Constructed Response
Mathematics of
Formulas & Equations
Mathematics of Formulas & Equations
Teacher Guide
Students will need about 30 minutes to complete these constructed response tasks.
Objective assessed:
• Determine molar mass and formula mass.
1. Molar mass is a concept used often in chemistry.
• Define the term molar mass and give one specific example of a substance and its
molar mass.
• Explain the difference between formula mass and molar mass, and describe the
relationship between the two.
• Explain how molar mass can be used to determine the number of molecules in a
sample of a compound if its mass and molecular formula are known.
Correct response(s):
Sample Correct Response: The molar mass of an element or compound is defined as the
mass of one mole of that element or compound. An example is the element hydrogen, which
has a mass of 1.008 grams per mole of hydrogen atoms. The formula mass of a compound
is the mass of one formula unit of the compound, measured in atomic mass units. To find
formula mass, the empirical formula or simplest ratio of elements is used.
Formula mass and molar mass of a compound are related by a whole number factor. If you
know the molecular formula of a compound, you can calculate its molar mass. If you also
know the mass of the sample, you can divide the mass by the molar mass to determine how
many moles are present in the sample. Once you know the number of moles, you can use
Avogadro’s constant to multiply by the number of moles to determine the number of
molecules in the sample.
Response scoring tool:
Score
Content
5
Provides each of the following:
• Correctly defines molar mass and notes the unit as grams per
mole
• gives a specific example of molar mass for an element or a
compound
• correctly explains the difference between formula and molar mass
for a compound, and notes the unit for formula mass as the
atomic mass unit
• indicates that the two differ by a whole number factor
• correctly summarizes the steps involved in converting grams to
moles and then moles to molecules
4
Includes four of the items listed above
3
Includes three of the items listed above
2
Includes two of the items listed above
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1
0
Includes one of the items listed above
No response, or response not appropriate to the question
Objective assessed:
• Determine the percent composition of a compound.
2. (a) Calculate the mass of 0.2 mol of calcium.
Correct response(s):
Sample correct response: One mole of calcium has a mass of 40.08 g, so:
mass of Ca = 0.200 mol Ca ×
40.08 g Ca
= 8.02 g Ca
1 mol Ca
(b) Calculate the number of atoms in a 12.0 g sample of carbon.
Sample correct response: One mole of carbon has a mass of 12.0 g, so there are
6.022 x 1023 atoms in 12.0 g of carbon.
Response scoring tool:
Score
Content
5
Provides each of the following:
• Correctly identifies the molar mass of calcium
• Correctly calculates the mass of 0.2 g of calcium
• Correctly identifies the molar mass of carbon
• Correctly identifies the number of atoms in one mole
4
Includes three of the items listed above
3
Includes two of the items listed above
2
Includes one of the items listed above
1
Makes some attempt to identify the molar masses of calcium and carbon
0
No response, or response not appropriate to the question
Objective assessed:
• Apply stoichiometric principles.
3. (a) Calculate the percent composition of glycerol, C3H8O3. You can assume that you are
working with one mole of glycerol.
Correct response(s):
Sample Correct Response: In one mole of glycerol, there are 3 mol C, 8 mol H, and 3 mol
O. Multiply the number of moles of each element by its molar mass to determine the mass of
each element in one mole of glycerol. Add the total to find the mass of one mole of glycerol.
Divide the mass of each element by the mass of one mole of glycerol and multiply by 100 to
obtain a percentage value.
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12.01 g C
= 36.03 g C
1 mol C
1.01 g H
= 8.08 g H
mass of H = 8 mol H ×
1 mol H
16.00 g O
mass of O = 3 mol O ×
= 48.00 g O
1 mol O
mass of C = 3 mol C ×
molar mass of glycerol = 36.03 + 8.08 + 48.00 = 92.11 g/mol
%C=
36.03 g C
× 100 = 39.12% C
92.11 g C 3H 8O 3
%H=
8.08 g H
× 100 = 8.77% H
92.11 g C 3H 8O 3
%O=
48.00 g O
× 100 = 52.11% O
92.11 g C 3H 8O 3
Response scoring tool:
Score
Content
5
Includes
• correct explanation or calculation steps shown
• correct calculation of molar mass for glycerol
• correct calculation for percent carbon
• correct calculation for percent hydrogen
• correct calculation for percent oxygen
4
Includes four of the above.
3
Includes three of the above.
2
Includes two of the above.
1
Includes one of the above.
0
No response, or response not appropriate to the question.
(b) A student is given the percent composition for an unknown compound: 81.68% C
and 18.32% H. The molecular mass of the compound is 44.11 g/mol. Calculate the
empirical formula and the molecular formula of the compound.
Sample Correct Response: To determine the empirical formula, I will assume that a
100 g sample is being used. I will assume each percentage value represents grams of
each element. First I will calculate the number of moles present.
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Mathematics of Formulas & Equations
moles of C =
moles of H =
81.68 g
12.01 g /mol
18.32 g
1.01 g /mol
= 6.800 mol C
= 18.1 mol H
Next I will examine the ratios of the number of moles:
18.1 mol
= 2.66
6.800 mol
6.800 mol
ratio for carbon:
= 1.000
6.800 mol
ratio for hydrogen:
When I multiply 2.66 by 3, I get 7.98, which is very close to the whole number: 8. There
are 8 hydrogen atoms in the empirical formula. I will multiply the ratio for carbon by 3
also. There are 3 carbon atoms in the empirical formula. The empirical formula is C3H8.
The molecular mass of the empirical formula is:
(3 × 12.01 g/mol) + (8 × 1.01 g/mol) = 44.11 g/mol
The molecular formula is also C3H8.
Response scoring tool:
Score
Content
5
Includes
• correct explanation or calculation steps shown
• correct calculation of moles for carbon
• correct calculation of moles for hydrogen
• correct calculation of ratios for hydrogen and carbon
• correct calculation of the empirical and molecular formulas
4
Includes four of the above.
3
Includes three of the above.
2
Includes two of the above.
1
Includes one of the above.
0
No response, or response not appropriate to the question.
Objective assessed:
• Apply stoichiometric principles.
4. Calculate the mass of HF needed to produce 10.0 g SnF2 according to the following
reaction:
Sn + 2HF Æ SnF2 + H2
Correct response(s):
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Mathematics of Formulas & Equations
Sample Correct Response: We can determine the molar mass of SnF2 and then divide the
mass yield of SnF2 by its molar mass to calculate the number of moles of SnF2 that will be
produced. Once we know the number of moles of SnF2, we can use the reaction
stoichiometry to determine how many moles of HF will be needed to produce that quantity of
SnF2. Finally, we can determine the molar mass of HF and use it to multiply by the moles of
HF to find the mass of HF required for the reaction.
The molar mass of SnF2 is determined by:
118.71 g Sn
= 118.71 g Sn
1 mol Sn
19.00 g F
= 38.00 g F
2 mol F ×
1 mol Sn
1 mol Sn ×
molar mass SnF2 = 118.71 + 38.00 = 156.71 g/mol SnF2
Determine the moles of SnF2 produced in the reaction:
moles SnF2 = 10.0 g SnF2 ×
1 mol SnF2
= 6.38 × 10 −2 mol SnF2
156.71 g SnF2
Use the reaction stoichiometry to determine the moles of HF needed :
6.38 × 10 −2 mol SnF2 ×
2 mol HF
= 1.28 × 10 −1 mol HF
1 mol SnF2
Determine the molar mass of HF:
1.01 g H
= 1.01 g H
1 mol H ×
1 mol H
19.00 g F
= 19.00 g F
1 mol F ×
1 mol Sn
molar mass HF = 1.01 + 19.00 = 20.01 g/mol HF
Determine the mass of HF corresponding to the required moles of HF:
1.28 × 10 −1 mol HF ×
20.01 g HF
= 2.55 g HF
1 mol HF
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Therefore, 2.55 g HF are required to form 10.0 g SnF2.
Response scoring tool:
Score
Content
5
Includes:
• correct calculation for the molar mass of SnF2
• correct calculation for the molar mass of HF
• using the molar mass values to convert between grams and moles
of SnF2
• using the molar mass values to convert between moles and grams
of HF
• using the reaction stoichiometry provided by the balanced
equation to convert between moles of SnF2 and moles of HF
4
Includes four of the above
3
Includes three of the above
2
Includes two of the above
1
Includes one of the above
0
No response, or response not appropriate to the question
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