Consider the chemical equations shown here:

[tex]\[
\begin{array}{l}
2 \text{NO}_2(g) \rightarrow 2 \text{NO}(g) + \text{O}_2(g) \\
2 \text{NO}(g) \rightarrow \text{N}_2(g) + \text{O}_2(g) \\
\text{N}_2(g) + 2 \text{O}_2(g) \rightarrow \text{N}_2\text{O}_4(g) \\
\end{array}
\][/tex]

What is the equation for the overall reaction obtained by adding these equations?

A. [tex]\[2 \text{NO}_2(g) \rightarrow \text{N}_2\text{O}_4(g)\][/tex]

B. [tex]\[2 \text{N}_2\text{O}_4(g) + 2 \text{NO}(g) \rightarrow 2 \text{NO}_2(g) + \text{O}_2(g)\][/tex]

C. [tex]\[\text{N}_2(g) + \text{O}_2(g) + 2 \text{NO}(g) \rightarrow \text{N}_2\text{O}_4(g)\][/tex]

To find the overall reaction from the given chemical equations, we will sum the equations step-by-step while ensuring the substances on both the reactant and product sides balance out. Here are the given chemical equations:

1. [tex]$ 2 \, NO_2(g) \rightarrow 2 \, NO(g) + O_2(g) $[/tex]
2. [tex]$ 2 \, NO(g) \rightarrow N_2(g) + O_2(g) $[/tex]
3. [tex]$ N_2(g) + 2 \, O_2(g) \rightarrow N_2O_4(g) $[/tex]

### Step-by-Step Solution:

1. First Equation:
[tex]\[ 2 \, NO_2(g) \rightarrow 2 \, NO(g) + O_2(g) \][/tex]

This means that 2 molecules of nitrogen dioxide decompose to produce 2 molecules of nitric oxide and 1 molecule of oxygen gas.

2. Second Equation:
[tex]\[ 2 \, NO(g) \rightarrow N_2(g) + O_2(g) \][/tex]

Here, 2 molecules of nitric oxide decompose to produce 1 molecule of nitrogen gas and 1 molecule of oxygen gas.

3. Combining the First Two Equations:

First, add the first and second equations:
[tex]\[ (2 \, NO_2(g) \rightarrow 2 \, NO(g) + O_2(g)) + (2 \, NO(g) \rightarrow N_2(g) + O_2(g)) \][/tex]

Combine the products and reactants and then cancel out the common species on both sides:
[tex]\[ 2 \, NO_2(g) + 2 \, NO(g) \rightarrow 2 \, NO(g) + O_2(g) + N_2(g) + O_2(g) \][/tex]

Cancel out [tex]$ 2 \, NO(g) $[/tex] from both sides:
[tex]\[ 2 \, NO_2(g) \rightarrow N_2(g) + 2 \, O_2(g) \][/tex]

4. Third Equation:
[tex]\[ N_2(g) + 2 \, O_2(g) \rightarrow N_2O_4(g) \][/tex]

This equation shows 1 molecule of nitrogen gas reacting with 2 molecules of oxygen gas to form dinitrogen tetroxide.

5. Combining All Equations:

Now, combine the result from step 3 with the third equation:
[tex]\[ (2 \, NO_2(g) \rightarrow N_2(g) + 2 \, O_2(g)) + (N_2(g) + 2 \, O_2(g) \rightarrow N_2O_4(g)) \][/tex]

Combine them:
[tex]\[ 2 \, NO_2(g) \rightarrow N_2(g) + 2 \, O_2(g) + N_2(g) + 2 \, O_2(g) \rightarrow N_2O_4(g) \][/tex]

Cancel out [tex]$ N_2(g) $[/tex] and [tex]$ 2 \, O_2(g) $[/tex] from both sides:
[tex]\[ 2 \, NO_2(g) \rightarrow N_2O_4(g) \][/tex]

### Final Overall Reaction:
[tex]\[ 2 \, NO_2(g) \rightarrow N_2O_4(g) \][/tex]

Thus, the overall reaction obtained by adding the given equations is:
[tex]\[ 2 NO_2(g) \rightarrow N_2O_4(g) \][/tex]