Balancing Chemical Equations

Getting Started with Algebra 2Problem 1 – Balancing Al O2 Al2O3Problem 1 walks students through how to balance the chemical equationAl O Al O . There are no actions to be performed by students for the first2 2 3three steps; they should just be sure they read and understand each step.Step 1: Assign a variable coefficient to each of thethree terms in the equation: a Al b O2 c Al2O3Step 2: Translate the chemical equation into amathematical system of equations, as shownin the screenshot to the right. There shouldbe an equation for each element in thechemical equation. If needed, remindstudents that the coefficients in these twoequations are derived from the number ofatoms of the element in each chemicalcompound.Step 3: Write the system of equations as a matrixequation. For students who are comfortablewith using matrices to solve equations, thismatrix equation should look familiar, exceptfor the appearance of the scalar, c. Tellstudents that a value will be chosen for c inthe next step.Step 4: Page 1.6 explains that the absolute value ofthe determinant of the coefficient matrixshould be used as the value of c.Using the determinant ensures that the values found for a and b inthe next step are integers. Ask students why it makes sense to use theabsolute value of the determinant (c must be a positive integer; itrepresents a number of molecules.)Students may recall that the determinant of aa b2×2 matrix A is given byc ddet( A)ad bc , but students can use themathematical capabilities of the Notesapplication to evaluate the determinant.Instruct them to hold down the SHIFT key(g) while they arrow over the expression toselect it, and choose Evaluate Selection fromthe Actions menu. Pressing · will return thevalue of c; here, 2.©2008 Texas Instruments Incorporated Page 2