To balance the equation FeCl2 + Cl2 = FeCl3 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 FeCl2 + b Cl2 = c FeCl3
Step 2: Create a System of Equations
Create an equation for each element (Fe, Cl) where each term represents the number of atoms of the element in each reactant or product.
Fe: 1a + 0b = 1c Cl: 2a + 2b = 3c
Step 3: Solve For All Variables
Use substitution, Gaussian elimination, or a calculator lớn solve for each variable.
- 1a - 1c = 0
- 2a + 2b - 3c = 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 0 -1 0] [ 2 2 -3 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 = 2 (FeCl2)
- b = 1 (Cl2)
- c = 2 (FeCl3)
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.
2 FeCl2 + Cl2 = 2 FeCl3
Since there is an equal number of each element in the reactants and products of 2FeCl2 + Cl2 = 2FeCl3, the equation is balanced.