To balance the chemical equation for photosynthesis:
\[ \text{_CO}_2 + \text{_H}_2\text{O} \rightarrow \text{_C}6\text{H}{12}\text{O}_6 + \text{_O}_2 \]
We'll determine the coefficients for each compound.
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Count the atoms for each element:
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On the left side (reactants):
- Carbon (C): 1 from CO₂; total = 1
- Oxygen (O): 2 from CO₂ and 1 from H₂O; total = 3
- Hydrogen (H): 2 from H₂O; total = 2
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On the right side (products):
- Carbon (C): 6 from C₆H₁₂O₆; total = 6
- Oxygen (O): 6 from C₆H₁₂O₆ and 2 from O₂; total = 8
- Hydrogen (H): 12 from C₆H₁₂O₆; total = 12
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Start with C: Balance the carbon first. \[ 6\text{CO}_2 + \text{H}_2\text{O} \rightarrow \text{C}6\text{H}{12}\text{O}_6 + \text{O}_2 \]
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Next, balance H: You have 12 H on the right side and need 12 on the left side: \[ 6\text{CO}_2 + 6\text{H}_2\text{O} \rightarrow \text{C}6\text{H}{12}\text{O}_6 + \text{O}_2 \]
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Now, balance O: On the left, you have: \[ 6 \times 2\text{O} , (\text{from } \text{CO}_2) + 6 \times 1\text{O} , (\text{from } \text{H}_2\text{O}) = 12 \text{O} \] On the right, you have: \[ 6 \text{O} , (\text{from } \text{C}6\text{H}{12}\text{O}_6) + x\text{O} , (\text{from } \text{O}_2) \]
To find \(x\): \[ 6 + x = 12 \implies x = 6 \]
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Final balanced equation: \[ 6\text{CO}_2 + 6\text{H}_2\text{O} \rightarrow \text{C}6\text{H}{12}\text{O}_6 + 6\text{O}_2 \]
Thus, the balanced coefficients are:
- 6 for CO₂
- 6 for H₂O
- 1 for C₆H₁₂O₆
- 6 for O₂
The final balanced equation is:
\[ \boxed{6\text{CO}_2 + 6\text{H}_2\text{O} \rightarrow \text{C}6\text{H}{12}\text{O}_6 + 6\text{O}_2} \]
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