To determine which equation represents the process of cellular respiration, we need to understand what cellular respiration involves. Cellular respiration is the process by which cells break down glucose ([tex]$C_6H_{12}O_6$[/tex]) and oxygen ([tex]$O_2$[/tex]) to produce water ([tex]$H_2O$[/tex]), carbon dioxide ([tex]$CO_2$[/tex]), and energy. The general equation for cellular respiration is:
[tex]\[ C_6H_{12}O_6 + 6O_2 \rightarrow 6H_2O + 6CO_2 \][/tex]
Now, let's match this equation with the options provided:
A. [tex]\( C_2H_4 + 3O_2 \rightarrow 2H_2O + 2CO_2 \)[/tex]
- This equation involves ethylene ([tex]$C_2H_4$[/tex]) and not glucose ([tex]$C_6H_{12}O_6$[/tex]).
B. [tex]\( C_6H_{12}O_6 + 6O_2 \rightarrow 6H_2O + 6CO_2 \)[/tex]
- This equation matches exactly with the general equation for cellular respiration. It shows glucose being broken down with oxygen to produce water and carbon dioxide.
C. [tex]\( 2C_2H_6 + 7O_2 \rightarrow 4CO_2 + 6H_2O \)[/tex]
- This equation involves ethane ([tex]$C_2H_6$[/tex]) and not glucose.
D. [tex]\( 6H_2O + 6CO_2 \rightarrow C_6H_{12}O_6 + 6O_2 \)[/tex]
- This equation describes photosynthesis, which is the reverse process of cellular respiration where water and carbon dioxide are used to produce glucose and oxygen.
Given these comparisons, the equation that accurately represents the process of cellular respiration is:
[tex]\[ C_6H_{12}O_6 + 6O_2 \rightarrow 6H_2O + 6CO_2 \][/tex]
Thus, the correct answer is option B.
