To balance the given chemical equation [tex]\( \text{CO} \rightarrow \text{C} + \text{O}_2 \)[/tex], we need to follow these steps:
1. Write the Unbalanced Equation:
[tex]\[
\text{CO} \rightarrow \text{C} + \text{O}_2
\][/tex]
2. Count the Number of Atoms of Each Element on Both Sides:
- On the reactant side:
- Carbon (C): 1
- Oxygen (O): 1
- On the product side:
- Carbon (C): 1
- Oxygen (O): 2 (since [tex]\( \text{O}_2 \)[/tex])
3. Determine the Necessary Coefficients to Balance Each Element:
- We observe that oxygen is not balanced because there is 1 oxygen atom on the reactant side and 2 oxygen atoms on the product side.
- For simplicity, start by balancing the oxygen atoms.
- If we have 2 molecules of CO, then we get 2 oxygen atoms on the reactant side (2 × O in CO).
4. Adjust the Coefficients to Balance the Equation:
- Changing the coefficient of CO to 2, we write:
[tex]\[
2\text{CO} \rightarrow \text{C} + \text{O}_2
\][/tex]
5. Update the Atom Count:
- On the reactant side now:
- Carbon (C): 2 (since [tex]\( 2 \times \text{CO} \)[/tex])
- Oxygen (O): 2 (since [tex]\( 2 \times \text{CO} \)[/tex])
- On the product side:
- Carbon (C): 1
- Oxygen (O): 2
6. Finally, Balance Carbon Atoms:
- We need 2 carbon atoms on the product side to match the 2 carbon atoms from the reactant side. Adjust the coefficient of C to 2:
[tex]\[
2 \text{CO} \rightarrow 2 \text{C} + \text{O}_2
\][/tex]
7. Final Check to Ensure the Equation is Balanced:
- Reactant side:
- Carbon (C): 2
- Oxygen (O): 2
- Product side:
- Carbon (C): 2
- Oxygen (O): 2
The coefficients that balance the equation are:
[tex]\[
\boxed{2, 2, 1}
\][/tex]
So, the balanced equation is:
[tex]\[
2 \text{CO} \rightarrow 2 \text{C} + \text{O}_2
\][/tex]
And the correct answer from the given options is [tex]\( \boxed{2, 2, 1} \)[/tex].
