To balance the chemical equation \( \text{CH}_4 + \text{Cl}_2 \rightarrow \text{CCl}_4 + \text{HCl} \), we need to ensure that the number of each type of atom is the same on both sides.
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On the left side, we have:
- Carbon (C): 1 (from CH4)
- Hydrogen (H): 4 (from CH4)
- Chlorine (Cl): 2 (from Cl2)
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On the right side, we have:
- Carbon (C): 1 (from CCl4)
- Hydrogen (H): 1 (from HCl)
- Chlorine (Cl): 4 (from CCl4) + 1 (from HCl) = 5
Balancing the number of atoms:
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We have 1 carbon atom on both sides (which is fine).
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To balance hydrogen, we need 4 H atoms on the right side, which can be achieved by having 4 HCl: \[ \text{CH}_4 + \text{Cl}_2 \rightarrow \text{CCl}_4 + 4\text{HCl} \] Now we have 4 H atoms on both sides.
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Now, count chlorine:
- Left side: 2 (from Cl2)
- Right side: 4 (from CCl4) + 4 (from 4 HCl) = 8
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To balance chlorine, we can adjust the Cl2 on the left: \[ \text{CH}_4 + 4\text{Cl}_2 \rightarrow \text{CCl}_4 + 4\text{HCl} \]
Now we have:
- Left side: 1 C, 4 H, 8 Cl
- Right side: 1 C, 4 H, 8 Cl
Final coefficients: 1 CH4, 4 Cl2, 1 CCl4, 4 HCl
The numbers that balance this equation are therefore 1, 4. However, in the options provided (1, 2), (4, 4), (3, 2), (2, 4), none match exactly with 1, 4. If we must choose from provided options, the first set (1, 2) might align with the representation of reactants/products based on ratios.
Thus, the closest or reasonable balanced ratio based on this analysis could be interpreted as 4, 4 if conservatively interpreted as a total balancing from reactants and products in view of significant overall contributions.
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