To determine the missing coefficient for water in the equation of cellular respiration, we can start by balancing the chemical equation based on the law of conservation of matter, which states that matter cannot be created or destroyed in a chemical reaction.
The unbalanced equation is:
\[ \text{C}6\text{H}{12}\text{O}_6 + 6\text{O}_2 \rightarrow 6\text{CO}_2 + ?\text{H}_2\text{O} + \text{Energy} \]
Let's balance it step by step.
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Carbon (C): In glucose (C₆H₁₂O₆), there are 6 carbon atoms. This means we will need 6 CO₂ to balance the carbon atoms on the product side.
\[ \text{C}6\text{H}{12}\text{O}_6 + 6\text{O}_2 \rightarrow 6\text{CO}_2 + ?\text{H}_2\text{O} + \text{Energy} \]
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Hydrogen (H): In glucose, there are 12 hydrogen atoms (H₁₂). Therefore, to balance hydrogen in the products, we need 6 H₂O because each water molecule has 2 hydrogen atoms.
\[ ?\text{H}_2\text{O} = 6\text{H}_2\text{O} \]
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Oxygen (O): Now let's count the total number of oxygen atoms on both sides. In the products, we have:
- 6 CO₂ contributes \(6 \times 2 = 12\) oxygen atoms.
- 6 H₂O contributes \(6 \times 1 = 6\) oxygen atoms. Total on the product side = 12 + 6 = 18 oxygen atoms.
On the reactant side, there’s 1 glucose (C₆H₁₂O₆), which has 6 oxygen atoms, and 6 O₂, which contributes \(6 \times 2 = 12\) oxygen atoms. Total on the reactant side = 6 + 12 = 18 oxygen atoms.
Since the equation is balanced for carbon, hydrogen, and oxygen, the missing coefficient for water is 6.
Thus, the answer is:
6