To balance the equation C6H5OH + HNO3 = C6H2(NO2)3OH + 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 tướng represent the unknown coefficients.

a C_{6}H_{5}OH + b HNO_{3} = c C_{6}H_{2}(NO_{2})_{3}OH + d H_{2}O

### Step 2: Create a System of Equations

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

**C**: 6a + 0b = 6c + 0d
**H**: 6a + 1b = 3c + 2d
**O**: 1a + 3b = 7c + 1d
**N**: 0a + 1b = 3c + 0d

### Step 3: Solve For All Variables

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

- 6a - 6c = 0
- 6a + 1b - 3c - 2d = 0
- 1a + 3b - 7c - 1d = 0
- 1b - 3c = 0

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

Xem thêm: ancol etylic ra etilen

[ 6 0 -6 0 0] [ 6 1 -3 -2 0] [ 1 3 -7 -1 0] [ 0 1 -3 0 0]

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

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

- a = 1 (C6H5OH)
- b = 3 (HNO3)
- c = 1 (C6H2(NO2)3OH)
- 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.

C_{6}H_{5}OH + 3 HNO_{3} = C_{6}H_{2}(NO_{2})_{3}OH + 3 H_{2}O

C | 6 | 6 | ✔️ |
---|---|---|---|

H | 9 | 9 | ✔️ |

O | 10 | 10 | ✔️ |

N | 3 | 3 | ✔️ |

Since there is an equal number of each element in the reactants and products of C6H5OH + 3HNO3 = C6H2(NO2)3OH + 3H2O, the equation is balanced.

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