To solve the problem of finding the overall equation for the reaction that produces [tex]\( \text{CCl}_4 \)[/tex] and [tex]\( \text{HCl} \)[/tex] from [tex]\( \text{CH}_4 \)[/tex] and [tex]\( \text{Cl}_2 \)[/tex], follow these steps:
### Step-by-Step Solution:
Given Chemical Equations:
1. [tex]\( \text{C} (s) + 2 \text{H}_2 (g) \rightarrow \text{CH}_4 (g) \)[/tex]
2. [tex]\( \text{C} (s) + 2 \text{Cl}_2 (g) \rightarrow \text{CCl}_4 (g) \)[/tex]
3. [tex]\( \text{H}_2 (g) + \text{Cl}_2 (g) \rightarrow 2 \text{HCl} (g) \)[/tex]
We need to derive an overall balanced equation that produces [tex]\( \text{CCl}_4 \)[/tex] and [tex]\( \text{HCl} \)[/tex] from [tex]\( \text{CH}_4 \)[/tex] and [tex]\( \text{Cl}_2 \)[/tex].
### Step 1: Writing the Target Reaction
Let's consider the desired reaction:
[tex]\[ \text{CH}_4 (g) + \text{Cl}_2 (g) \rightarrow \text{CCl}_4 (g) + \text{HCl} (g) \][/tex]
### Step 2: Balancing the Equation
In this reaction, we need both carbon and chlorine atoms to balance out on both sides, and we should also ensure the hydrogen atoms are equally balanced.
- Carbon Balance: One C atom on both sides (from [tex]\( \text{CH}_4 \)[/tex] and [tex]\( \text{CCl}_4 \)[/tex]).
- Chlorine Balance: Start with 4 chlorine atoms from [tex]\( \text{Cl}_2 \)[/tex] to match the [tex]\( \text{CCl}_4 \)[/tex] on the product side.
- Hydrogen Balance: [tex]\( \text{CH}_4 \)[/tex] has 4 hydrogen atoms, which will form 4 molecules of [tex]\( \text{HCl} \)[/tex] since each [tex]\( \text{HCl} \)[/tex] contains 1 hydrogen atom.
### Step 3: Adjusting Coefficients
The equation must be balanced such that the number of each type of atom on the reactants side equals the number of those atoms on the products side.
[tex]\[ \text{CH}_4 (g) + 4 \text{Cl}_2 (g) \rightarrow \text{CCl}_4 (g) + 4 \text{HCl} (g) \][/tex]
- Carbon atoms: 1 on both sides.
- Hydrogen atoms: 4 on both sides.
- Chlorine atoms: 8 on both sides (each [tex]\( \text{Cl}_2 \)[/tex] provides 2 atoms, so 4 [tex]\( \text{Cl}_2 \)[/tex] contribute 8 chlorine atoms, which are distributed as 4 in [tex]\( \text{CCl}_4 \)[/tex] and 4 in [tex]\( \text{HCl} \)[/tex]).
### Conclusion:
The overall balanced equation for the reaction that produces [tex]\( \text{CCl}_4 \)[/tex] and [tex]\( \text{HCl} \)[/tex] from [tex]\( \text{CH}_4 \)[/tex] and [tex]\( \text {Cl}_2 \)[/tex] is:
[tex]\[ \text{CH}_4 (g) + 4 \text{Cl}_2 (g) \rightarrow \text{CCl}_4 (g) + 4 \text{HCl} (g) \][/tex]
So, the balanced chemical equation is:
[tex]\[ \boxed{\text{CH}_4 (g) + 4 \text{Cl}_2 (g) \rightarrow \text{CCl}_4 (g) + 4 \text{HCl} (g)} \][/tex]
