 3.88 x 10 23 # S atoms
mole ratio
definition of mole
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7. How many sulfur atoms are present in 5.50 g of carbon disulfide (CS 2 )?
i) given: 5.50 g CS 2
wanted: # S
ii) plan: g CS 2 mole CS 2 mole S # S
iii)
problem solving:
5.50 g CS 2
x 1 mole CS 2 2 mole S
x
76.13 g CS 2 1 mole CS 2
x
6.022 x 1023 # S
1 mole S
= 8.70 x 10 22 # S atoms
molar mass
mole ratio
definition of mole
8. Iron metal reacts with oxygen gas to produce iron(III) oxide.
a) Write a balanced chemical equation.
4Fe (s) + 3O 2(g) 2Fe 2 O 3(s)
b) Write the mole-mole conversion factors (or mole ratio) between the pairs below.
Iron and oxygen gas:
4 moles Fe
3 mole O 2
or
3 mole O 2
4 moles Fe
Iron and iron(III) oxide:
4 moles Fe
2 moles Fe 2 O 3
or
2 moles Fe 2 O 3
4 moles Fe
Oxygen and iron(III) oxide:
3 mole O 2
2 moles Fe 2 O 3
or
2 moles Fe 2 O 3
3 mole O 2
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9. Complete combustion of propane gas (C 3 H 8 ) produces carbon dioxide and water.
a) Write a balanced chemical equation.
C 3 H 8 + 5O 2 3CO 2 + 4H 2 O
b) How many moles of carbon dioxide will be produced if 12.0 g of propane gas reacted
with excess amount of oxygen gas?
i) given: 12.0 g C 3 H 8
wanted: mole CO 2
ii) plan: g C 3 H 8 mole C 3 H 8 mole CO 2
iii)
problem solving:
12.0 g C 3 H 8
x 1 mole C 3H 8 3 mole CO
x
2
44.11 g C 3 H 8 1 mole C 3 H 8
= 0.816 mole CO 2
molar mass
mole ratio
10. How many moles of HCl gas can be obtained by reacting 11.5 g of hydrogen gas with 45.8
g of chlorine gas? Which substance is the limiting reactant?
H 2(g) + Cl 2(g) 2HCl (g)
First, the amount of product (in moles) that can be produced from each reactant.
Then, identify the limiting reactant. Reactant that gives the least amount of product is the
limiting reactant.
i) given: 20.5 g H 2
wanted: mole HCl
plan: g H 2 mole H 2 mole H 2
problem solving:
11.5 g H 2 2 mole HCl
x 1 mole H 2
x
2.02 g H 2 1 mole H 2
= 11.4 moles HCl
molar mass
mole ratio
12

ii) given: 45.8 g Cl 2
wanted: mole HCl
plan g Cl 2 mole Cl 2 mole HCl
problem solving:
45.8 g Cl 2 2 mole HCl
x 1 mole Cl 2
x
70.90 g Cl 2 1 mole Cl 2
= 1.29 moles HCl
molar mass
mole ratio
iii)
From the comparison of moles of HCl from i) and ii), reactant Cl 2 gives less amount
of moles of HCl than other reactant H 2 .
1.29 moles HCl < 11.4 moles HCl
Therefore, Cl 2 is a limiting reactant.
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