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Consider the chemical equations shown here:

[tex]\[
\begin{aligned}
2 NO_2(g) & \rightarrow 2 NO(g) + O_2(g) \\
2 NO(g) & \rightarrow N_2(g) + O_2(g) \\
N_2(g) + 2 O_2(g) & \rightarrow N_2O_4(g)
\end{aligned}
\][/tex]

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

A. \(2 NO_2(g) \rightarrow N_2O_4(g)\)

B. \(2 N_2O_4(g) + 2 NO(g) \rightarrow 2 NO_2(g) + O_2(g)\)

C. [tex]\(N_2(g) + O_2(g) + 2 NO(g) \rightarrow N_2O_4(g)\)[/tex]



Answer :

GinnyAnswer
In order to determine the overall reaction, let's add the given chemical equations and see what cancels out in the process.

The given chemical equations are:

1. \(2 \text{NO}_2(\text{g}) \rightarrow 2 \text{NO}(\text{g}) + \text{O}_2(\text{g})\)
2. \(2 \text{NO}(\text{g}) \rightarrow \text{N}_2(\text{g}) + \text{O}_2(\text{g})\)
3. \(\text{N}_2(\text{g}) + 2 \text{O}_2(\text{g}) \rightarrow \text{N}_2\text{O}_4(\text{g})\)

Let's add these equations step-by-step:

First, rewrite equations to add them:
1. \(2 \text{NO}_2(\text{g}) \rightarrow 2 \text{NO}(\text{g}) + \text{O}_2(\text{g})\)
2. \(2 \text{NO}(\text{g}) \rightarrow \text{N}_2(\text{g}) + \text{O}_2(\text{g})\)
3. \(\text{N}_2(\text{g}) + 2 \text{O}_2(\text{g}) \rightarrow \text{N}_2\text{O}_4(\text{g})\)

Now, sum the reactants and products of all three equations:

Reactants:
[tex]\[ 2 \text{NO}_2(\text{g}) + 2 \text{NO}(\text{g}) + \text{N}_2(\text{g}) + 2 \text{O}_2(\text{g}) \][/tex]

Products:
[tex]\[ 2 \text{NO}(\text{g}) + \text{O}_2(\text{g}) + \text{N}_2(\text{g}) + \text{O}_2(\text{g}) + \text{N}_2\text{O}_4(\text{g}) \][/tex]

Now, let’s look at what cancels out:
- The \(2 \text{NO}(\text{g})\) on both sides
- The \(\text{N}_2(\text{g})\) on both sides
- The \(\text{O}_2(\text{g})\) from the one in first and second reaction will contribute to cancelling out one \(\text{O}_2(\text{g})\) in the products.

This leaves us with:
- \(2 \text{NO}_2(\text{g})\)
- Production of \(\text{N}_2 \text{O}_4(\text{g})\)
- Remaining \(2 \text{O}_2(\text{g})\) cancels two \(\text{O}_2(\text{g})\) in product side

So, the overall reaction is:
[tex]\[2 \text{NO}_2(\text{g}) \rightarrow \text{N}_2\text{O}_4(\text{g})\][/tex]

This matches with the balanced overall reaction:

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

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