LEARN NC

4 Determining the atomic mass of elements in a compound using matrices

By Jennifer Elmo

Provided by Kenan Fellows Program.

This lesson is designed to show students a practical application for matrices within the context of chemistry.

Learning outcomes

Students will be able to:

  • Set up a system of equations to solve for the mass of an unknown element in a compound
  • Use a matrix to solve the system
  • Determine the atomic mass of the unknown element
  • Identify the unknown element from the atomic mass and the periodic table

Teacher planning

Time required

90 minutes

Materials needed

graphing calculators

Student handouts

Determining atomic mass
Document by the author
Open as PDF (20 KB, 1 page; also available as Microsoft Word document)

Pre-activities

  • Students will need to solve system of equations using a matrix.
  • Students will need to know how to determine the mass of a compound given the chemical formula.

Activities

  1. Tell students that they will practice using a matrix to determine the identity of an unknown element by finding its atomic mass. Explain that the mass of a compound is determined by adding the masses of the elements in the compound together. For example, H2O has a mass of 18 because hydrogen has a mass of 1, since there are 2 hydrogens you multiply 2 × 1 and then add the mass of oxygen, which is 16.
  2. On the board or an overhead write, “What is the mass of N2O5?” Explain how to solve this problem as you write the answer.
    (2 x 14 [mass of nitrogen]) + (5 x 16 [mass of oxygen]) = 108
  3. Pass out the Determining Atomic Mass worksheets.
  4. Have students complete the matrices in class. Answer questions and provide guidance to any students struggling with the concept. As an alternative, the class can complete the worksheet as a group.
  5. Students will be solving the following matrices.
    6. Determine the atomic mass of element X. Then use your periodic table to identify it.
    X2O O: 16 X: ? Compound: 62
    XCl Cl: 35 X: ? Compound: 58
    X3N2 N: 14 X: ? Compound: 97
    Determine the atomic mass of element T. Then use your periodic table to identify it.
    T2O3 O: 16 T: ? Compound: 158
    TCl2 Cl: 35 T: ? Compound: 125
    TN N: 14 T: ? Compound: 69
    Determine the atomic mass of element X. Then use your periodic table to identify it.
    MgX Mg: 24 X: ? Compound: 40
    Fe2X3 Fe: 55 X: ? Compound: 158
    NX2 N: 14 X: ? Compound: 46

Critical vocabulary

matrix
a rectangular array of mathematical elements (as the coefficients of simultaneous linear equations) that can be combined to form sums and products with similar arrays having an appropriate number of rows and columns
system of equations
a collection of two or more equations with a same set of unknowns
formula mass
(of a compound) is the sum of the atomic masses of all the atoms (not merely each kind of atom) in the formula
atomic mass
the mass of an atom of a chemical element expressed in atomic mass units
chemical formula
expression of the composition or structure of a chemical compound

Formulas for molecules use chemical symbols with subscript numbers to show the number of atoms of each element.

Comments

This activity worked best when the Chemistry teacher has students complete the activity after they learn how to determine the mass of a compound given the chemical formula and the Algebra II teacher has taught them how to write systems of equations and solve them using matrices.

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 3: The learner will build an understanding of regularities in chemistry.
    • Objective 3.02: Apply the mole concept, Avogadro's number and conversion factors to chemical calculations.
      • Particles to moles.
      • Mass to moles.
      • Volume of a gas to moles.
      • Molarity of solutions.
      • Empirical and molecular formula.
      • Percent composition.

  • Common Core State Standards

    • Mathematics (2010)

      • High School: Number & Quantity

        • Vector & Matrix Quantities
          • NQ.VMQ.6(+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.

  • North Carolina Essential Standards

    • Science (2010)

      • Chemistry

        • Chm.1.2 Understand the bonding that occurs in simple compounds in terms of bond type, strength, and properties. Chm.1.2.1 Compare (qualitatively) the relative strengths of ionic, covalent, and metallic bonds. Chm.1.2.2 Infer the type of bond and chemical formula...
        • Chm.1.3 Understand the physical and chemical properties of atoms based on their position in the Periodic Table. Chm.1.3.1 Classify the components of a periodic table (period, group, metal, metalloid, nonmetal, transition). Chm.1.3.2 Infer the physical properties...