# fe2o3 ra fe

To balance the equation Fe2O3 + CO = Fe + CO2 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 vĩ đại represent the unknown coefficients.

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a Fe2O3 + b CO = c Fe + d CO2

### Step 2: Create a System of Equations

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

```Fe:	2a	+	0b	=	1c	+	0d
O:	3a	+	1b	=	0c	+	2d
C:	0a	+	1b	=	0c	+	1d

```

### Step 3: Solve For All Variables

Use substitution, Gaussian elimination, or a calculator vĩ đại solve for each variable.

• 2a - 1c = 0
• 3a + 1b - 2d = 0
• 1b - 1d = 0

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

Xem thêm: baso4 hcl

```[ 2	 0	-1	 0	0]
[ 3	 1	 0	-2	0]
[ 0	 1	 0	-1	0]
```

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

Simplify the result vĩ đại get the lowest, whole integer values.

• a = 1 (Fe2O3)
• b = 3 (CO)
• c = 2 (Fe)
• d = 3 (CO2)

### 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.

Fe2O3 + 3 CO = 2 Fe + 3 CO2

Reactants Products Fe 2 2 ✔️ 6 6 ✔️ 3 3 ✔️

Since there is an equal number of each element in the reactants and products of Fe2O3 + 3CO = 2Fe + 3CO2, the equation is balanced.