To balance the given chemical equation:
[tex]\[
\text{KNO}_3 \rightarrow \text{KNO}_2 + \text{O}_2
\][/tex]
we need to ensure that we have the same number of each type of atom on both sides of the equation. Let's identify the number of atoms of each element in the unbalanced equation:
1. Potassium (K):
- On the left side: 1 atom in KNO[tex]\(_3\)[/tex]
- On the right side: 1 atom in KNO[tex]\(_2\)[/tex]
2. Nitrogen (N):
- On the left side: 1 atom in KNO[tex]\(_3\)[/tex]
- On the right side: 1 atom in KNO[tex]\(_2\)[/tex]
3. Oxygen (O):
- On the left side: 3 atoms in KNO[tex]\(_3\)[/tex]
- On the right side: 2 atoms in KNO[tex]\(_2\)[/tex] + 2 atoms in O[tex]\(_2\)[/tex] = 4 atoms
Now, let's balance the equation step-by-step.
1. We balance the potassium (K) and nitrogen (N) first, as they are already balanced:
[tex]\[
\text{KNO}_3 \rightarrow \text{KNO}_2 + \text{O}_2
\][/tex]
2. Next, we need to balance the oxygen atoms. Currently, we have:
- 3 oxygen atoms on the left
- 4 oxygen atoms on the right (2 from KNO[tex]\(_2\)[/tex] and 2 from O[tex]\(_2\)[/tex])
To balance the oxygen atoms, we notice that if we place a coefficient of 2 in front of KNO[tex]\(_3\)[/tex] and KNO[tex]\(_2\)[/tex], the equation looks like this:
[tex]\[
2 \text{KNO}_3 \rightarrow 2 \text{KNO}_2 + \text{O}_2
\][/tex]
Now, let's verify the number of atoms:
- Potassium (K):
- Left side: 2 atoms in 2 KNO[tex]\(_3\)[/tex]
- Right side: 2 atoms in 2 KNO[tex]\(_2\)[/tex]
- Nitrogen (N):
- Left side: 2 atoms in 2 KNO[tex]\(_3\)[/tex]
- Right side: 2 atoms in 2 KNO[tex]\(_2\)[/tex]
- Oxygen (O):
- Left side: 3 x 2 = 6 atoms in 2 KNO[tex]\(_3\)[/tex]
- Right side: 2 x 2 = 4 atoms in 2 KNO[tex]\(_2\)[/tex] + 2 atoms in O[tex]\(_2\)[/tex] = 4 + 2 = 6 atoms
All the atoms are now balanced. Therefore, the balanced chemical equation is:
[tex]\[
2 \text{KNO}_3 \rightarrow 2 \text{KNO}_2 + \text{O}_2
\][/tex]
Thus, the coefficients for the reaction are:
[tex]\[
2 \text{KNO}_3 \rightarrow 2 \text{KNO}_2 + 1 \text{O}_2
\][/tex]
So, the answer is:
[tex]\[
2, \quad 2, \quad 1
\][/tex]
