To determine the missing coefficient for water in the equation for cellular respiration, we can balance the equation according to the law of conservation of matter, which states that the number of atoms of each element must be equal on both sides of the equation.
The unbalanced equation is:
\[ \text{C}6\text{H}{12}\text{O}_6 + 6\text{O}_2 \rightarrow 6\text{CO}_2 + ?\text{H}_2\text{O} + \text{Energy} \]
Balancing the equation:
-
Carbons:
- 6 carbons in \( \text{C}6\text{H}{12}\text{O}_6 \) which produce 6 \( \text{CO}_2 \) (balanced).
-
Oxygens:
- In the reactants, there are 6 \( O_2 \) molecules contributing 12 oxygen atoms (6 x 2 = 12) and 1 glucose molecule contributing 6 oxygen atoms.
- Total on the left: 12 + 6 = 18 oxygen atoms.
- On the right, we have \( 6\text{CO}_2 \) which contributes 12 oxygen atoms (6 x 2 = 12).
- To find the number of \( H_2O \) needed to have 18 oxygen atoms total, we can set up the equation:
\[
12 (from , CO_2) + ? (from , H_2O) = 18
\]
This implies that:
\[
? = 18 - 12 = 6.
\]
-
Hydrogens:
- In glucose, there are 12 hydrogen atoms and each water molecule (\( H_2O \)) has 2 hydrogen atoms, so to balance:
\[
\text{Number of } H_2O = \frac{12}{2} = 6.
\]
Therefore, the missing coefficient for water \( H_2O \) is 6.
The balanced equation is:
\[ C_6H_{12}O_6 + 6O_2 \rightarrow 6CO_2 + 6H_2O + \text{Energy} \]