To determine the missing oxidation number in the chemical reaction you provided, let's first clarify the reaction itself:
\[ \text{CO}_2 + \text{H}_2\text{O} \rightarrow \text{CH}_2\text{O} + \text{O}_2 \]
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Identify the oxidation states:
- In carbon dioxide (\( \text{CO}_2 \)):
- Carbon (C) has an oxidation state of +4.
- Oxygen (O) has an oxidation state of -2.
- In water (\( \text{H}_2\text{O} \)):
- Hydrogen (H) has an oxidation state of +1.
- Oxygen (O) has an oxidation state of -2.
- In formaldehyde (\( \text{CH}_2\text{O} \)):
- Carbon (C) has an oxidation state of +2.
- Hydrogen (H) has an oxidation state of +1.
- Oxygen (O) has an oxidation state of -2.
- In molecular oxygen (\( \text{O}_2 \)):
- Oxygen (O) has an oxidation state of 0 (as it is in its elemental form).
- In carbon dioxide (\( \text{CO}_2 \)):
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Balance the oxidation states:
- On the left side, the total oxidation state is the sum of contributions from \( \text{CO}_2 \) (+4 from C and -4 from two O) and \( \text{H}_2\text{O} \) (+2 from two H and -2 from O), giving +4 - 4 + 2 - 2 = 0.
- On the right side, we have \( \text{CH}_2\text{O} \) (+2 from C + 2 from two H - 2 from O = 2) and \( \text{O}_2 \) (oxidation state 0), leading to +2 + 0 = +2.
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Calculate the missing oxidation number:
- To balance the half-reaction, we can observe that there is a gain of oxidation state from +4 on the left (in \( \text{CO}_2 \)) to +2 on the right (in \( \text{CH}_2\text{O} \)), and a release of O in the formation of \( \text{O}_2 \).
- Given that all oxidation states must balance out, the missing oxidation state should also account for the change in oxidation states between carbon in \( \text{CO}_2\) moving to \( \text{CH}_2\text{O} \) and the formation of \( \text{O}_2 \).
In conclusion, the missing oxidation number in the reaction provided can be considered to balance according to the changes in the oxidation states throughout the reaction. If it is specifically asking for a singular oxidation state, it is likely referring to either the final oxidation state of a carbon when moving from +4 to +2, or something related to how many electrons were transferred.
Thus, numerically interpreting the situation, the final answer reflecting the balancing act in terms of common states would be 2.