Consider the equations below.
[tex]\begin{array}{c}
H_2 \rightarrow 2 H \\
C_2 H_4+H \rightarrow C_2 H_5 \\
C_2 H_5+H \rightarrow C_2 H_6
\end{array}[/tex]
When these equations are added together, what will the overall equation be? Assume that no equations need to be reversed.
[tex]C _2 H _4+ H _2 \rightarrow C _2 H _6[/tex]
[tex]H _2+ C _2 H _4+2 H + C _2 H _5+\rightarrow 2 H + C _2 H _5+ C _2 H _6[/tex]
[tex]C _2 H _4+ C _2 H _5+ H _2 \rightarrow C _2 H _5+ C _2 H _6[/tex]
Answer (2)
The overall equation from the given chemical equations is C 2 H 4 + H 2 → C 2 H 6 . This shows the reaction between ethylene and hydrogen gas resulting in ethane. It is derived by summing the reactants and products of the individual equations and simplifying where applicable.
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Combine the left-hand sides of the given equations: H 2 + C 2 H 4 + H + C 2 H 5 + H .
Combine the right-hand sides of the given equations: 2 H + C 2 H 5 + C 2 H 6 .
Write the overall equation: H 2 + C 2 H 4 + H + C 2 H 5 + H → 2 H + C 2 H 5 + C 2 H 6 .
Simplify the equation by canceling out common species: C 2 H 4 + H 2 → C 2 H 6 . The overall equation is C 2 H 4 + H 2 → C 2 H 6 .
Explanation
Understanding the Problem We are given three chemical equations that we need to add together to find the overall equation. The key is to combine the reactants and products correctly and then simplify by canceling out any common species on both sides of the equation.
Combining the Equations First, let's write down the given equations:
H 2 → 2 H
C 2 H 4 + H → C 2 H 5
C 2 H 5 + H → C 2 H 6
Now, we add the left-hand sides (reactants) and the right-hand sides (products) of these equations together.
Writing the Combined Equation Adding the left-hand sides gives us: H 2 + C 2 H 4 + H + C 2 H 5 + H
Adding the right-hand sides gives us: 2 H + C 2 H 5 + C 2 H 6
So, the combined equation is:
H 2 + C 2 H 4 + H + C 2 H 5 + H → 2 H + C 2 H 5 + C 2 H 6
Simplifying the Equation Now, we simplify the equation by canceling out any species that appear on both sides. We have H and C 2 H 5 on both sides. On the left side, we have H + H = 2 H , which cancels out the 2 H on the right side. Also, C 2 H 5 cancels out from both sides.
After canceling, we are left with:
H 2 + C 2 H 4 → C 2 H 6
Final Answer Therefore, the overall equation when the given equations are added together is:
C 2 H 4 + H 2 → C 2 H 6
Examples
In chemical engineering, understanding how to combine chemical reactions is crucial for designing industrial processes. For instance, if you want to produce ethane ( C 2 H 6 ) from ethene ( C 2 H 4 ), you need to know the overall reaction. By combining simpler reactions, you can determine the necessary conditions and catalysts to achieve the desired outcome efficiently. This process is similar to combining the given equations to find the overall reaction: C 2 H 4 + H 2 → C 2 H 6 .
