1. 12.2 Chemical Calculations
Read the lesson title aloud to students.

2. Mole Ratios
Coefficients in a chemical equation show the mole ratios of substances involved in the reaction.
N2(g) H2(g)  NH3(g)
1.00 mol
3.00 mol
2.00 mol
Remind students that the coefficients in a chemical equation give the number of moles of each substance involved.
Ask one or two students to write the number of moles of each substance shown by the chemical equation.
Click to reveal the correct answer.
Ask: What is the mole ratio of nitrogen to hydrogen in the reaction?
Answer: 1:3
Click to reveal the mole ratio of nitrogen to hydrogen.
Ask students to identify the mole ratios of ammonia to nitrogen and hydrogen to ammonia.
Answer: Ammonia to nitrogen is 2:1; hydrogen to ammonia is 3:2.
Click to reveal each ratio.

3. Mole-to-Mole Conversions
Use mole ratios to convert from moles to moles.
How many moles of NH3 are produced when 0.60 mol of nitrogen reacts with hydrogen?
N2(g) + 3H2(g) 2NH3(g)
Remind students that stoichiometry involves calculations used to determine the amounts of substances involved in a chemical reaction. The amounts can be moles, grams, liters, or any other measurement of quantity.
Ask: What is the first thing we need to know to solve this problem?
Answer: the balanced chemical equation
Click to reveal the balanced chemical equation.
Ask one or two students to identify the known and unknown quantities.
Click to reveal these quantities.

4. Mole-to-Mole Conversions, cont.
Use conversion factors to solve for the unknown quantity.
N2(g) + 3H2(g) 2NH3(g)
Conversion factor:
Explain that conversion factors are very important in stoichiometry problems because they allow us to convert one unit to another.
Ask: Is the amount of hydrogen gas that reacts with nitrogen gas needed to complete the calculation?
Answer: No. The mole ratio is used to convert from the amount of one substance in a reaction to the amount of another substance. The amount of ammonia can be computed if the amount of nitrogen gas is known.
Guide students to use the balanced chemical equation to write the mole ratio needed to convert moles of N2 to moles of NH3.
Click to reveal the conversion factor.
Explain that the moles of N2 are in the denominator of the mole ratio, so the unit mol N2 cancels when the mole ratio is multiplied by the known number of moles of N2 that react.
Click to reveal the equation setup.
Perform the multiplication and show students how the answer has units of mol NH3 and how the rest of the units in the multiplication cancel.
Click to show the units cancelled.
Tell students that the numbers in the mole ratio do not affect the number of significant figures in the answer because the coefficients in the chemical equation are exact numbers.
Ask a student to write the answer to the calculation.
Click to reveal the correct answer.
1.2 mol NH3

5. Mass-to-Mass Conversions
To calculate masses, use both mole ratios and molar masses as conversion factors.
Explain that in most cases, we are interested in the masses of substances involved in a chemical equation. So, we need to be able to convert between moles and mass.
Ask: What quantity can be used to convert between mass and moles?
Answer: molar mass
Click to reveal the flowchart for converting the mass of a given quantity to the mass of a wanted quantity.
Explain that students can think about this conversion as having three parts: Convert the mass of given to the moles of given; convert the moles of given to the moles of wanted; and convert the moles of wanted to the mass of wanted. If necessary, remind students that a and b represent coefficients in a chemical equation.
Ask students to identify the two conversion factors that are based on molar mass.
Click to highlight the two conversion factors.

6. Practicing Mass-to-Mass Conversions
How many grams of NH3 are produced when 5.40 grams of H2 reacts with nitrogen?
N2(g) + 3H2(g) 2NH3(g)
Have students read the problem statement.
Ask: What are we given in this problem?
Answer: balanced equation, mass of one reactant
Ask: What are we asked to find?
Answer: mass of product formed
Ask: What conversion factors will we need?
Answer: mole ratio of ammonia to hydrogen; molar mass of hydrogen; molar mass of ammonia
Ask: Why is the molar mass of nitrogen gas not needed for this problem?
Answer: The mole ratio that is being used only involves hydrogen gas and ammonia gas.
Click to reveal the knowns and unknowns for the problem.

7. Mass-to-Mass Conversions, cont.
Use conversion factors to solve for the unknown quantity.
31 g NH3
Remind students that in a stoichiometry problem, all units except the units that are wanted should cancel out.
Review the steps of a mass-to-mass conversion: Convert grams of given to moles of given; convert moles of given to moles of wanted; convert moles of wanted to grams of wanted.
Click to reveal the equation setup.
Point out the ratios that are used to perform each conversion.
Ask one or two students to show how the units in the equation cancel.
Click once to reveal each unit cancellation (three clicks total).
Ask a student to calculate the mass of ammonia.
Click to reveal the correct answer.

8. Performing Other Conversions
Convert the given quantity to moles, use mole ratios to calculate moles, and then calculate the wanted quantity.
Explain that a similar method can be used to solve any type of stoichiometry problem. The general method is the same: Convert the given to moles; convert moles of given to moles of wanted; and then convert moles of wanted to the required units.
Ask: What are some conversion factors you are likely to need to use in stoichiometry problems?
Answer: mole ratios, molar masses, molar volume of a gas, Avogadro’s number
Ask students to trace a path through the flowchart for each of the following types of stoichiometry problems: converting number of particles to volume; converting volume to mass; converting mass to volume.
Click to reveal each path through the flowchart.

9. Calculating Product Quantity
How many molecules of oxygen are produced when 29.2 grams of water are decomposed by electrolysis according to this balanced equation?
2H2O (l)  2H2 (g) + O2 (g)
Have students read the problem statement.
Ask: What are we given in this problem?
Answer: balanced equation, mass of reactant
Ask: What are we asked to find?
Answer: number of molecules of product formed
Ask: What conversion factors will we need?
Answer: mole ratio of oxygen to water; molar mass of water; Avogadro’s number
Click to reveal the knowns and unknowns for the problem.

10. Strategy for Calculating Product Quantity
Always start a stoichiometry problem by identifying the conversion steps.
Convert mass of H2O to moles of H2O.
Convert moles of H2O to moles of O2.
Convert moles of O2 to molecules of O2.
Conversion factor: molar mass
Conversion factor: mole ratio
Review with students the conversions they will need to perform in this calculation.
Click to reveal the steps.
Ask students to identify the conversion factor to be used for each of the conversions.
Click to reveal the conversion factors.
Conversion factor: Avogadro’s number

11. Calculating Product Quantity, cont.
Use conversion factors to solve for the unknown quantity.
Remind students that in a stoichiometry problem, all units except the units that are wanted should cancel out.
Guide students in writing the conversion steps following the order outlined.
Click to reveal the equation setup.
Point out the ratios that are used to perform each conversion.
Encourage students to cancel units before performing the calculation to make sure that all the conversion factors are set up properly. Ask one or two students to show how the units in the equation cancel.
Click once to reveal each unit cancellation (three clicks total).
Ask a student to calculate and write the number of molecules of oxygen.
Click to reveal the correct answer. =
4.88 × 1023 molecules O2

12. Calculating Reactant Quantity
Assuming STP, how many milliliters of oxygen are needed to produce 20.4 milliliters of SO3 according to this balanced equation?
2SO2 (g) + O2 (g)  2SO3 (g)
Have students read the problem statement.
Ask: What are we given in this problem?
Answer: balanced equation, volume of product
Ask: What are we asked to find?
Answer: volume of reactant needed
Ask: What conversion factors will we need?
Answer: mole ratio of oxygen to sulfur trioxide, molar volume of a gas
Click to reveal the knowns and unknowns for the problem.

13. Calculating Reactant Quantity, cont.
Use conversion factors to solve for the unknown quantity.
10.2 mL O2
Remind students that in a stoichiometry problem, all units except the units that are wanted should cancel out.
Explain that a shortcut for volume-to-volume calculations uses a volume ratio. Since the molar volume of every gas is the same at STP, the ratio of any two coefficients in a balanced chemical equation also represents a ratio of volumes as long as both substances are gases. This is not possible with mass-to-mass conversions, but it simplifies volume-to-volume calculations.
Ask one or two students to show how the units in the equation cancel.
Click to reveal the unit cancellation.
Ask a student to calculate and write the volume of oxygen required.
Click to reveal the correct answer.