To determine the overall equation by adding the provided reactions, let's start by writing down the equations and analyzing each step:
1. [tex]\( \text{H}_2 \rightarrow 2 \text{H} \)[/tex]
This equation tells us that one molecule of [tex]\(\text{H}_2\)[/tex] dissociates into two hydrogen atoms.
2. [tex]\( \text{C}_2\text{H}_4 + \text{H} \rightarrow \text{C}_2\text{H}_5 \)[/tex]
This reaction shows that one molecule of ethene ([tex]\(\text{C}_2\text{H}_4\)[/tex]) reacts with one hydrogen atom to form one molecule of [tex]\(\text{C}_2\text{H}_5\)[/tex].
3. [tex]\( \text{C}_2\text{H}_5 + \text{H} \rightarrow \text{C}_2\text{H}_6 \)[/tex]
Here, one molecule of [tex]\(\text{C}_2\text{H}_5\)[/tex] reacts with one hydrogen atom to form one molecule of ethane ([tex]\(\text{C}_2\text{H}_6\)[/tex]).
Now, let's sum these equations:
[tex]\[
\begin{aligned}
\text{H}_2 &\rightarrow 2 \text{H} \\
\text{C}_2\text{H}_4 + \text{H} &\rightarrow \text{C}_2\text{H}_5 \\
\text{C}_2\text{H}_5 + \text{H} &\rightarrow \text{C}_2\text{H}_6 \\
\end{aligned}
\][/tex]
Adding them together, we get:
[tex]\[
\text{H}_2 + \text{C}_2\text{H}_4 + \text{H} + \text{C}_2\text{H}_5 + \text{H} \rightarrow 2 \text{H} + \text{C}_2\text{H}_5 + \text{C}_2\text{H}_6
\][/tex]
Notice that [tex]\(\text{C}_2\text{H}_5\)[/tex] appears on both sides of the equation, and so do the [tex]\(\text{H}\)[/tex] atoms. They can be canceled out:
[tex]\[
\text{H}_2 + \text{C}_2\text{H}_4 \rightarrow \text{C}_2\text{H}_6
\][/tex]
Therefore, the overall equation is:
[tex]\[
\text{C}_2\text{H}_4 + \text{H}_2 \rightarrow \text{C}_2\text{H}_6
\][/tex]
So, the overall balanced chemical equation is:
[tex]\[
\text{C}_2\text{H}_4 + \text{H}_2 \rightarrow \text{C}_2\text{H}_6
\][/tex]
