# fe2so43 hno3

To balance the equation Fe2(SO4)3 + HNO3 = Fe(NO3)3 + SO3 + 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 Fe2(SO4)3 + b HNO3 = c Fe(NO3)3 + d SO3 + f H2O

### Step 2: Create a System of Equations

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

```Fe:	2a	+	0b	=	1c	+	0d	+	0f
S:	3a	+	0b	=	0c	+	1d	+	0f
O:	12a	+	3b	=	9c	+	3d	+	1f
H:	0a	+	1b	=	0c	+	0d	+	2f
N:	0a	+	1b	=	3c	+	0d	+	0f

```

### Step 3: Solve For All Variables

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

• 2a - 1c = 0
• 3a - 1d = 0
• 12a + 3b - 9c - 3d - 1f = 0
• 1b - 2f = 0
• 1b - 3c = 0

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

```[ 2	 0	-1	 0	 0	0]
[ 3	 0	 0	-1	 0	0]
[ 12	 3	-9	-3	-1	0]
[ 0	 1	 0	 0	-2	0]
[ 0	 1	-3	 0	 0	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 = 1 (Fe2(SO4)3)
• b = 6 (HNO3)
• c = 2 (Fe(NO3)3)
• d = 3 (SO3)
• f = 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.

Fe2(SO4)3 + 6 HNO3 = 2 Fe(NO3)3 + 3 SO3 + 3 H2O

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Reactants Products Fe 2 2 ✔️ 3 3 ✔️ 30 30 ✔️ 6 6 ✔️ 6 6 ✔️

Since there is an equal number of each element in the reactants and products of Fe2(SO4)3 + 6HNO3 = 2Fe(NO3)3 + 3SO3 + 3H2O, 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 over of a chemical reaction as at the beginning. To be balanced, every element in Fe2(SO4)3 + HNO3 = Fe(NO3)3 + SO3 + 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
Fe2(SO4)3HNO3TotalFe(NO3)3SO3H2OTotal
Fe2211
S3311
O1231593113
H1122
N1133

### 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. Fe is not balanced. Add 1 molecule of Fe(NO3)3 vĩ đại the product (right-hand) side vĩ đại balance Iron:
Fe2(SO4)3 + HNO3 = 2Fe(NO3)3 + SO3 + H2O

ReactantsProducts
Fe22✔️
S31
O1522
H12
N16
2. S is not balanced. Add 2 molecules of SO3 vĩ đại the product (right-hand) side vĩ đại balance Sulfur:
Fe2(SO4)3 + HNO3 = 2Fe(NO3)3 + 3SO3 + H2O

ReactantsProducts
Fe22✔️
S33✔️
O1528
H12
N16
3. H is not balanced. Add 1 molecule of HNO3 vĩ đại the reactant (left-hand) side vĩ đại balance Hydrogen:
Fe2(SO4)3 + 2HNO3 = 2Fe(NO3)3 + 3SO3 + H2O

ReactantsProducts
Fe22✔️
S33✔️
O1828
H22✔️
N26
4. N is not balanced. Add 4 molecules of HNO3 vĩ đại the reactant (left-hand) side vĩ đại balance Nitrogen:
Fe2(SO4)3 + 6HNO3 = 2Fe(NO3)3 + 3SO3 + H2O

ReactantsProducts
Fe22✔️
S33✔️
O3028
H62
N66✔️
5. O is not balanced. Add 2 molecules of H2O vĩ đại the product (right-hand) side vĩ đại balance Oxygen:
Fe2(SO4)3 + 6HNO3 = 2Fe(NO3)3 + 3SO3 + 3H2O

ReactantsProducts
Fe22✔️
S33✔️
O3030✔️
H66✔️
N66✔️

### Step 3: Verify that the equation is balanced

Since there are an equal number of atoms of each element on both sides, the equation is balanced.

Fe2(SO4)3 + 6HNO3 = 2Fe(NO3)3 + 3SO3 + 3H2O