# fe oh 3 + hcl

To balance the equation Fe(OH)3 + HCl = FeCl3 + 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.

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### 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.

a Fe(OH)3 + b HCl = c FeCl3 + d H2O

### Step 2: Create a System of Equations

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

Fe: 1a + 0b = 1c + 0d O: 3a + 0b = 0c + 1d H: 3a + 1b = 0c + 2d Cl: 0a + 1b = 3c + 0d

### Step 3: Solve For All Variables

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

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

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

Xem thêm: fe2o3

[ 1 0 -1 0 0] [ 3 0 0 -1 0] [ 3 1 0 -2 0] [ 0 1 -3 0 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.

• a = 1 (Fe(OH)3)
• b = 3 (HCl)
• c = 1 (FeCl3)
• d = 3 (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.

Fe(OH)3 + 3 HCl = FeCl3 + 3 H2O

Reactants Products Fe 1 1 ✔️ 3 3 ✔️ 6 6 ✔️ 3 3 ✔️

Since there is an equal number of each element in the reactants and products of Fe(OH)3 + 3HCl = FeCl3 + 3H2O, the equation is balanced.