# fe(no3)2 + hno3

To balance the equation Fe(NO3)2 + HNO3 = Fe(NO3)3 + NO + 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.

### 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.

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a Fe(NO3)2 + b HNO3 = c Fe(NO3)3 + d NO + f H2O

### Step 2: Create a System of Equations

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

```Fe:	1a	+	0b	=	1c	+	0d	+	0f
N:	2a	+	1b	=	3c	+	1d	+	0f
O:	6a	+	3b	=	9c	+	1d	+	1f
H:	0a	+	1b	=	0c	+	0d	+	2f

```

### Step 3: Solve For All Variables

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

• 1a - 1c = 0
• 2a + 1b - 3c - 1d = 0
• 6a + 3b - 9c - 1d - 1f = 0
• 1b - 2f = 0

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

```[ 1	 0	-1	 0	 0	0]
[ 2	 1	-3	-1	 0	0]
[ 6	 3	-9	-1	-1	0]
[ 0	 1	 0	 0	-2	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 = 3 (Fe(NO3)2)
• b = 4 (HNO3)
• c = 3 (Fe(NO3)3)
• d = 1 (NO)
• f = 2 (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.

3 Fe(NO3)2 + 4 HNO3 = 3 Fe(NO3)3 + NO + 2 H2O

Reactants Products Fe 3 3 ✔️ 10 10 ✔️ 30 30 ✔️ 4 4 ✔️

Since there is an equal number of each element in the reactants and products of 3Fe(NO3)2 + 4HNO3 = 3Fe(NO3)3 + NO + 2H2O, the equation is balanced.

The law of conservation of mass states that matter cannot be created or destroyed, which means there must be the same number atoms at the kết thúc of a chemical reaction as at the beginning. To be balanced, every element in Fe(NO3)2 + HNO3 = Fe(NO3)3 + NO + H2O must have the same number of atoms on each side of the equation. When using the inspection method (also known as the trial-and-error method), this principle is used vĩ đại balance one element at a time until both sides are equal and the chemical equation is balanced.

### Step 1: Count the number of each element on the left and right hand sides

Reactants (Left Hand Side)Products (Right Hand Side)
ReactantsProducts
Fe(NO3)2HNO3TotalFe(NO3)3NOH2OTotal
Fe1111✔️
N213314
O63991111
H1122

### Step 2: Multiply coefficients for compounds vĩ đại balance out each element

For each element that is not equal, try vĩ đại balance it by adding more of it vĩ đại the side with less. Sometimes there may be multiple compounds with that element on one side, so sánh you'll need vĩ đại use your best judgement and be prepared vĩ đại go back and try the other options.

1. N is not balanced. Add 1 molecule of HNO3 vĩ đại the reactant (left-hand) side vĩ đại balance Nitrogen:
Fe(NO3)2 + 2HNO3 = Fe(NO3)3 + NO + H2O

ReactantsProducts
Fe11✔️
N44✔️
O1211
H22✔️
2. O is not balanced. Add 1 molecule of H2O vĩ đại the product (right-hand) side vĩ đại balance Oxygen:
Fe(NO3)2 + 2HNO3 = Fe(NO3)3 + NO + 2H2O

ReactantsProducts
Fe11✔️
N44✔️
O1212✔️
H24
3. H is not balanced. Add 2 molecules of HNO3 vĩ đại the reactant (left-hand) side vĩ đại balance Hydrogen:
Fe(NO3)2 + 4HNO3 = Fe(NO3)3 + NO + 2H2O

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ReactantsProducts
Fe11✔️
N64
O1812
H44✔️

We could not determine all the steps needed vĩ đại balance the equation using trial and error. This may mean it requires too many steps and the chemical equation is too complex vĩ đại use this method, or that the equation is invalid (e.g. has 0 or non-integer coefficients). The algebraic method is likely better suited for balancing this equation.

If you would lượt thích vĩ đại attempt vĩ đại guess the next steps, the final element counts in the balanced equation should be:

3Fe(NO3)2 + 4HNO3 = 3Fe(NO3)3 + NO + 2H2O

ReactantsProducts
Fe33✔️
N1010✔️
O3030✔️
H44✔️