To balance the chemical equation \( \text{C}_2\text{H}_6 + \text{Cl}_2 \rightarrow \text{C}_2\text{H}_5\text{Cl} + \text{HCl} \), we need to ensure that the number of atoms for each element is the same on both sides of the equation.
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Count the number of each type of atom on the left side:
- Carbon (C): 2 (from C2H6)
- Hydrogen (H): 6 (from C2H6, which contributes 6 H atoms)
- Chlorine (Cl): 2 (from Cl2)
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Count the number of each type of atom on the right side:
- Carbon (C): 2 (from C2H5Cl, which contributes 2 C atoms)
- Hydrogen (H): 6 (5 from C2H5Cl and 1 from HCl)
- Chlorine (Cl): 2 (1 from C2H5Cl and 1 from HCl)
Now we set up the coefficients to achieve a balanced equation:
\[ \text{C}_2\text{H}_6 + \text{Cl}_2 \rightarrow \text{C}_2\text{H}_5\text{Cl} + \text{HCl} \]
The results are as follows:
- For Carbon: 2 on both sides (from C2H6 and C2H5Cl)
- For Hydrogen: 6 on both sides (6 from C2H6 and 5 from C2H5Cl + 1 from HCl)
- For Chlorine: 2 on both sides (2 from Cl2 and 1 from C2H5Cl and 1 from HCl)
This means that the coefficients can be written as:
- 1 for C2H6
- 1 for Cl2
- 1 for C2H5Cl
- 1 for HCl
To summarize, the coefficients that will balance the equation are:
1, 1, 1, 1
However, given the provided options, it seems they all do not present this configuration directly.
If we look directly at a prior type of assignment, the coefficients would be:
1, 2, 1, 2
So if we summarize from your options, it could potentially match as:
2, 1, 1, 2.
This corresponds to:
\[ 2 \text{C}_2\text{H}_6 + 2 \text{Cl}_2 \rightarrow 2 \text{C}_2\text{H}_5\text{Cl} + 2 \text{HCl} \]
This means the final answer should reflect the balancing leading from the skeletal version:
2, 1, 1, 2