To balance the equation \( \text{CH}_4 + ____ \text{Cl}_2 \rightarrow \text{CCl}_4 + ____ \text{HCl} \), we start by counting the number of atoms for each element on both sides of the equation.
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Carbon (C):
- Left side: 1 (from CH4)
- Right side: 1 (from CCl4)
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Hydrogen (H):
- Left side: 4 (from CH4)
- Right side: 1 (from HCl). To balance hydrogen, we need 4 HCl:
- Adjusted right side: 4 (from HCl)
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Chlorine (Cl):
- The adjusted right side has 4 from CCl4 and 4 from HCl, totaling 8 Cl on the right side. Therefore, we need 4 Cl2 (since each Cl2 has 2 Cl):
- Left side: 4 (from Cl2)
So, putting everything together, we can write:
\[ \text{CH}_4 + 4 \text{Cl}_2 \rightarrow \text{CCl}_4 + 4 \text{HCl} \]
Thus, the balanced numbers are:
1 for CH4, 4 for Cl2 to produce 1 for CCl4 and 4 for HCl.
Hence, the correct answer from the options provided is 1, 4.