Let's analyze each reaction to identify which one fulfills the criteria of being both a combustion reaction and a synthesis reaction.
### Reaction A: [tex]\( \mathrm{CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O} \)[/tex]
- Combustion Reaction: This reaction involves methane ([tex]\(\mathrm{CH_4}\)[/tex]) reacting with oxygen ([tex]\(\mathrm{O_2}\)[/tex]) to produce carbon dioxide ([tex]\(\mathrm{CO_2}\)[/tex]) and water ([tex]\(\mathrm{H_2O}\)[/tex]). This is a typical combustion reaction.
- Synthesis Reaction: In a synthesis reaction, two or more reactants combine to form a more complex compound. This reaction does not fit that criterion as it breaks down methane into simpler substances: carbon dioxide and water.
Conclusion: This reaction is a combustion reaction but not a synthesis reaction.
### Reaction B: [tex]\( \mathrm{2Mg + O_2 \rightarrow 2MgO} \)[/tex]
- Combustion Reaction: Magnesium ([tex]\(\mathrm{Mg}\)[/tex]) reacts with oxygen ([tex]\(\mathrm{O_2}\)[/tex]) to form magnesium oxide ([tex]\(\mathrm{MgO}\)[/tex]). This reaction releases heat and light, which is characteristic of combustion.
- Synthesis Reaction: In this reaction, two simpler substances (magnesium and oxygen) combine to form a more complex compound, magnesium oxide.
Conclusion: This reaction is both a combustion reaction and a synthesis reaction.
### Reaction C: [tex]\( \mathrm{2NaCl \rightarrow 2Na + Cl_2} \)[/tex]
- Combustion Reaction: There is no evidence of this reaction releasing heat and light or involving oxygen in a way typical of combustion reactions.
- Synthesis Reaction: This reaction is actually a decomposition reaction where sodium chloride ([tex]\(\mathrm{NaCl}\)[/tex]) breaks down into sodium ([tex]\(\mathrm{Na}\)[/tex]) and chlorine ([tex]\(\mathrm{Cl_2}\)[/tex]).
Conclusion: This reaction is neither a combustion reaction nor a synthesis reaction.
### Reaction D: [tex]\( \mathrm{Fe + Cl_2 \rightarrow FeCl_3} \)[/tex]
- Combustion Reaction: There is no indication that this reaction involves the release of heat and light typical of combustion reactions.
- Synthesis Reaction: Iron ([tex]\(\mathrm{Fe}\)[/tex]) and chlorine ([tex]\(\mathrm{Cl_2}\)[/tex]) combine to form iron (III) chloride ([tex]\(\mathrm{FeCl_3}\)[/tex]), which is a more complex compound. This fits the criterion for a synthesis reaction.
Conclusion: This reaction is a synthesis reaction but not a combustion reaction.
### Final Conclusion
After analyzing all the reactions, we can conclude that:
Reaction B [tex]\(2 \mathrm{Mg} + \mathrm{O_2} \rightarrow 2\mathrm{MgO}\)[/tex] is both a combustion reaction and a synthesis reaction.
