Considering the activity series given below for metals and nonmetals, which reaction will occur?

[tex]\[
\begin{array}{l}
Al \ \textgreater \ Mn \ \textgreater \ Zn \ \textgreater \ Cr \ \textgreater \ Fe \ \textgreater \ Cd \ \textgreater \ Co \ \textgreater \ Ni \ \textgreater \ Sn \ \textgreater \ Pb \ \textgreater \ H \ \textgreater \ Sb \ \textgreater \ Bi \ \textgreater \ Cu \ \textgreater \ Ag \ \textgreater \ Pd \ \textgreater \ Hg \ \textgreater \ Pt \\
F \ \textgreater \ Cl \ \textgreater \ Br \ \textgreater \ I
\end{array}
\][/tex]

A. $2 \, \text{NaBr} + I_2 \rightarrow 2 \, \text{NaI} + \text{Br}_2$

B. $2 \, \text{Fe} + \text{Al}_2\text{O}_3 \rightarrow 2 \, \text{Al} + \text{Fe}_2\text{O}_3$

C. $2 \, \text{AgNO}_3 + \text{Ni} \rightarrow \text{Ni}(\text{NO}_3)_2 + 2 \, \text{Ag}$

D. [tex]$\text{Pb} + \text{Zn}(\text{C}_2\text{H}_3\text{O}_2)_2 \rightarrow \text{Zn} + \text{Pb}(\text{C}_2\text{H}_3\text{O}_2)_2$[/tex]

To determine if the given reactions will occur, we need to refer to the activity series for metals and nonmetals. The activity series tells us which elements are more reactive and can displace others in chemical reactions.

### Reaction 1: $2 \text{NaBr} + \text{I}_2 \rightarrow 2 \text{NaI} + \text{Br}_2$
- The nonmetal reactivity series is: $ \text{F} > \text{Cl} > \text{Br} > \text{I} $.
- Here, Iodine ($\text{I}_2$) is below Bromine ($\text{Br}$) in the activity series.
- Since Iodine is less reactive than Bromine, it can displace Bromine from the compound $ \text{NaBr} $.
- Therefore, this reaction will occur.

### Reaction 2: $2 \text{Fe} + \text{Al}_2\text{O}_3 \rightarrow 2 \text{Al} + \text{Fe}_2\text{O}_3$
- The metal reactivity series is: $ \text{Al} > \text{Mn} > \text{Zn} > \text{Cr} > \text{Fe} > \text{Cd} > \text{Co} > \text{Ni} > \text{Sn} > \text{Pb} > \text{H} > \text{Sb} > \text{Bi} > \text{Cu} > \text{Ag} > \text{Pd} > \text{Hg} > \text{Pt} $.
- Here, Iron ($\text{Fe}$) is below Aluminum ($\text{Al}$) in the activity series.
- Since Iron is less reactive than Aluminum, it cannot displace Aluminum from the compound $ \text{Al}_2\text{O}_3 $.
- Therefore, this reaction will not occur.

### Reaction 3: $2 \text{AgNO}_3 + \text{Ni} \rightarrow \text{Ni(NO}_3\text{)}_2 + 2 \text{Ag}$
- The metal reactivity series is: $ \text{Al} > \text{Mn} > \text{Zn} > \text{Cr} > \text{Fe} > \text{Cd} > \text{Co} > \text{Ni} > \text{Sn} > \text{Pb} > \text{H} > \text{Sb} > \text{Bi} > \text{Cu} > \text{Ag} > \text{Pd} > \text{Hg} > \text{Pt} $.
- Here, Nickel ($\text{Ni}$) is above Silver ($\text{Ag}$) in the activity series.
- Since Nickel is more reactive than Silver, it can displace Silver from the compound $ \text{AgNO}_3 $.
- Therefore, this reaction will occur.

### Reaction 4: $\text{Pb} + \text{Zn(C}_2\text{H}_3\text{O}_2\text{)}_2 \rightarrow \text{Zn} + \text{Pb(C}_2\text{H}_3\text{O}_2\text{)}_2 $
- The metal reactivity series is: $ \text{Al} > \text{Mn} > \text{Zn} > \text{Cr} > \text{Fe} > \text{Cd} > \text{Co} > \text{Ni} > \text{Sn} > \text{Pb} > \text{H} > \text{Sb} > \text{Bi} > \text{Cu} > \text{Ag} > \text{Pd} > \text{Hg} > \text{Pt} $.
- Here, Zinc ($\text{Zn}$) is above Lead ($\text{Pb}$) in the activity series.
- Since Zinc is more reactive than Lead, it cannot be displaced by Lead from the compound $ \text{Zn(C}_2\text{H}_3\text{O}_2\text{)}_2 $.
- Therefore, this reaction will not occur.

### Summary:
Based on the activity series, the following reactions will occur:
1. $2 \text{NaBr} + \text{I}_2 \rightarrow 2 \text{NaI} + \text{Br}_2$
2. [tex]$2 \text{AgNO}_3 + \text{Ni} \rightarrow \text{Ni(NO}_3\text{)}_2 + 2 \text{Ag}$[/tex]