To balance the equation Fe(OH)2 + O2 + H2O = Fe(OH)3 using the algebraic method step-by-step, you must have experience solving systems of linear equations. The most common methods are substitution/elimination and linear algebra, but any similar method will work.
Step 1: Label Each Compound With a Variable
Label each compound (reactant or product) in the equation with a variable to lớn represent the unknown coefficients.
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a Fe(OH)2 + b O2 + c H2O = d Fe(OH)3
Step 2: Create a System of Equations
Create an equation for each element (Fe, O, H) where each term represents the number of atoms of the element in each reactant or product.
Fe: 1a + 0b + 0c = 1d O: 2a + 2b + 1c = 3d H: 2a + 0b + 2c = 3d
Step 3: Solve For All Variables
Use substitution, Gaussian elimination, or a calculator to lớn solve for each variable.
- 1a - 1d = 0
- 2a + 2b + 1c - 3d = 0
- 2a + 2c - 3d = 0
Use your graphing calculator's rref() function (or an online rref calculator) to lớn convert the following matrix into reduced row-echelon-form:
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[ 1 0 0 -1 0] [ 2 2 1 -3 0] [ 2 0 2 -3 0]
The resulting matrix can be used to lớn determine the coefficients. In the case of a single solution, the last column of the matrix will contain the coefficients.
Simplify the result to lớn get the lowest, whole integer values.
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- a = 4 (Fe(OH)2)
- b = 1 (O2)
- c = 2 (H2O)
- d = 4 (Fe(OH)3)
Step 4: Substitute Coefficients and Verify Result
Count the number of atoms of each element on each side of the equation and verify that all elements and electrons (if there are charges/ions) are balanced.
4 Fe(OH)2 + O2 + 2 H2O = 4 Fe(OH)3
| Fe | 4 | 4 | ✔️ |
|---|---|---|---|
| O | 12 | 12 | ✔️ |
| H | 12 | 12 | ✔️ |
Since there is an equal number of each element in the reactants and products of 4Fe(OH)2 + O2 + 2H2O = 4Fe(OH)3, the equation is balanced.
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