# fe + cu(no3)2

To balance the equation Fe + CuNO3 = Cu + Fe(NO3)2 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.

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### 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.

a Fe + b CuNO3 = c Cu + d Fe(NO3)2

### Step 2: Create a System of Equations

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

Fe: 1a + 0b = 0c + 1d Cu: 0a + 1b = 1c + 0d N: 0a + 1b = 0c + 2d O: 0a + 3b = 0c + 6d

### Step 3: Solve For All Variables

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

• 1a - 1d = 0
• 1b - 1c = 0
• 1b - 2d = 0
• 3b - 6d = 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: p+h2so4 đặc

[ 1 0 0 -1 0] [ 0 1 -1 0 0] [ 0 1 0 -2 0] [ 0 3 0 -6 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 (Fe)
• b = 2 (CuNO3)
• c = 2 (Cu)
• d = 1 (Fe(NO3)2)

### 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.

Fe + 2 CuNO3 = 2 Cu + Fe(NO3)2

Reactants Products Fe 1 1 ✔️ 2 2 ✔️ 2 2 ✔️ 6 6 ✔️

Since there is an equal number of each element in the reactants and products of Fe + 2CuNO3 = 2Cu + Fe(NO3)2, the equation is balanced.

Xem thêm: fes2 ra fe2o3