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Consider the chemical equations shown here:
[tex]\[
\begin{array}{l}
C (s) + 2H_2 (g) \rightarrow CH_4 (g) \\
C (s) + 2Cl_2 (g) \rightarrow CCl_4 (g) \\
H_2 (g) + Cl_2 (g) \rightarrow 2HCl (g)
\end{array}
\][/tex]

What is the overall equation for the reaction that produces [tex]\(CCl_4\)[/tex] and [tex]\(HCl\)[/tex] from [tex]\(CH_4\)[/tex] and [tex]\(Cl_2\)[/tex]?
A. [tex]\(CH_4 (g) + Cl_2 (g) \rightarrow CO_4 (g) + HCl (g)\)[/tex]
B. [tex]\(CH_4 (g) + 4Cl_2 (g) \rightarrow CCl_4 (g) + 4HCl (g)\)[/tex]
C. [tex]\(CH_4 (g) + Cl_2 (g) + H_2 (g) \rightarrow CCl_4 (g) + HCl (g)\)[/tex]

Sagot :

GinnyAnswer
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]
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