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 tát 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 tát 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 tát 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 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 = 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
| K | 4 | 4 | ✔️ |
|---|---|---|---|
| Mn | 4 | 4 | ✔️ |
| O | 40 | 40 | ✔️ |
| H | 12 | 12 | ✔️ |
| S | 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 kết thúc 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 tát balance one element at a time until both sides are equal and the chemical equation is balanced.
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Step 1: Count the number of each element on the left and right hand sides
| Reactants (Left Hand Side) | Products (Right Hand Side) | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Reactants | Products | ||||||||
| KMnO4 | H2SO4 | Total | K2SO4 | MnSO4 | H2O | O2 | Total | ||
| K | 1 | 1 | 2 | 2 | ❌ | ||||
| Mn | 1 | 1 | 1 | 1 | ✔️ | ||||
| O | 4 | 4 | 8 | 4 | 4 | 1 | 2 | 11 | ❌ |
| H | 2 | 2 | 2 | 2 | ✔️ | ||||
| S | 1 | 1 | 1 | 1 | 2 | ❌ | |||
Step 2: Multiply coefficients for compounds to tát balance out each element
For each element that is not equal, try to tát balance it by adding more of it to tát the side with less. Sometimes there may be multiple compounds with that element on one side, so sánh you'll need to tát use your best judgement and be prepared to tát go back and try the other options.
K is not balanced. Add 1 molecule of KMnO4 to tát the reactant (left-hand) side to tát balance Potassium:
2KMnO4 + H2SO4 = K2SO4 + MnSO4 + H2O + O2Reactants Products K 2 2 ✔️ Mn 2 1 ❌ O 12 11 ❌ H 2 2 ✔️ S 1 2 ❌ Mn is not balanced. Add 1 molecule of MnSO4 to tát the product (right-hand) side to tát balance Manganese:
2KMnO4 + H2SO4 = K2SO4 + 2MnSO4 + H2O + O2Reactants Products K 2 2 ✔️ Mn 2 2 ✔️ O 12 15 ❌ H 2 2 ✔️ S 1 3 ❌ S is not balanced. Add 2 molecules of H2SO4 to tát the reactant (left-hand) side to tát balance Sulfur:
2KMnO4 + 3H2SO4 = K2SO4 + 2MnSO4 + H2O + O2Reactants Products K 2 2 ✔️ Mn 2 2 ✔️ O 20 15 ❌ H 6 2 ❌ S 3 3 ✔️ O is not balanced. Add 1 molecule of K2SO4 to tát the product (right-hand) side to tát balance Oxygen:
2KMnO4 + 3H2SO4 = 2K2SO4 + 2MnSO4 + H2O + O2Reactants Products K 2 4 ❌ Mn 2 2 ✔️ O 20 19 ❌ H 6 2 ❌ S 3 4 ❌ K is not balanced. Add 2 molecules of KMnO4 to tát the reactant (left-hand) side to tát balance Potassium:
4KMnO4 + 3H2SO4 = 2K2SO4 + 2MnSO4 + H2O + O2Reactants Products K 4 4 ✔️ Mn 4 2 ❌ O 28 19 ❌ H 6 2 ❌ S 3 4 ❌ Mn is not balanced. Add 2 molecules of MnSO4 to tát the product (right-hand) side to tát balance Manganese:
4KMnO4 + 3H2SO4 = 2K2SO4 + 4MnSO4 + H2O + O2Reactants Products K 4 4 ✔️ Mn 4 4 ✔️ O 28 27 ❌ H 6 2 ❌ S 3 6 ❌ O is not balanced. Add 1 molecule of H2O to tát the product (right-hand) side to tát balance Oxygen:
4KMnO4 + 3H2SO4 = 2K2SO4 + 4MnSO4 + 2H2O + O2Reactants Products K 4 4 ✔️ Mn 4 4 ✔️ O 28 28 ✔️ H 6 4 ❌ S 3 6 ❌ H is not balanced. Add 1 molecule of H2O to tát the product (right-hand) side to tát balance Hydrogen:
4KMnO4 + 3H2SO4 = 2K2SO4 + 4MnSO4 + 3H2O + O2Xem thêm: cá bạc má có chứa thủy ngân không
Reactants Products K 4 4 ✔️ Mn 4 4 ✔️ O 28 29 ❌ H 6 6 ✔️ S 3 6 ❌
We could not determine all the steps needed to tát balance the equation using trial and error. This may mean it requires too many steps and the chemical equation is too complex to tát 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 tát attempt to tát guess the next steps, the final element counts in the balanced equation should be:
4KMnO4 + 6H2SO4 = 2K2SO4 + 4MnSO4 + 6H2O + 5O2
| Reactants | Products | ||
|---|---|---|---|
| K | 4 | 4 | ✔️ |
| Mn | 4 | 4 | ✔️ |
| O | 40 | 40 | ✔️ |
| H | 12 | 12 | ✔️ |
| S | 6 | 6 | ✔️ |
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