Sure, let's balance the given chemical equation step-by-step.
The given unbalanced equation is:
[tex]$CO_2 + C \rightarrow CO$[/tex]
### Step 1: Identify the number of atoms for each element on both sides of the equation.
Initially, on the left side:
- Carbon (C): 1 atom (from [tex]\(CO_2\)[/tex]) + 1 atom (from C) = 2 atoms of Carbon
- Oxygen (O): 2 atoms (from [tex]\(CO_2\)[/tex])
On the right side:
- Carbon (C): 1 atom (in [tex]\(CO\)[/tex])
- Oxygen (O): 1 atom (in [tex]\(CO\)[/tex])
### Step 2: Balance the equation
We see that on the right side, the number of carbon atoms (1) and the number of oxygen atoms (1) are not equal to the number of these atoms on the left side.
To balance the carbon atoms, we need 2 carbon atoms on the right side. Therefore, we need 2 molecules of [tex]\(CO\)[/tex]:
[tex]$CO_2 + C \rightarrow 2 CO$[/tex]
Now let's recount the atoms:
- On the left side:
- Carbon (C): 1 (from [tex]\(CO_2\)[/tex]) + 1 (from C) = 2 atoms
- Oxygen (O): 2 atoms (from [tex]\(CO_2\)[/tex])
- On the right side:
- Carbon (C): 2 atoms (from 2 [tex]\(CO\)[/tex])
- Oxygen (O): 2 atoms (from 2 [tex]\(CO\)[/tex])
### Step 3: Verify the balance
Both sides now have:
- 2 carbon atoms
- 2 oxygen atoms
### Conclusion:
The equation is now balanced:
[tex]$CO_2 + C \rightarrow 2 CO$[/tex]
Thus, the correctly balanced form of the equation is given by option:
C. [tex]\(CO_2 + C \rightarrow 2 CO\)[/tex]
The correct answer is C.
