Consider these chemical equations.

[tex]\[
\begin{array}{l}
N_2(g) + 3H_2(g) \rightarrow 2NH_3(g) \\
C(s) + 2H_2(g) \rightarrow CH_4(g) \\
4H_2(g) + 2C(s) + N_2(g) \rightarrow 2HCN(g) + 3H_2(g)
\end{array}
\][/tex]

Which equation(s) do you need to reverse in order to calculate the overall equation for the formation of $HCN$ and $H_2$ from $NH_3$ and $CH_4$? Check all that apply.

[tex]\[
\begin{array}{l}
N_2(g) + 3H_2(g) \rightarrow 2NH_3(g) \\
C(s) + 2H_2(g) \rightarrow CH_4(g) \\
4H_2(g) + 2C(s) + N_2(g) \rightarrow 2HCN(g) + 3H_2(g)
\end{array}
\][/tex]

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.