# cl2 + naoh

To balance the equation NaOH + Cl2 = NaCl + NaClO + 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 NaOH + b Cl2 = c NaCl + d NaClO + f H2O

### Step 2: Create a System of Equations

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

Na: 1a + 0b = 1c + 1d + 0f O: 1a + 0b = 0c + 1d + 1f H: 1a + 0b = 0c + 0d + 2f Cl: 0a + 2b = 1c + 1d + 0f

### Step 3: Solve For All Variables

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

• 1a - 1c - 1d = 0
• 1a - 1d - 1f = 0
• 1a - 2f = 0
• 2b - 1c - 1d = 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 -1 0 0] [ 1 0 0 -1 -1 0] [ 1 0 0 0 -2 0] [ 0 2 -1 -1 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 = 2 (NaOH)
• b = 1 (Cl2)
• c = 1 (NaCl)
• d = 1 (NaClO)
• f = 1 (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 NaOH + Cl2 = NaCl + NaClO + H2O

Reactants Products Na 2 2 ✔️ 2 2 ✔️ 2 2 ✔️ 2 2 ✔️

Since there is an equal number of each element in the reactants and products of 2NaOH + Cl2 = NaCl + NaClO + H2O, the equation is balanced.

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