To determine which reaction forms products that are more stable than the reactants, we need to consider the reactivities of the elements involved. One helpful approach is to analyze the reactivity series of metals and assess if a more reactive metal can replace a less reactive metal in a compound.
The reactivity series of some common elements (from most reactive to least reactive) is:
[tex]\[ \text{K} > \text{Na} > \text{Ca} > \text{Mg} > \text{Al} > \text{Zn} > \text{Fe} > \text{H} > \text{Cu} > \text{Ag} > \text{Au} \][/tex]
Let’s evaluate each reaction based on this reactivity series:
A. [tex]\[ 2 \text{AlBr}_3 + 3 \text{Zn} \rightarrow 3 \text{ZnBr}_2 + 2 \text{Al} \][/tex]
- In this reaction, Zinc (Zn) is trying to replace Aluminum (Al) in Aluminum Bromide (AlBr[tex]\(_3\)[/tex]).
- Aluminum (Al) is more reactive than Zinc (Zn), so this reaction is not feasible, meaning the products would not be more stable than the reactants.
B. [tex]\[ \text{CaBr}_2 + 2 \text{Na} \rightarrow 2 \text{NaBr} + \text{Ca} \][/tex]
- Sodium (Na) is more reactive than Calcium (Ca).
- Sodium can replace Calcium in Calcium Bromide (CaBr[tex]\(_2\)[/tex]).
- This indicates that the reaction is feasible and the products (NaBr and Ca) are more stable than the reactants.
C. [tex]\[ \text{MgBr}_2 + \text{H}_2 \rightarrow 2 \text{HBr} + \text{Mg} \][/tex]
- Magnesium (Mg) is more reactive than Hydrogen (H).
- However, Hydrogen is not in its ionic form (like H[tex]\(^+\)[/tex]), making it less clear whether the replacement will happen in this context.
- Generally, Magnesium will not react with Hydrogen gas to produce HBr.
D. [tex]\[ \text{BaBr}_2 + \text{Ca} \rightarrow \text{CaBr}_2 + \text{Ba} \][/tex]
- Calcium (Ca) is more reactive than Barium (Ba).
- Since Calcium can replace Barium in Barium Bromide (BaBr[tex]\(_2\)[/tex]), the reaction is feasible and the products (CaBr[tex]\(_2\)[/tex] and Ba) will be more stable.
E. [tex]\[ 2 \text{LiBr} + \text{Ba} \rightarrow \text{BaBr}_2 + 2 \text{Li} \][/tex]
- Lithium (Li) is more reactive than Barium (Ba).
- Lithium would not normally be replaced by Barium in Lithium Bromide (LiBr), making this reaction unlikely.
Based on the analysis:
- Reaction A is not feasible because Aluminum is more reactive than Zinc.
- Reaction B is feasible because Sodium is more reactive than Calcium and can replace it.
- Reaction C is not clear because Mg will not react with H[tex]\(_2\)[/tex] to form HBr.
- Reaction D is feasible because Calcium is more reactive than Barium and can replace it.
- Reaction E is not feasible because Lithium is more reactive than Barium.
Therefore, the correct answer is:
[tex]\[ \boxed{B} \][/tex]
