As teachers of chemistry, we have all encountered students who are overwhelmed with the process of stoichiometry. When the process is broken down into smaller steps, the student can complete the calculations easily: changing grams to moles, changing moles of one chemical into moles of a different chemical, and then changing moles of the different chemical into the unit the problem asks for. However, students often have a difficult time performing the correct mathematical process at the right time. The following mechanism has enabled many such students to solve stoichiometric problems by creating a map that enables them to identify what unit and chemical they are starting with and the final unit and chemical that is being calculated.

Steps for the stoichiometry set-up method

1. Write a balanced chemical equation.
2. Write what is given and what needs to be calculated (X) on the equation.
   1. Data in moles go under the equation.
   2. Data in other units go above the equation.
3. Draw a path, using arrows, from the given amount to what needs to be calculated on your chemical equation.
   1. Separate vertical and horizontal arrows.
   2. Horizontal arrows must go under the equation.
4. Perform the appropriate calculations along the path.  

Putting the steps into practice

To show how this method is used to convert the given unit to the unit asked for in the problem, I will solve a typical stoichiometric problem using this mechanism. Here is a two-part sample problem:

            If a 2.8 g sample of mercuric oxide is decomposed by heating:

(a) How many grams of mercury will be produced?
(b) How many moles of oxygen will be produced?

Steps for solving sample question part (a):

1. Write the balanced chemical equation.
   

2. Write what is given and what needs to be calculated on the equation (moles go under the equation all other units go above the equation).

3. Draw a path from what is given to what needs to be calculated on your chemical equation (separating vertical and horizontal arrows and having horizontal arrows go under the equation).

4. Perform the calculations along the path. Here is where the arrows provide a map for the student to follow. Just like the animal mole lives underground, the unit of mole lives under the equation. So the first arrow directs the student to convert what they are given (the 2.8 g of mercuric oxide) to moles of mercuric oxide (under the HgO, which is where the moles live).

Corresponding calculation for the first arrow:

The second arrow goes from under HgO to under Hg. Therefore, it asks the student to convert moles of HgO to moles of Hg.

Corresponding calculation for the second arrow:

The last arrow goes from under Hg (from moles of Hg) to above Hg (to grams of Hg).

Corresponding calculation for the third arrow:

Steps for solving sample question part b

1. Balanced chemical equation.

2. The student would place X under the oxygen (because the student is asked to solve for moles of oxygen).

3. Draw a path from the given data to what needs to be calculated.

4. Perform the calculations along the path. The first arrow shows the student to go from above the HgO (grams of HgO ) to under the HgO (moles of HgO).

Corresponding calculation for the first arrow:

The second arrow shows the student to go from under the HgO (moles of HgO) to under the O₂
(moles of O₂).

Corresponding calculation for the second arrow:

Notice that the number of arrows corresponds to the number of conversion factors in the dimensional analysis.

Why it works

Most students know that moles live underground and find it easy to remember to place the moles unit under the chemical equation when drawing their map. Many students get frustrated in the middle of a stoichiometric problem when they must determine what calculation to perform next. Using this method, a student can point to where they are on their map and they can see where the next arrow leads them, giving the required guidance. If the arrow points under the given chemical formula, the student needs to convert to moles of that given chemical. If the arrow points above a given chemical formula, the student needs to convert to a unit other than moles that the problem requests.

I do not require all of my students to draw the map (the stronger students will not need it). However, for students who have a difficult time organizing the many steps of stoichiometry, using this method generates appropriate guidance. A common mistake that some students make while using this method is to draw a continuous arrow from the given information to the X rather than separate horizontal and vertical arrows. If a struggling student draws a continuous arrow, it makes it more difficult to identify the steps of the stoichiometric solution and how to use the map to guide them to the next conversion factor. However, if they use separate horizontal and vertical arrows, I can simply ask them how many multiplication signs are written in their attempted solution.

For example, if one multiplication sign is written, they have completed the first arrow on their map, so their next conversion will be shown by the second arrow on their map. If a continuous arrow is drawn, they might have trouble seeing where the first step ends and the second begins on their map. If two multiplication signs are written in their attempted solution, they have completed through the second arrow on their map and they need to look to where the third arrow ends to complete the next conversion factor.

This stoichiometric problem set-up method provides a road map for solving any type of stoichiometry problem. The only possible difference is in the type of molar conversion. When the vertical arrow goes through a material measured in grams, students should use the molar mass for the conversion. When the vertical arrow goes through a gas, they should use the ideal gas law or molar volume conversion. When the vertical arrow goes through a solution, the solution’s molarity will need to be used. When the vertical arrow goes through an electron, students need the amperage and Faraday’s constant. If the unit above the equation is particles (atoms, molecules, or formula units), to perform the molar conversion they use Avogadro’s number. Use the links below to access samples of each of these maps.

• Stoichiometry/mass method
  
• Gas laws method
  
• Molarity method
  
• Electrolysis method
  
• Summary of methods

All of us chemistry teachers work hard to help our students learn various molar conversions. This method gives the student visual cues for the number of calculations to complete as well as assigning the appropriate unit so that he or she can correctly use conversions while following the path shown by the arrows.