LEARN NC

2 Balancing equations using matrices

By Jennifer Elmo

Provided by Kenan Fellows Program.

Learning outcomes

Students will be able to:

  • Set up a system of equations to solve for the coefficients in a chemical reaction
  • Use a matrix to solve the system
  • Determine the coefficients required to make the chemical reaction balanced
  • Explain that the reaction must be balanced in order to be in compliance with the Law of Conservation of Mass

Teacher planning

Classroom time required

90 minutes

Materials needed

Students will need graphing calculators.

Student handouts

Balancing equations using matrices
Document by the author
Open as PDF (19 KB, 1 page; also available as Microsoft Word document)
Try it out
Document by the author
Open as PDF (34 KB, 1 page; also available as Microsoft Word document)

Activities

  1. Distribute the Balancing Equations Using Matrices handout to students. Go over the handout as a class.
  2. Tell students that eventually in their chemistry studies, they will have ample opportunity to balance equations. Balancing equations means writing chemical equations such that the amount of stuff they start with in the reaction equals the amount of stuff they end up with as a product. In other words, if they start baking bread with ten pounds of flour, they should end up with tend pounds of bread, unless some is lost on the floor or if some of it goes up in smoke! Remember this is the law of conservation of mass.
  3. Demonstrate the following example. Tell students they can form water by combing hydrogen gas (H2) and oxygen (O2) in the presence of electricity. The reaction looks like this:

    H2 + O2 —> H2O

    If they do some of the mass calculations they will find this:

    2 grams of hydrogen + 32 grams of oxygen = 18 grams of water

  4. Explain to students that this mass calculation shows that they started with 34 grams of stuff and ended up with 18 grams of stuff. Remind students they just lost 16 grams of stuff, and the law of conservation of mass says that doesn’t happen! Ask students where they think the 16 grams went.
  5. Tell students they just haven’t balanced the equation. They might have also noticed that there are two oxygens on the left and only one on the right. They’ll need to get things in the correct proportions for this reaction to be balanced. The balanced reaction looks like this:

    2 H2 + O2 —> 2 H2O

    Explain that the equation shows that two hydrogen molecules are necessary to combine with one oxygen molecule to form two new water molecules.

  6. Next, demonstrate the math for students.
    (2 × 2 grams of hydrogen) + 32 grams of oxygen = (2 x 18 grams of water)
    Reinforce the fact that now there are 36 grams of stuff on the left and 36 grams on the right. There are also now 4 hydrogens on the left, 4 hydrogens on the right, 2 oxygens on the left, and 2 on the right.

Assessment

Check students responses on the Try It Out worksheet.

Critical vocabulary

matrix
a rectangular array of mathematical elements that can be combined to form sums and products with similar arrays having an appropriate number of rows and columns
system of equations
simultaneous equations containing multiple variables
chemical reaction
a process that leads to the transformation of one set of chemical substances to another
balance
equality with respect to the net number of reduced symbolic quantities on each side of an equation
law of conservation of mass
a fundamental principle of classical physics that matter cannot be created or destroyed in an isolated system

Comments

This activity works best when the Algebra 2 teacher has students do it after they learn how to solve a matrix using their calculator. This allows students another method for balancing equations other than the method taught in chemistry. We used this activity before the students learned about chemical reactions.

North Carolina curriculum alignment

Mathematics (2004)

Grade 9–12 — Algebra 2

  • Goal 1: Number and Operations - The learner will perform operations with complex numbers, matrices, and polynomials.

Science (2005)

Grade 9–12 — Chemistry

  • Goal 5: The learner will develop an understanding of chemical reactions.
    • Objective 5.02: Evaluate the Law of Conservation of Matter.
      • Write and balance formulas and equations.
      • Write net ionic equations.