# kmno4 h2so4

To balance the equation KMnO4 + H2SO4 = K2SO4 + MnSO4 + H2O + O2 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 to tướng represent the unknown coefficients.

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a KMnO4 + b H2SO4 = c K2SO4 + d MnSO4 + f H2O + g O2

### Step 2: Create a System of Equations

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

```K:	1a	+	0b	=	2c	+	0d	+	0f	+	0g
Mn:	1a	+	0b	=	0c	+	1d	+	0f	+	0g
O:	4a	+	4b	=	4c	+	4d	+	1f	+	2g
H:	0a	+	2b	=	0c	+	0d	+	2f	+	0g
S:	0a	+	1b	=	1c	+	1d	+	0f	+	0g

```

### Step 3: Solve For All Variables

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

• 1a - 2c = 0
• 1a - 1d = 0
• 4a + 4b - 4c - 4d - 1f - 2g = 0
• 2b - 2f = 0
• 1b - 1c - 1d = 0

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

```[ 1	 0	-2	 0	 0	 0	0]
[ 1	 0	 0	-1	 0	 0	0]
[ 4	 4	-4	-4	-1	-2	0]
[ 0	 2	 0	 0	-2	 0	0]
[ 0	 1	-1	-1	 0	 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 = 4 (KMnO4)
• b = 6 (H2SO4)
• c = 2 (K2SO4)
• d = 4 (MnSO4)
• f = 6 (H2O)
• g = 5 (O2)

### 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.

4 KMnO4 + 6 H2SO4 = 2 K2SO4 + 4 MnSO4 + 6 H2O + 5 O2

Reactants Products K 4 4 ✔️ 4 4 ✔️ 40 40 ✔️ 12 12 ✔️ 6 6 ✔️

Since there is an equal number of each element in the reactants and products of 4KMnO4 + 6H2SO4 = 2K2SO4 + 4MnSO4 + 6H2O + 5O2, 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 KMnO4 + H2SO4 = K2SO4 + MnSO4 + H2O + O2 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 to tướng 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
KMnO4H2SO4TotalK2SO4MnSO4H2OO2Total
K1122
Mn1111✔️
O448441211
H2222✔️
S11112

### Step 2: Multiply coefficients for compounds to tướng balance out each element

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

1. K is not balanced. Add 1 molecule of KMnO4 to tướng the reactant (left-hand) side to tướng balance Potassium:
2KMnO4 + H2SO4 = K2SO4 + MnSO4 + H2O + O2

ReactantsProducts
K22✔️
Mn21
O1211
H22✔️
S12
2. Mn is not balanced. Add 1 molecule of MnSO4 to tướng the product (right-hand) side to tướng balance Manganese:
2KMnO4 + H2SO4 = K2SO4 + 2MnSO4 + H2O + O2

ReactantsProducts
K22✔️
Mn22✔️
O1215
H22✔️
S13
3. S is not balanced. Add 2 molecules of H2SO4 to tướng the reactant (left-hand) side to tướng balance Sulfur:
2KMnO4 + 3H2SO4 = K2SO4 + 2MnSO4 + H2O + O2

ReactantsProducts
K22✔️
Mn22✔️
O2015
H62
S33✔️
4. O is not balanced. Add 1 molecule of K2SO4 to tướng the product (right-hand) side to tướng balance Oxygen:
2KMnO4 + 3H2SO4 = 2K2SO4 + 2MnSO4 + H2O + O2

ReactantsProducts
K24
Mn22✔️
O2019
H62
S34
5. K is not balanced. Add 2 molecules of KMnO4 to tướng the reactant (left-hand) side to tướng balance Potassium:
4KMnO4 + 3H2SO4 = 2K2SO4 + 2MnSO4 + H2O + O2

ReactantsProducts
K44✔️
Mn42
O2819
H62
S34
6. Mn is not balanced. Add 2 molecules of MnSO4 to tướng the product (right-hand) side to tướng balance Manganese:
4KMnO4 + 3H2SO4 = 2K2SO4 + 4MnSO4 + H2O + O2

ReactantsProducts
K44✔️
Mn44✔️
O2827
H62
S36
7. O is not balanced. Add 1 molecule of H2O to tướng the product (right-hand) side to tướng balance Oxygen:
4KMnO4 + 3H2SO4 = 2K2SO4 + 4MnSO4 + 2H2O + O2

ReactantsProducts
K44✔️
Mn44✔️
O2828✔️
H64
S36
8. H is not balanced. Add 1 molecule of H2O to tướng the product (right-hand) side to tướng balance Hydrogen:
4KMnO4 + 3H2SO4 = 2K2SO4 + 4MnSO4 + 3H2O + O2

Xem thêm: cho tam giác abc có

ReactantsProducts
K44✔️
Mn44✔️
O2829
H66✔️
S36

We could not determine all the steps needed to tướng balance the equation using trial and error. This may mean it requires too many steps and the chemical equation is too complex to tướng 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 to tướng attempt to tướng guess the next steps, the final element counts in the balanced equation should be:

4KMnO4 + 6H2SO4 = 2K2SO4 + 4MnSO4 + 6H2O + 5O2

ReactantsProducts
K44✔️
Mn44✔️
O4040✔️
H1212✔️
S66✔️