Chemistry 11 Solutions
mass percent of O
2 × 16.00 g/mol
272.42 g/mol
× 100%
11.7465%
11.75%
The compound is 79.36% carbon, 8.89% hydrogen, and 11.75% oxygen. The
percentages add to 100.0%. These percentages are in the range of the given
percentage composition.
Section 6.2 Empirical and Molecular Formulas
Solutions for Practice Problems
Student Edition pages 278
51. Practice Problem (page 278)
Calculate the percent by mass of water in the compound MgSO3•6H2O(s).
What Is Required?
You need to calculate the percent by mass of water in the hydrate
MgSO3•6H2O(s).
What Is Given?
You know the chemical formula for the sample: MgSO3•6H2O
Plan Your Strategy
Determine the molar mass of MgSO3•6H2O(s).
Calculate the percent by mass of water.
Act on Your Strategy
Molar mass, M, of MgSO3•6H2O(s):
M MgSO3 •6H2O 1M Mg 1M S 3M O 6M H2O
1 24.31 g/mol + 1(32.07 g/mol + 3 16.00 g/mol + 6[2 1.01 g/mol + 116.00 g/mol ]
1 24.31 g/mol + 1(32.07 g/mol) + 3 16.00 g/mol + 6(18.02 g/mol)
212.5 g/mol
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mass percent water
mass of H 2 O
u 100%
molar mass of MgSO3 •6H 2 O
6 × 18.02 g/mol
212.5 g/mol
u 100%
50.88%
Check Your Solution
The mass of water is approximately half the molar mass. The answer is
reasonable and the number of significant digits matches those used in the
molar masses.
52. Practice Problem (page 278)
Calculate the percent by mass of water in the compound LiCl•4H2O(s).
What Is Required?
You need to calculate the percent by mass of water in the hydrate
LiCl•4H2O(s).
What Is Given?
You know the chemical formula for the sample: LiCl•4H2O
Plan Your Strategy
Determine the molar mass of LiCl•4H2O(s).
Calculate the percent by mass of water.
Act on Your Strategy
M LiCl•4H2O 1M Li 1M Cl 4M H2O
1 6.94 g/mol + 1(35.45 g/mol)+ 4[2 1.01 g/mol 116.00 g/mol ]
1 6.94 g/mol + 1(35.45 g/mol) + 4(18.02 g/mol)
114.47 gmol
mass percent of water
mass of H 2 O
u 100%
molar mass of LiCl • 4H 2 O
4 × 18.02 g/mol
114.47 g/mol
u 100%
62.968%
62.97%
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Check Your Solution
The atomic molar masses have been substituted and added correctly. The
answer seems reasonable and the number of significant digits matches that
used in the molar masses.
53. Practice Problem (page 278)
Calculate the percent by mass of water in the compound CaSO4•2H2O(s).
What Is Required?
You need to calculate the percent by mass of water in the hydrate
CaSO4•2H2O(s).
What Is Given?
You know the chemical formula for the sample: CaSO4•2H2O
Plan Your Strategy
Determine the molar mass of CaSO4•2H2O(s).
Calculate the percent by mass of water.
Act on Your Strategy
Molar mass, M, of CaSO4•2H2O(s):
M CaSO4 •2H2O 1M Ca 1M S 4M O 2M H 2O
1 40.08 g/mol + 1(32.07 g/mol) + 4(16.00 g/mol) + 2[2 1.01 g/mol 116.00 g/mol ]
1 40.08 g/mol + 1(32.07 g/mol) + 4(16.00 g/mol) + 2(18.02 g/mol)
172.19 gmol
mass percent of water
mass of H 2 O
u 100%
molar mass of CaSO 4 g2H 2O
2 × 18.02 g/mol
172.19 g/mol
u 100%
20.9303%
20.93%
Check Your Solution
The atomic molar masses have been substituted and added correctly. The
answer is reasonable and the number of significant digits matches that used in
the molar masses.
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54. Practice Problem (page 278)
Calculate the percent by mass of water in the compound Na2CO3•10H2O(s).
What Is Required?
You need to calculate the percent by mass of water in the hydrate
Na2CO3•10H2O(s).
What Is Given?
You know the chemical formula for the sample: Na2CO3•10H2O
Plan Your Strategy
Determine the molar mass of Na2CO3•10H2O(s).
Calculate the percent by mass of water.
Act on Your Strategy
Molar mass, M, of Na2CO3•10H2O(s):
M Na 2CO3 •10H 2O 2M Na 1M C 3M O 10M H2O
2 22.99 g/mol + 1(12.01 g/mol) + 3(16.00 g/mol) + 10[2 1.01 g/mol 116.00 g/mol ]
2 22.99 g/mol + 1(12.01 g/mol) + 3(16.00 g/mol) + 10(18.02 g/mol)
286.19 g/mol
mass percent of water
mass of H 2 O
u 100%
molar mass of Na 2 CO3 •10H 2O
10 × 18.02 g/mol
286.19 g/mol
u 100%
62.9651%
62.97%
Check Your Solution
The atomic molar masses have been substituted and added correctly. The
answer is reasonable and the number of significant digits matches that used in
the molar masses.
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Whole-number ratio:
0.011513 0.057713
:
0.011513 0.011515
Ratio: 1:5
There are 5 moles of water molecules for 1 mol of strontium thiosulfate. The
value of x in the chemical formula SrS2O3•xH2O(s) is 5. The chemical formula
is SrS2O3•5H2O(s).
Check Your Solution
The atomic molar masses have been substituted and added correctly. A wholenumber amount in moles of water is expected. The answer is reasonable.
57. Practice Problem (page 278)
A hydrate of zinc chlorate, Zn(ClO3)2• xH2O(s), contains 21.5% zinc by mass.
Find the value of x.
What Is Required?
You need to determine the value of x that represents the mole amount of water
per mole of Zn(ClO3)2(s).
What Is Given?
You know the hydrate is 21.5% zinc by mass.
Plan Your Strategy
Determine the atomic molar masses of each element using the periodic table.
Write an expression representing the molar mass of Zn(ClO3)2• xH2O(s).
Write the expression for the percent by mass of zinc.
Equate this expression to the given percentage of zinc.
Solve this equation for x, the mole amount of water per mole of Zn(ClO3)2(s).
Act on Your Strategy
From the periodic table:
The molar mass of zinc is 65.41 g/mol.
The molar mass of chlorine is 35.45 g/mol.
The molar mass of hydrogen is 1.01 g/mol.
The molar mass of oxygen is 16.00 g/mol.
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Molar mass, M, of Zn(ClO3)2• xH2O(s):
M Zn ClO3 • xH2O 1M Zn 2 M ClO3 xM H2O
2
1 65.38 g/mol + 2[1(35.45 g/mol) + 3(16.00 g/mol)] + x[2(1.01 g/mol)
+ 1(16.00 g/mol)]
65.38 g/mol + 2(35.45 g/mol + 48 g/mol) + x(18.02 g/mol)
232.28 g/mol + x(18.02 g/mol)
mass percent of Zn
65.41 g
(232.28 xH 2O) g
× 100%
21.5%
Equating the given percent by mass of Zn (21.5% = 0.215):
65.41 g/mol
0.215
232.38 g/mol x 18.02 g/mol 65.41 g/mol 0.215 ª¬ 232.28 g/mol x 18.02 g/mol º¼
65.41 g/mol 49.940 g/mol x(3.8743) g/mol
x 3.8743 g/mol 65.41 g/mol 49.940 g/mol
x 3.8743 g/mol 15.47 g/mol
x
15.47 g/mol
3.8743 g/mol
3.993
4 nearest whole number There are 4 moles of water for 1 mol of Zn(ClO3)2(s).
The molecular formula for the hydrate is Zn(ClO3)2•4H2O(s).
Check Your Solution
Work backward. Determine the molar mass of Zn(ClO3)2• 4H2O(s).
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Molar mass, M, of Zn(ClO3)2• 4H2O(s):
M Zn ClO3 •4H2O 1M Zn 2 M ClO3 4 M H2O
2
1 65.41 g/mol + 2[1(35.45 g/mol) + 3(16.00 g/mol)] + 4[2(1.01 g/mol)
+ 1(16.00 g/mol)]
65.41 g/mol + 2(35.45 g/mol + 48.00 g/mol) + 4(18.02 g/mol)
232.31 g/mol + 4(18.02 g/mol)
304.39 g/mol
mass percent of zinc:
65.41 g/mol
304.39 g/mol
u 100%
21.488%
21.5%
This is the same as the given percent by mass of zinc.
58. Practice Problem (page 278)
Determine the formula for the hydrate of chromium(III) nitrate that is 40.50%
water by mass.
What Is Required?
You need to determine the chemical formula for the hydrate of chromium(III)
nitrate.
What Is Given?
You know the compound is a hydrate of chromium(III) nitrate.
You know the percent by mass of water in the hydrate: 40.50%
Plan Your Strategy
Write a chemical formula for a hydrate of chromium(III) nitrate. Let x be the
mole amount of water per mole of chromium(III) nitrate.
Determine the atomic molar masses of each element using the periodic table.
Write an expression representing the molar mass of this hydrate.
Write the expression for the percent by mass of water.
Equate this expression to the given percentage of water.
Solve this equation for x, the mole amount of water per mole of chromium(III)
nitrate.
Act on Your Strategy
The chemical formula for the hydrate of chromium(III) nitrate is
Cr(NO3)3•xH2O.
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Molar mass, M, of Cr(NO3)3•9H2O(s):
1M Cr 3M NO3 9 M H2O
M Cr NO3 •9H2O
3
1 52.00 g/mol + 3[1(14.01 g/mol) + 3(16.00 g/mol)] + 9[2(1.01 g/mol) + 1(16.00 g/mol)]
52.00 g/mol +3(14.01 g/mol + 48 g/mol) + 9(18.02 g/mol)
238.03 g/mol + 9(18.02 g/mol)
400.21 g/mol
mass percent of H2O
9 u 18.02 g
400.21g
u 100%
40.523%
40.52%
This is close to the given percent by mass of water.
59. Practice Problem (page 278)
The mass of a sample of a hydrate of magnesium iodide is 1.628 g. It is heated
until it is anhydrous and its mass is 1.072 g. Determine the formula for the
hydrate.
What Is Required?
You need to determine the formula for a hydrate of magnesium iodide.
What Is Given?
You know the compound is a hydrate of magnesium iodide.
You know the mass of the hydrate: 1.628 g
You know the mass of magnesium iodide: 1.072 g
Plan Your Strategy
Write a chemical formula to represent a hydrated form of magnesium iodide.
Determine the mass of water in the hydrate by subtracting the mass of
magnesium iodide from the mass of the hydrate.
Determine the atomic molar masses of each element using the periodic table.
Calculate the molar masses, M, of magnesium iodide and H2O.
Calculate the amount in moles of magnesium iodide in the sample using the
m
.
relationship n
M
Calculate the amount in moles of water in the sample.
Determine the amount in moles of water per mole of magnesium iodide by
dividing each amount in moles by the amount in moles of magnesium iodide.
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Act on Your Strategy
Chemical formula for the hydrated form of magnesium iodide: MgI2•xH2O
mass of water mass of hydrate mass of magnesium iodide
1.628 g 1.072 g
0.556 g
From the periodic table:
The molar mass of magnesium is 24.31 g/mol.
The molar mass of iodine is 126.90 g/mol.
The molar mass of hydrogen is 1.01 g/mol.
The molar mass of oxygen is 16.00 g/mol.
Molar mass, M, of MgI2:
M MgI2 1M Mg 2M I
1 24.31 g/mol + 2(126.9 g/mol)
278.11 g/mol
Molar mass, M, of water:
M H2O 2M H 1M O
2 1.01 g/mol 116.00 g/mol 18.02 g/mol
Amount in moles, n, of MgI2:
m
nMgI2
M
1.072 g
278.11 g /mol
0.0038545 mol
Amount in moles, n, of water:
m
nH2O
M
0.556 g
18.02 g /mol
0.0308546 mol
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Whole-number ratio:
0.0038545 0.0308546
:
0.0038545 0.0038545
Ratio: 1:8
There are 8 moles of water molecules for 1 mol of magnesium iodide. The
value of x in the chemical formula MgI2•xH2O is 8. The chemical formula is
MgI2•8H2O(s).
Check Your Solution
The atomic molar masses have been substituted and added correctly. A wholenumber amount in moles of water is expected. The answer is reasonable.
60. Practice Problem (page 278)
A chemist needs 1.28 g of sodium hypochlorite, NaOCl(s), for an experiment,
but she only has
sodium hypochlorite pentahydrate, NaOCl•5H2O(s). How many grams of the
hydrate should she use?
What Is Required?
You need to determine a mass of sodium hypochlorite pentahydrate.
What Is Given?
You know the chemical formulas for sodium hypochlorite: NaOCl
You know the chemical formula for sodium hypochlorite pentahydrate:
NaOCl•5H2O.
You know the mass of NaOCl(s): 1.28 g
Plan Your Strategy
Determine the atomic molar masses of each element using the periodic table.
Calculate the molar masses of NaOCl(s) and NaOCl•5H2O(s).
Calculate the amount in moles of NaOCl(s).
The molar masses are directly proportional to the masses of each compound
since the mole ratio is 1:1.
Calculate the mass of NaOCl•5H2O(s) using the ratio of the molar masses.
Act on Your Strategy
From the periodic table:
The molar mass of sodium is 22.99 g/mol.
The molar mass of chlorine is 35.45 g/mol.
The molar mass of hydrogen is 1.01 g/mol.
The molar mass of oxygen is 16.00 g/mol.
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