To determine which equations need to be reversed to form [tex]$HCN$[/tex] and [tex]$H_2$[/tex] from [tex]$NH_3$[/tex] and [tex]$CH_4$[/tex], let's analyze the given equations and the desired overall reaction.
The given equations are:
1. \( N_2(g) + 3 H_2(g) \rightarrow 2 NH_3(g) \)
2. \( C(s) + 2 H_2(g) \rightarrow CH_4(g) \)
3. \( 4 H_2(g) + 2 C(s) + N_2(g) \rightarrow 2 HCN(g) + 3 H_2(g) \)
Our goal is the formation of \( HCN \) and \( H_2 \) from \( NH_3 \) and \( CH_4 \).
### Step-by-Step Solution:
Step 1: Reverse the first equation to decompose \( NH_3 \):
[tex]\[ 2 NH_3(g) \rightarrow N_2(g) + 3 H_2(g) \][/tex]
By reversing this equation, we obtain \( N_2 \) and \( H_2 \) from \( NH_3 \).
Step 2: Reverse the second equation to decompose \( CH_4 \):
[tex]\[ CH_4(g) \rightarrow C(s) + 2 H_2(g) \][/tex]
By reversing this equation, we obtain \( C \) and \( H_2 \) from \( CH_4 \).
Step 3: The third equation is already in the required form:
[tex]\[ 4 H_2(g) + 2 C(s) + N_2(g) \rightarrow 2 HCN(g) + 3 H_2(g) \][/tex]
This equation directly forms \( HCN \) and \( H_2 \).
### Conclusion:
To find the overall equation for the formation of \( HCN \) and \( H_2 \) from \( NH_3 \) and \( CH_4 \), we need to reverse the following equations:
- The first equation: \( N_2(g) + 3 H_2(g) \rightarrow 2 NH_3(g) \)
- The second equation: \( C(s) + 2 H_2(g) \rightarrow CH_4(g) \)
Thus, the equations that need to be reversed are:
1. \( N_2(g) + 3 H_2(g) \rightarrow 2 NH_3(g) \)
2. \( C(s) + 2 H_2(g) \rightarrow CH_4(g) \)
In summary, the correct equations to reverse are the first and second equations.
