Consider the following intermediate chemical equations:
[tex]
\begin{array}{l}
CH_4(g)+2 O_2(g) \rightarrow CO_2(g)+2 H_2 O(g) \
2 H_2 O(g) \rightarrow 2 H_2 O(l)
\end{array}
[/tex]
Which overall chemical equation is obtained by combining these intermediate equations?
[tex]CH _4(g)+2 O _2(g) \rightarrow CO _2(g)+2 H _2 O ( l )[/tex]
[tex]CH _4(g)+2 O _2(g) \rightarrow CO _2(g)+2 H _2 O ( g )[/tex]
[tex]CH _4(g)+2 O _2(g) \rightarrow CO _2(g)+4 H _2 O ( g )+2 H _2 O ( l )[/tex]
[tex]CH _4(g)+2 O _2(g) \rightarrow CO _2(g)+6 H _2 O ( g )[/tex]
Answer (2)
By combining the two given chemical equations and canceling out the common terms, we find that the overall equation is C H 4 ( g ) + 2 O 2 ( g ) → C O 2 ( g ) + 2 H 2 O ( l ) . This corresponds to the first option provided. The final reaction illustrates the combustion of methane with oxygen, producing carbon dioxide and liquid water.
;
Add the two intermediate chemical equations.
Identify the common term 2 H 2 O ( g ) on both sides of the equation.
Cancel out the common term.
The overall chemical equation is C H 4 ( g ) + 2 O 2 ( g ) → C O 2 ( g ) + 2 H 2 O ( l ) .
C H 4 ( g ) + 2 O 2 ( g ) → C O 2 ( g ) + 2 H 2 O ( l )
Explanation
Understanding the Equations We are given two chemical equations:
Equation 1: C H 4 ( g ) + 2 O 2 ( g ) → C O 2 ( g ) + 2 H 2 O ( g )
Equation 2: 2 H 2 O ( g ) → 2 H 2 O ( l )
Our goal is to combine these equations to find the overall chemical equation.
Adding the Equations To combine the equations, we add them together:
C H 4 ( g ) + 2 O 2 ( g ) + 2 H 2 O ( g ) → C O 2 ( g ) + 2 H 2 O ( g ) + 2 H 2 O ( l )
Cancelling Common Terms Now, we look for terms that appear on both sides of the equation. We have 2 H 2 O ( g ) on both the left and right sides. We can cancel these out:
C H 4 ( g ) + 2 O 2 ( g ) + 2 H 2 O ( g ) − 2 H 2 O ( g ) → C O 2 ( g ) + 2 H 2 O ( g ) − 2 H 2 O ( g ) + 2 H 2 O ( l )
This simplifies to:
C H 4 ( g ) + 2 O 2 ( g ) → C O 2 ( g ) + 2 H 2 O ( l )
Final Overall Equation The overall chemical equation is:
C H 4 ( g ) + 2 O 2 ( g ) → C O 2 ( g ) + 2 H 2 O ( l )
Examples
Understanding chemical equations is crucial in many real-world applications. For instance, in environmental science, it helps us analyze combustion processes and their impact on air quality. The balanced equation we derived shows how methane ( C H 4 ) reacts with oxygen to produce carbon dioxide and liquid water. This is similar to the process occurring in natural gas power plants, where methane combustion generates electricity. By understanding these reactions, engineers can optimize combustion processes to reduce harmful emissions and improve energy efficiency.
