Certainly! Let's go through this step by step.
### Understanding the Chemical Reaction:
We have the chemical equation:
[tex]\[
3 \text{H}_2 \text{O}_2 \rightarrow 2 \text{H}_2\text{O} + \text{O}_2
\][/tex]
This is a decomposition reaction, where hydrogen peroxide (H_2O_2) breaks down into water (H_2O) and oxygen gas (O_2).
### Balancing the Equation:
#### Step 1: Write the Unbalanced Equation
[tex]\[
\text{H}_2 \text{O}_2 \rightarrow \text{H}_2 \text{O} + \text{O}_2
\][/tex]
#### Step 2: Count the Number of Atoms of Each Element on Both Sides
- Reactants (Left Side):
- H: 2
- O: 2
- Products (Right Side):
- H: 2 (in H_2O)
- O: 1 (in H_2O) + 2 (in O_2) = 3
We can see that the number of atoms of oxygen is not balanced.
#### Step 3: Balance the Oxygen Atoms
Since there are more oxygen atoms on the products side, we will try to equalize the numbers by adjusting the coefficients.
To balance the equation, we realize that balancing oxygen is a bit tricky since O_2 is diatomic. The coefficient for water (H_2O) is already balanced in terms of hydrogen.
If we set the coefficient for H_2O to 2, we will get:
[tex]\[
2 \text{H}_2 \text{O}
\][/tex]
That gives us:
- Hydrogen atoms: 2 2 = 4
- Oxygen atoms: 2 1 = 2
Increasing the coefficient of H_2O on the product side to 2, we need to balance with H_2O_2 accordingly.
Set the coefficient for H_2O_2 to 3:
[tex]\[
3 \text{H}_2 \text{O}_2 \rightarrow 2 \text{H}_2 \text{O} + \text{O}_2
\][/tex]
This gives us:
- On the reactants side: 3 H_2O_2 = 3 (2 H atoms + 2 O atoms) = 6 H atoms, 6 O atoms
- On the products side: 2 H_2O = 2 (2 H atoms + 1 O atoms) = 4 H atoms, 2 O atoms and 1 O_2 molecule = 2 O atoms = 6 atoms total
Now, both sides have:
- Hydrogen atoms = 4 H on both sides
- Oxygen atoms = 6 O on both sides (2 in water and 4 in oxygen gas brings us to 6)
#### Step 4: Rewrite the Balanced Equation:
[tex]\[
3 \text{H}_2 \text{O}_2 \rightarrow 2 \text{H}_2 \text{O} + \text{O}_2
\][/tex]
### Conclusion:
Following the steps for balancing, we find that the correct balanced equation of the chemical reaction is:
[tex]\[
3 \text{H}_2 \text{O}_2 \rightarrow 2 \text{H}_2 \text{O} + \text{O}_2
\][/tex]
This represents the balanced equation for the decomposition of hydrogen peroxide to water and oxygen gas.
