To balance the equation CH3COOC6H5 + NaOH = C6H5ONa + CH3COONa + 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 to tát represent the unknown coefficients.

a CH_{3}COOC_{6}H_{5} + b NaOH = c C_{6}H_{5}ONa + d CH_{3}COONa + f H_{2}O

### Step 2: Create a System of Equations

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

**C**: 8a + 0b = 6c + 2d + 0f
**H**: 8a + 1b = 5c + 3d + 2f
**O**: 2a + 1b = 1c + 2d + 1f
**Na**: 0a + 1b = 1c + 1d + 0f

### Step 3: Solve For All Variables

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

- 8a - 6c - 2d = 0
- 8a + 1b - 5c - 3d - 2f = 0
- 2a + 1b - 1c - 2d - 1f = 0
- 1b - 1c - 1d = 0

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

Xem thêm: feso4 + naoh

[ 8 0 -6 -2 0 0] [ 8 1 -5 -3 -2 0] [ 2 1 -1 -2 -1 0] [ 0 1 -1 -1 0 0]

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

Simplify the result to tát get the lowest, whole integer values.

- a = 1 (CH3COOC6H5)
- b = 2 (NaOH)
- c = 1 (C6H5ONa)
- d = 1 (CH3COONa)
- 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.

CH_{3}COOC_{6}H_{5} + 2 NaOH = C_{6}H_{5}ONa + CH_{3}COONa + H_{2}O

C | 8 | 8 | ✔️ |
---|---|---|---|

H | 10 | 10 | ✔️ |

O | 4 | 4 | ✔️ |

Na | 2 | 2 | ✔️ |

Since there is an equal number of each element in the reactants and products of CH3COOC6H5 + 2NaOH = C6H5ONa + CH3COONa + H2O, the equation is balanced.

Xem thêm: ba(oh)2 + na2co3

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