fexoy + h2so4 = fe2(so4)3 + so2 + h2o

To balance the equation Fe + H2SO4 = Fe2(SO4)3 + SO2 + H2O 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 đồ sộ represent the unknown coefficients.

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a Fe + b H2SO4 = c Fe2(SO4)3 + d SO2 + f H2O

Step 2: Create a System of Equations

Create an equation for each element (Fe, H, S, O) where each term represents the number of atoms of the element in each reactant or product.

Fe:	1a	+	0b	=	2c	+	0d	+	0f
H:	0a	+	2b	=	0c	+	0d	+	2f
S:	0a	+	1b	=	3c	+	1d	+	0f
O:	0a	+	4b	=	12c	+	2d	+	1f

Step 3: Solve For All Variables

Use substitution, Gaussian elimination, or a calculator đồ sộ solve for each variable.

  • 1a - 2c = 0
  • 2b - 2f = 0
  • 1b - 3c - 1d = 0
  • 4b - 12c - 2d - 1f = 0

Use your graphing calculator's rref() function (or an online rref calculator) đồ sộ convert the following matrix into reduced row-echelon-form:

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[ 1	 0	-2	 0	 0	0]
[ 0	 2	 0	 0	-2	0]
[ 0	 1	-3	-1	 0	0]
[ 0	 4	-12	-2	-1	0]

The resulting matrix can be used đồ sộ determine the coefficients. In the case of a single solution, the last column of the matrix will contain the coefficients.

Simplify the result đồ sộ get the lowest, whole integer values.

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  • a = 2 (Fe)
  • b = 6 (H2SO4)
  • c = 1 (Fe2(SO4)3)
  • d = 3 (SO2)
  • f = 6 (H2O)

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 Fe + 6 H2SO4 = Fe2(SO4)3 + 3 SO2 + 6 H2O

Reactants Products
Fe22✔️
H1212✔️
S66✔️
O2424✔️

Since there is an equal number of each element in the reactants and products of 2Fe + 6H2SO4 = Fe2(SO4)3 + 3SO2 + 6H2O, the equation is balanced.