Ringwood Public Schools
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More Practice Finding Mass from a Count
Lesson 10.1
Step-by-Step Practice
1. What is the mass of 90 apples if one dozen apples have a mass of 2.0 kg?
( Analyze List the knowns and the unknown.
( Calculate Solve for the unknown.
First, identify the sequence of conversions needed to do the calculation.
number of apples
mass of apples
dozens of apples
1 dozen apples
Write the conversion factor that can be used
to convert from number of apples to dozens of apples.
Write the factor that can be used to convert from dozens of apples to mass of apples.
12 apples
2.0 kg
1 dozen apples
2.0 kg
× 1 dozen apples
1 dozen apples
Multiply the number of apples by the two
conversion factors.
90 apples ×
12 apples
= 15 kg
( Evaluate Does the result make sense?
A dozen apples has a mass of 2.0 kg and 90 apples is less than 10 dozen apples. So it makes sense that the mass is less than 20 kg (10 dozen × 2.0 kg per dozen).
Knowns
12 apples =
1 dozen apples
1 dozen apples =
2.0 kg apples
Name Class Date
mass of 90 apples = ? kg
Unknown
number of apples =
90 apples
mass of 0.50 bushel
of apples = ? kg
Unknown
0.20 bushel of apples =
1 dozen apples
2. If 0.20 bushel is one dozen apples, and the mass of one dozen apples is 2.0 kg,
what is the mass of 0.50 bushel?
( Analyze List the knowns and the unknown.
( Calculate Solve for the unknown.
Identify the sequence of conversions needed to do the calculation.
bushels of apples
of apples
of apples
Write the factor to convert from bushels of apples to
dozens of apples. Then write the factor that can be used
to convert from dozens of apples to mass of apples.
1 dozen apples
1 dozen apples
1 dozen apples
Multiply the bushels of apples by the two
conversion factors.
0.50 bushel of apples ×
× 1 dozen apples =
( Evaluate Does the result make sense?
On Your Own
3. If an apple has eight seeds, and one apple has a mass of 0.2 kg, how many apple seeds are in 14 kg of apples?
4. A case of paper has a mass of 2000 g. A case of paper contains 10 reams of paper.
One ream of paper is 500 sheets. What is the mass, in grams, of 50 sheets of paper?
Hint: You will need three conversion factors.
Knowns
bushels of apples =
0.50 bushel
1 dozen apples =
2.0 kg apples
Name Class Date
Interpret Data
Mass Ratio of Carbon to Hydrogen
Lesson 10.1
Preview the Table
Mass hydrogen
=
=
2 amu
1
=
10 amu
1
=
50 amu
1
(6.02 × 10 ) × (12)
12
=
This table compares the mass of carbon atoms to the mass of hydrogen atoms. The unit of
mass is the atomic mass unit (amu). Remember that an amu is one-twelfth the mass of a
carbon-12 atom.
Look at the first column. Dots are used to represent the number of carbon atoms in the first
four rows. How many carbon atoms are in the fourth row?
Look at the column labeled “Hydrogen Atoms.” It looks a lot like the first column. One
difference is the size of the dots representing the atoms. What is another difference?
Look at the third column. Data from the first two columns is presented as a ratio. The
mass of a given number of carbon atoms is the numerator of the ratio. The mass of the same
number of hydrogen atoms is the denominator.
Carbon Atoms
Hydrogen Atoms
Mass Ratio
Number Mass (amu)
Number Mass (amu)
12
1
12 amu 12
1 amu 1
24
(2 × 12)
2
(2 × 1)
24 amu 12
120
(10 × 12)
10 (10 × 1)
120 amu 12
600
(50 × 12)
50 (50 × 1)
600 amu 12
Avogadro’s (6.02 × 1023) × (12)
number
Avogadro’s (6.02 × 1023) × (1)
number
23
(6.02 × 1023) × (1) 1
Name Class Date
Mass carbon
Try it! Find the row that has 10 dots.
Analyze the Table
Now you are ready to answer some more questions. As you read the questions:
[pic] Highlight key words.
[pic] Circle numbers and units.
Use the first question as an example.
1.
Read Tables What is the mass of 10 carbon atoms? What is the
mass of 10 hydrogen atoms?
2.
Read Tables What is the mass ratio of 10 carbon atoms to 10
hydrogen atoms?
3.
Calculate What is the mass of 25 carbon atoms? What is the
mass of 25 hydrogen atoms?
On Your Own
4.
Calculate What is the mass ratio of 25 carbon atoms to 25 hydrogen atoms?
5.
Read Tables What is the ratio when the number of carbon atoms is 6.02 × 1023 and the
number of hydrogen atoms is 6.02 × 1023?
6.
Make Generalizations What is the mass ratio of x number of carbon atoms to x
number of hydrogen atoms? Give a reason for your answer.
7.
Infer Do 36.0 kg of carbon atoms and 3.0 kg of hydrogen atoms have the same number of atoms? Hint: Divide the mass of carbon (36.0 kg) by the mass of hydrogen (3.0 kg).
Try it! Multiply the mass of one atom (in amu) by the number of atoms.
Try it! Divide the mass
of 10 carbon atoms by the mass of 10 hydrogen atoms.
Name Class Date
chemical formula
= CaCl2
molar mass of N2H4 = ? g/mol
molar mass of CaCl2 = ? g/mol
mass of 1 mol Cl
=
Unknown
mass of 1 mol H
= 1.0 g
mass of 1 mol N
= 14.0 g
chemical formula
= N2H4
Unknown
mass of 1 mol Ca
=
More Practice Finding the Molar Mass of a Compound
Lesson 10.1
Step-by-Step Practice
1. What is the molar mass of hydrazine (N2H4)?
( Analyze List the knowns and the unknown.
( Calculate Solve for the unknown.
To find the molar mass of a compound, you need to sum the masses of the elements in the compound.
Find the number of moles of N and H in 1 mol of N2H4.
2 mol N atoms
4 mol H atoms
14.0 g N
Multiply the number of moles of each
element by the molar mass of the element.
2 mol N ×
= 28.0 g N
1 mol N
1.0 g H
4 mol H ×
= 4.0 g H
1 mol H
Find the sum of the masses.
( Evaluate Does the result make sense?
mass of 1 mol N2H4 = 28.0 g N + 4.0 g H = 32.0 g
molar mass of N2H4 = 32.0 g/mol
Check the math without the units to make sure your
answer makes sense. 2 × 14 + 4 × 1 = 28 + 4 = 32.
Yes, the answers match.
2. Calcium chloride (CaCl2) is used to de-ice roadways and sidewalks. Calculate the molar mass of this compound.
( Analyze List the knowns and the unknown.
Knowns
Knowns
Name Class Date
1 mol Ca
mol Cl ×
mol Ca ×
( Calculate Solve for the unknown.
Find the number of moles of Ca and Cl in
1 mol of CaCl2.
mol Ca atoms
mol Cl atoms
Multiply the number of moles of each element
by the molar mass of that element.
= g Ca
= g Cl
Find the total mass of the compound.
mass of 1 mol CaCl2 = g Ca + g Cl
= g
molar mass CaCl2 = g
( Evaluate Does the result make sense?
On Your Own
3. The compound aluminum selenide (Al2Se3) is used to make semiconductors. Calculate the molar mass of aluminum selenide.
4. Table sugar, or sucrose, has the formula C12H22O11. Calculate the molar mass of this molecule.
Name Class Date
mass of SO4
number of moles SO4
= ? mol SO4
Unknown
= 0.250 mol
number of moles of K2CO3
mass = ? g K2CO3
Unknown
mol K
mol K
mol C
mol C
mol O
mol O
mol K CO
mol K CO
34.6 g K2CO3
More Practice Converting Between Moles and Mass
Lesson 10.2
Step-by-Step Practice
1. What is the mass, in grams, of 0.250 mol K2CO3?
( Analyze List the known and the unknown.
( Calculate Solve for the unknown.
Use the molar mass of the compound as a conversion factor to convert from moles to mass.
First, find the mass of 1 mol of K2CO3. The mass is the sum of the masses of the individual elements.
One mole K2CO3 is made of:
39.1 g K
×
1
= 78.2 g K
2 mol K atoms
2
12.0 g C
1 mol C atoms
1
×
= 12.0 g C
1
16.0 g O
3 mol O atoms.
×
= 48.0 g O
3
1
1 mol K2CO3 = 78.2 g K + 12.0 g C + 48.0 g O
= 138.2 g K2CO3
138.2 g K2CO3
Multiply the number of moles to be converted
by the molar mass.
( Evaluate Does the result make sense?
0.250
×
3
1
2
2
3
=
The molar mass of K2CO3 is about 140 g/mol. The value to be converted is 0.250 mol, or 1/4 of a mol. So 1/4 × 140 g
is about 35 g. The answer 34.6 g makes sense.
2. How many moles are in 20.0 g of sulfur tetroxide?
( Analyze List the known and the unknown.
= g
Known
Known
Name Class Date
× 16.0 g O
mol O
mol S
mol O
mol S
g SO
( Calculate Solve for the unknown.
Use the molar mass of the compound as a conversion factor.
Determine the molar mass of SO4.
1 mol SO4 = mol S + mol O
32.1 g S
×
= S
1
= O
1
1 mol SO4 = g S + g O = SO4
Use the molar mass to convert from
mass of SO4 to moles.
( Evaluate Does the result make sense?
×
= SO
4
4
The molar mass of sulfur tetroxide is about 100 g/mol. The value to be converted is
20.0 g, which is 1/5 of the molar mass. 1/5 = 0.2. Is the calculated value of moles of
sulfate the same fraction?
On Your Own
3. What is the mass of 2.50 mol of methane (CH4)?
4. The compound phenol (C6H6O) was used as an antiseptic because it kills germs quickly.
How many moles are in 83.0 g of phenol?
Name Class Date
percent by mass of
Al = ?% Al
mass of Al = mass of compound – mass of Se mass of Al = 10.0 g compound – 8.0 g Se
mass of Al = 2.0 g Al
mass of compound
( Evaluate Does the result make sense?
The mass of the selenium is more than half of the total mass, so it makes sense that the percentage would be greater than 50 percent.
( Calculate Solve for the unknown.
Divide the mass of the element by the mass of the compound. Then multiply by 100%.
The compound has a mass of 10.0 g. The selenium in the compound has a mass of 8.0 g. Subtract to find the mass of aluminum in the compound.
Write and solve the equation for percent
by mass for each element in the compound.
% by mass of element = mass of element × 100%
Unknowns
percent by mass of Zn = ?% Zn
percent by mass of C = ?% C
percent by mass of O = ?% O
chemical
formula = ZnCO3
Unknowns
percent by mass of
Se = ?% Se
mass of selenium in compound = 8.0 g
mass of compound =
10.0 g
80.0% Se
20.0% Al
More Practice Calculating Percent Composition
Lesson 10.3
Step-by-Step Practice
1. A 10.0 g sample of a compound made of aluminum and selenium contains 8.0 g of selenium. What is the percent composition of this compound?
( Analyze List the knowns and the unknowns.
8.0 g
%Se = 10.0 g × 100% =
2.0 g
%Al = 10.0 g × 100% =
2. Zinc carbonate (ZnCO3) is used as a zinc supplement
in animal feed. What is the percent composition of zinc
carbonate?
( Analyze List the known and the unknowns.
Known
Knowns
Name Class Date
onate?
( Analyze List the known and the unknowns.
Known
Knowns
Name Class Date
mol C
mol O
mol O
mol Zn
mol Zn
➋ Calculate Solve for the unknown.
Divide the mass of the element by the total molar mass of the compound. Then multiply by 100%.
65.4 g Zn
Determine the molar mass of ZnCO3.
1 mol ZnCO3 = g Zn + g C + g O
1
×
=
1
12.0 g C
1 mol C ×
=
1
= g ZnCO3
16.0 g O
3
×
=
1
Determine the percent by mass of zinc.
mass of Zn in 1 mol of ZnCO3
65.4 g
% Zn =
% Zn =
× 100% = % Zn
molar mass ZnCO3
125.4 g
Determine the percent by mass of carbon and oxygen.
mass of C in 1 mol of ZnCO3
% C =
% C =
× 100% =
125.4 g
molar mass ZnCO3
mass of O in 1 mol of ZnCO3
% O =
% O =
× 100% =
molar mass ZnCO3
➌ Evaluate Does the result make sense?
Make sure that the percentages add up to about 100%:
% + % + % = %.
On Your Own
3. A 2.5 g sample of a potassium and bromine compound contains 0.75 g K and 1.75 g Br.
What is the percent composition of each element in this compound?
4. A 40.0 g sample of ore contains 18.0 g Fe and the rest of the mass is oxygen. What is the
percent composition of this sample? Hint: Subtract the mass of Fe from the total mass to
find the mass of oxygen.
Name Class Date
D =
E =
(A) MnO
(B) MnO2
(C) Mn2O3
(D) Mn2O7
(E) Mn3O4
Standardized Test Prep Tutor
Read the question. The highlighted words tell you what property
the correct nitrogen compound will have.
5. Which of these compounds has the largest percent by mass of nitrogen?
Notes and Calculations
(A) N2O
(B) NO
(C) NO4
➊ Analyze
(D) N2O3
(E) N2O4
You could calculate the molar mass of each compound and
then figure out what percent of the mass is nitrogen. But
for this problem, there is a shortcut. Because the same two
elements are in each compound, you only need to find the
compound that has the greatest ratio of nitrogen to oxygen.
➋ Solve
The ratios are based on the number of atoms of nitrogen and oxygen in a molecule of the compound.
The ratio of nitrogen to oxygen in answer A is 2:1. The ratio of nitrogen to oxygen in answer B is 1:1. The ratio of nitrogen to oxygen in answer C is 1:4. What is the ratio of nitrogen to oxygen in answer D? What is the ratio of nitrogen to oxygen in answer E?
➌ Choose an Answer
Which compound has the greatest ratio of nitrogen to oxygen? The correct answer is A.
Now you try it.
Which of these compounds has the largest percent by mass of oxygen?
Name Class Date
3 C atoms
21
(C) 1.8 × 1021
(A) 4.0 × 1025
(B) 2.0 × 1025
(C) 8.0 × 1025
(D) 1.0 × 1026
(A) 1.4 × 1019
(B) 2.8 × 1019
(C) 4.2 × 1019
(D) 8.4 × 1019
(B) 1.0 × 1021
➊ Analyze
(D) 5.0 × 1021
Use the ratio of hydrogen to carbon atoms in the formula.
For every 10 atoms of hydrogen in C6H10S2O, there are
6 atoms of carbon. The ratio of hydrogen atoms to carbon
atoms is 10:6, or 5:3.
➋ Solve
Multiply the number of carbon atoms by the ratio.
➌ Choose an Answer
Look at the answer choices. Find the choice that matches the calculation. The correct answer is D.
Now you try it.
A sample of calcium carbonate, CaCO3, contains 1.4 × 10
A sample of NH4NO3 contains 4.0 × 10 atoms of nitrogen. How many hydrogen atoms does this sample contain?
Read the question. The highlighted phrase tells what you are
looking for.
7. Allicin (C6H10S2O) is the compound that gives garlic its odor.
A sample of allicin contains 3.0 × 1021 atoms of carbon.
How many hydrogen atoms does this sample contain?
(A) 10
3.0 × 1021 C atoms × 5 H atoms
= 5.0 × 10 H atoms
19
atoms of carbon. How many oxygen atoms does this sample
contain?
25
Name Class Date
................
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