To balance the equation Fe(NO3)2 = Fe2O3 + NO2 + O2 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 lớn represent the unknown coefficients.
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a Fe(NO3)2 = b Fe2O3 + c NO2 + d O2
Step 2: Create a System of Equations
Create an equation for each element (Fe, N, O) where each term represents the number of atoms of the element in each reactant or product.
Fe: 1a = 2b + 0c + 0d N: 2a = 0b + 1c + 0d O: 6a = 3b + 2c + 2d
Step 3: Solve For All Variables
Use substitution, Gaussian elimination, or a calculator lớn solve for each variable.
- 1a - 2b = 0
- 2a - 1c = 0
- 6a - 3b - 2c - 2d = 0
Use your graphing calculator's rref() function (or an online rref calculator) lớn convert the following matrix into reduced row-echelon-form:
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[ 1 -2 0 0 0] [ 2 0 -1 0 0] [ 6 -3 -2 -2 0]
The resulting matrix can be used lớn determine the coefficients. In the case of a single solution, the last column of the matrix will contain the coefficients.
Simplify the result lớn get the lowest, whole integer values.
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- a = 4 (Fe(NO3)2)
- b = 2 (Fe2O3)
- c = 8 (NO2)
- d = 1 (O2)
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(NO3)2 = 2 Fe2O3 + 8 NO2 + O2
Since there is an equal number of each element in the reactants and products of 4Fe(NO3)2 = 2Fe2O3 + 8NO2 + O2, the equation is balanced.