lesson 9-4 Mixed Mass-Volume Problems

Lesson 9-4

Mixed Mass-Volume Problems

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Mixed mass-volume problems include mass-volume problems and volume-mass problems. In order to become proficient at solving mixed mass-volume problems, it is imperative that you solve problems logically as opposed to mechanically. Many students are able to do all of the Math work involved in these problems, but they still get them wrong on exams, because they fail to identify the exact type of problem that it is. If you go through the motions of the calculations, and never check to see if they make sense, you are missing an important chance to catch a mistake. Read each problem carefully, try to understand it, and think about what you are doing with each calculation. Does it make sense to divide a mass by the molar volume of a gas? Would you multiply the number of moles by the molar mass of helium to get its volume? Avoid foolish mistakes and these problems will become quite easy, with practice.

For many types of mixed mass-volume problems, you will follow these same basic steps;

1. Start with a balanced chemical equation.

2. Identify and label the given and the unknown, cross out the rest.

3. Turn the given quantity into moles by;
     A) dividing by molar mass in the event that a mass is given, or
     B) dividing by molar volume in the event that a volume is given.

4. Determine the number of moles of the unknown that will by produced, by comparing the molar
     ratio shown in the balance chemical equation.

number of moles of given      number of moles of unknown
--------------------------------   =    --------------------------------------
coefficient of given    coefficient of unknown

5. Change the number of moles of the unknown to the units that the question asked for by;
     A) multiplying by the molar mass, if the question asks for grams, or
     B) multiplying by the molar volume (22.4 dm³/mole) if the question asks for dm³.

It should be noted that not all questions are going to fit into this neat format. You need to be able to make adjustments based on any special circumstances that arise in a problem. What will you do if the question asks for cm3 instead of dm3? What will you do if the question gives you number of particles, instead of mass or volume? These special circumstances are exactly why you need to strive to understand these problems, not just solve them mechanically.

Example 1. At STP, what would be the volume of the carbon dioxide produced when 90.0 grams of glucose react with an excess of oxygen?

1. Start with a balanced chemical equation.

C₆H₁₂O_6(s) + 6O_2(g) ----> 6H₂O_(g) + 6CO_2(g)

2. Identify and label the given and the unknown, cross out the rest.

Given                                                                              Unknown
C₆H₁₂O_6(s) + ~~6O_2(g)~~ ----> ~~6H₂O_(g)~~ + 6CO_2(g)
90.0 g                                                 X dm³

3. Turn the given quantity into moles by;
     A) dividing by molar mass in the event that a mass is given, or
     B) dividing by molar volume in the event that a volume is given.

mass given
# of moles = ----------------------
molar mass

90.0 g
# of moles glucose = ----------------------
180.1 g/mole

# of moles of glucose = 0.500 moles

4. Determine the number of moles of the unknown that will by produced, by comparing the molar ratio shown in the balance chemical equation.

moles of the given (glucose) = 0.500 moles
moles of the unknown (carbon dioxide) = X
coefficient of the given (glucose) = 1
coefficient of the unknown (carbon dioxide) = 6

number of moles of given      number of moles of unknown
--------------------------------   =    --------------------------------------
coefficient of given    coefficient of unknown

0.500 moles     X moles
      ------------    =     -------------
1                      6

X = 3.00 moles

# of moles of carbon dioxide = 3.00 moles

5. Change the number of moles of the unknown to the units that the question asked for by;
A) multiplying by the molar mass, if the question asks for grams, or
B) multiplying by the molar volume (22.4 dm³/mole) if the question asks for dm³.

# of moles of carbon dioxide = 3.00 moles
molar volume of a gas at STP = 22.4 dm³/mole

volume of a gas at STP = # of moles of the gas x molar volume of gases at STP (22.4 dm³/mole)

volume of the carbon dioxide gas at STP = 3.00 ~~moles~~ x 22.4 dm³/~~mole~~

volume of carbon dioxide at STP = 67.2 dm³

Our final answer, 67.2 dm³ of carbon dioxide are produced when 90.0 grams of glucose react with an excess of oxygen gas.

Now, practice what you have learned with the worksheets and lesson links below.

Mixed Mass-Volume Quizzes

Mixed Mass-Volume Worksheets

Worksheet 9-4a - Mixed Mass-Volume Problems