The Physics Classroom » Chemistry Tutorial » Stoichiometry » Conversions and Connections

Lesson 1: A Framework for Thinking Stoichiometrically

Part c: Conversions and Connections

Part a: Recipes, Ratios, and Relationships
Part b: The Law of Conservation of Mass
Part c: Conversions and Connections

 

A Framework for Thinking

As stated earlier in Lesson 1, stoichiometry is the study of the quantitative relationship between the amounts of reactants and products involved in a chemical reaction. Stoichiometry focuses on the how much? questions of chemical reactions. The stoichiometry unit of a typical introductory Chemistry course will consist of a collection of stoichiometry problems. For instance, given the mass of a reactant for a stated chemical reaction, the student is asked to determine how much product (in grams) is produced. There are many variants to this problem, but the point is that this unit is full of word problems to be solved.
 
Lesson 1 is our introduction to solving stoichiometry problems. The student who is equipped with a strong conceptual understanding of coefficients, mole ratios, molar mass, and conversion factors will be prepared to make sense of and solve such problems. Lesson 1 is our attempt to help students comprehend the landscape surrounding such problems. This page will focus on making connections between the various how much? quantities and to see the value of conversion factors in relating such quantities.
 
 
 

Making Connections

The main how much? quantities of stoichiometry problems include:

  1. moles of a reactant (in grams)
  2. moles of a product (in grams)
  3. mass of a reactant (in grams)
  4. mass of a product (in grams)
 
Two big questions to ponder regarding these quantities is what is related to what? and how are they related?
 
 
 

Coefficients and Mole-to-Mole Relationships

Consider the ammonia synthesis reaction again:
N2(g)  +  3 H2(g)  →  2 NH3(g)
 
The numbers in front of the formulae (plural for formula) are the coefficients. The missing coefficient for N2(g) means that it can be assumed to be 1. These coefficients indicate the relative number of moles of each reactant and product involved in the reaction. The following claims can be made:
 
  • For every 1 mole of N2 that react, 3 moles of H2 react.
  • For every 1 mole of N2 that react, 2 moles of NH3 are produced.
  • For every 3 moles of H2 that react, 2 moles of NH3 are produced.
    (and from the last statement: for every 1 mole of H2 that react, 2/3-rds mole of NH3 are produced.)
 
If we are pondering what is related to what? and how are they related?, then we have our first answer. The moles of a reactant or product are related to the moles of the other reactants or product. The coefficients of the balanced chemical equation indicate the manner in which they are related.


 
For any reaction, the coefficients allow a student to determine the number of moles of any of reactant and product from a given amount of reactant and product. Whenever a stoichiometry problem is encountered that gives the moles of a reactant or products and asks to determine the moles of another substance, the coefficients must be used. They are the mole ratio that allows for such a conversion.

 
 
 

Molar Mass and Gram-to-Mole Relationships

Now let’s ponder how mass fits into this web of relationships. The mass in grams of a substance is related to the number of moles of that same substance. As we learned in Chapter 7, they are related to one another by the molar mass of the substance. The molar mass of a substance is the mass in grams of 1 mole of that substance.
 
Molar mass values for a substance can be determined by use of a periodic table. If needed, review our page on determining the molar mass of a compound. For N2, the molar mass is approximately 28.01 g/mol. For H2, the molar mass is approximately 2.02 g/mol. For NH3, the molar mass is approximately 17.05 g/mol. These values indicate the mass in grams per 1 mole of each substance. They can be used to relate the grams of a substance to the mole of a substance.
 
 
This is our second answer to the question of what is related to what? and how are they related? The mass in grams of a substance is related to moles of that same substance by the molar mass.
 
 
 

Combining Relationships

We have now learned of two relationships in this web of relationships.
  • The moles of one substance is related to the moles of another substance by the coefficients.
  • The mass (grams) of one substance is related to the moles of the same substance by the molar mass.
 
If we put these two of relationships together, we generate more answers to the question of what is related to what? and how are they related? For instance, the mass (in grams) of N2 is related to the moles of NH3. This is not a direct relationship; it is two relationships combined. Molar mass relates the mass of N2 to the moles of N2. And coefficients relate the moles of N2 to the moles of NH3.
 
 
These are not the only two relationships that be combined to relate the mass of one substance to the moles of another substance. The mass (in grams) of NH3 is related to the moles of N2 by combining a different set of relationships.
 
 
Finally, three relationships can be combined to relate the mass of a reactant (or product) to the mass of a product (or another reactant). For instance, the mass (in grams) of N2 can be related to the mass (in grams) of NH3. Once more, this is not a direct relationship; it is three relationships combined. Molar mass relates the mass of N2 to the moles of N2. Coefficients relate the moles of N2 to the moles of NH3. And the molar mass of NH3 relates the moles of NH3 to the mass of NH3.
 
 
As you can see, an understanding of the meaning of molar mass and the coefficients of the balanced chemical equation allows a student to make the connections between quantities. The four main how much? quantities of stoichiometry problems can be quickly related using these two big concepts. Success in a stoichiometry unit is achievable with an understanding of molar mass and coefficients.
 
 
 

Mole Island

One thing to note about the above discussion is that moles are central to all calculations. Every calculation discussed thus far involves a calculation of moles or a calculation of another quantity from a known amount of moles. The mole is a central quantity in stoichiometry. For that reason, a discussion of stoichiometry is not complete without a discussion of mole island.
 
The graphic below, often referred to as Mole Island, depicts the relationships between the various stoichiometry quantities. The graphic is based on the generic reaction between reactants A and B and products C and D. The coefficients in the balanced equation are w, x, y, and z. The question of what is related to what? and how are they related? is addressed by the arrows on the diagram. There is a direct relationship between any two quantities connected by arrows. The manner in which they are related – either by molar mass values or coefficients – is written next to the arrow.
 
 
 
Mole Island serves as a convenient tool for plotting out a conversion pathway between any given quantity and a desired quantity. All stoichiometry problems will either start on Mole Island, end on Mole Island, or pass through Mole Island. Mole Island describes the landscape that a Chemistry student must navigate to be an effective stoichiometrist. (Sorry. We made that last word up.)




 
To illustrate the use of Mole Island, let’s consider two examples.

Example 1 – Mole Island:

Determine the mass of C (in grams) produced from the reaction of 5.48 g of A.
 
Solution: The given quantity (grams of A) and the desired quantity (grams of C) are connected by three arrows. The conversion begins on A Island. The molar mass of A must be determined from the periodic table. It is then used to calculate the moles of A. You have now arrived on Mole Island. Then the coefficients in the balanced equation are used to convert from moles of A to moles of C. This takes you to the opposite side of Mole Island. The last step is the conversion from moles of C to grams of C. Use the periodic table to determine the molar mass of C. Then use it to convert from moles of C to grams of C.
 
 
 

Example 2 – Mole Island:

Determine the mass of B (in grams) that will react with 5.48 g of A.
 
Solution: The given quantity (grams of A) and the desired quantity (grams of B) are connected by three arrows. The conversion begins on A Island. The molar mass of A must be determined from the periodic table. It is then used to calculate the moles of A. You have now arrived on Mole Island. Then the coefficients in the balanced equation are used to convert from moles of A to moles of B. This takes you to the lower side of Mole Island. The last step is the conversion from moles of B to grams of B. Use the periodic table to determine the molar mass of B. Then use it to convert from moles of B to grams of B.
 
 
 

The Factor Label Method

Most student difficulties with stoichiometry can be traced to the tendency to make the topic memory intensive. The tendency (and not a good one) is to attempt to memorize rules for solving stoichiometry problems. If you must memorize, then memorize these two things:
 
  1. Molar mass is the grams per 1 mole and relates grams of a substance to the moles of the same substance.
  2. The coefficients of a chemical equation relate the moles of one substance to the moles of another substance involved in a reaction.
 
The substitute to memorizing is the use of the factor label method. This method was introduced in Chapter 1. The factor label method involves the use of conversion factors to convert from a given quantity in one set of units to the same or a different quantity in a different set of units. The factor label method is all about unit conversions. And because it is, units are essential. In fact, units are the driver of every factor label problem. Numbers take a back seat to units.
 
The factor label method was used in Chapter 7 to convert between particles and moles and between moles and grams. If you are not familiar with the factor label method, we recommend you review our Chapter 7 page on molar conversions.
 
Lesson 2 will include solutions to numerous stoichiometry problems. We will save detailed solutions for that Lesson. For now, we simply wish to show one relatively simple example.
 
 
 
 

Example 3 – Mole Island

Given:  N2(g)  +  3 H2(g)  →  2 NH3(g)
Determine the moles of NH3 produced from the reaction of 42.0 g of N2.
 
Solution: An ammonia synthesis version of Mole Island is shown below. The starting point is on N2 Island since the grams of N2 is given. We wish to determine the moles of NH3. The conversion pathway is shown with blue ovals and arrows. There are two arrows between the given quantity (grams of N2) and the desired quantity (moles of NH3). Thus, there are two conversion steps. Two conversion steps translates into the use of two conversion factors.
 
 
The setup of those conversion factors is shown below. The starting point is the given quantity - 42.0 g N2. The first conversion factor is used to convert from grams of N2 to moles of N2 (abbreviated mol N2). The second conversion factor is used to convert from moles of N2 to moles of NH3. Observe how the units cancel when identical units appear in the numerator (or the given quantity) and the denominator. The unit that does not cancel is the unit on your answer.
 
 
Once the conversion factors are set up so that the units cancel, the numbers can be inserted into the numerators and denominators. The first conversion factor is a molar mass conversion factor; it indicates the number of grams per 1 mole. So, the 1 goes with mol N2 and the 28.01 goes with grams N2. The second conversion factor is a mole ratio; it uses coefficients. Check the balanced chemical equation. The 1 in front of N2 (imagine a bit) goes with mol N2 and the 2 in front of NH3 goes with mol NH3. You’re now done with your unit cancellation set up.
 
 
The numerical answer to the problem is determined by taking the given number and multiplying it by all numbers in the numerator and dividing it by all the numbers in the denominator. You’re done.
 
 
When the factor label method is used in stoichiometry, there is no need to memorize when you should divide by the molar mass and when you should multiply by the molar mass. You don’t need to memorize any set of rules about when you should multiply or divide by the reactant coefficient and when you should multiply or divide by the product coefficient. There are too many things to memorize if you refuse to rely on the factor label method. When you become comfortable with its use, you will realize that the numbers will fall into the proper location of the solution without the use of a memorized rule. The units are the driver and do all the work for you. The numbers are in the back seat enjoying the ride.
 
 
 

Final Wisdom

Our last bit of wisdom: there’s an order that is important when it comes to solving stoichiometry problems. It’s a simple order – units first, numbers second, calculator last. All too often, students skip the units, pull out their calculator, and try to figure out what numbers to plug in to get the answer. This is a good recipe for failure and frustration. Stick to the plan: Units first. Numbers second. Calculator last.
 
Here is an effective strategy:
  1. Put your calculator far enough away that you can’t reach it.
  2. Use the factor label method to set up the solution without numbers; write out the conversion factors with units. Make sure the units cancel. Use the Mole Island graphic if you need to.
  3. Insert coefficients and molar mass values as the numbers in the numerator and denominator. The molar mass is defined as the grams per 1 mole of a substance; so, there will be a 1 with “mole” in the conversion factor.  We recommended that you memorize two things. This is the one step that you can use your memory for.
  4. Reach for your calculator and calculate the answer. This last step is the easiest and the least important. Errors seldom happen on step 4 if you have done steps 1, 2, and 3.
 
 
 
 

Before You Leave

  • Download our Study Card on Stoichiometric Conversions. Save it to a safe location and use it as a review tool. (Coming Soon.)
  • The Check Your Understanding section below include questions with answers and explanations. It provides a great chance to self-assess your understanding.

 
 
 

Check Your Understanding

Use the following questions to assess your understanding. Tap the Check Answer buttons when ready.
 
1. Consider the reaction:  N2(g)  +  3 H2(g)  →  2 NH3(g). Complete the following statements:

  1. For every one mole of N2 that react, ______ mole of H2 will react. 
    Check Answer

     
  2. For every one mole of NH3 that is produced, ______ mole of N2 will react. 
    Check Answer

     
  3. For every five mole of N2 that react, ______ mole of NH3 will be produced. 
    Check Answer

     
  4. For every five mole of N2 that react, ______ mole of H2 will react. 
    Check Answer

     
  5. For every 10 mole of NH3 that is produced, ______ mole of N2 will react. 
    Check Answer

     
  6. For every 10 mole of NH3 that is produced, ______ mole of H2 will react. 
    Check Answer

     
 
 
2. Consider the reaction:  N2(g)  +  3 H2(g)  →  2 NH3(g). For each of the given stoichiometry conversions, identify what information is required in the solution – molar mass values, coefficients from the equation, both of these.
  1. How many grams of N2 react if 3.89 moles of N2 react? 
    Check Answer

     
  2. How many grams of NH3 are produced if 3.89 moles of N2 react? 
    Check Answer

     
  3. How many moles of NH3 are produced if 24.6 moles of H2 react? 
    Check Answer

     
  4. How many grams of NH3 are produced if 3.10 grams of H2 react? 
    Check Answer

     

 
 
3. Review Examples 1 and 2 if necessary. Then describe the conversion pathway for the solution to the following problem:
Determine the moles of D produced from the reaction of 21.9 g of B.

Check Answer



 
4. Review Examples 1 and 2 if necessary. Then describe the conversion pathway for the solution to the following problem:
Determine the mass (in grams) of C produced from the reaction of 3.52 moles of A.
 
 
Check Answer

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