The information below describes a redox reaction.

[tex]\[
\begin{array}{l}
Ag^{+}(aq) + Al(s) \longrightarrow Ag(s) + Al^{3+}(aq) \\
Ag^{+}(aq) + e^{-} \longrightarrow Ag(s) \\
Al(s) \longrightarrow Al^{3+}(aq) + 3e^{-}
\end{array}
\][/tex]

What is the coefficient of silver in the final, balanced equation for this reaction?

A. 1
B. 2
C. 3
D. 4



Answer :

To determine the coefficient of silver in the final, balanced equation for the given redox reaction, we need to balance the half-reactions for both oxidation and reduction.

First, let's write down the oxidation and reduction half-reactions:

1. The oxidation half-reaction:
[tex]\[ \text{Al (s)} \rightarrow \text{Al}^{3+} (aq) + 3e^{-} \][/tex]

2. The reduction half-reaction:
[tex]\[ \text{Ag}^{+} (aq) + e^{-} \rightarrow \text{Ag (s)} \][/tex]

To balance the overall redox reaction, we need to ensure that the electrons lost in the oxidation half-reaction are equal to the electrons gained in the reduction half-reaction.

The oxidation half-reaction involves the loss of 3 electrons by aluminum:
[tex]\[ \text{Al (s)} \rightarrow \text{Al}^{3+} (aq) + 3e^{-} \][/tex]

The reduction half-reaction involves the gain of 1 electron by each silver ion:
[tex]\[ \text{Ag}^{+} (aq) + e^{-} \rightarrow \text{Ag (s)} \][/tex]

To balance the electrons, we need to multiply the reduction half-reaction by 3 so that the number of electrons gained equals the number of electrons lost:
[tex]\[ 3[\text{Ag}^{+} (aq) + e^{-} \rightarrow \text{Ag (s)}] \][/tex]
This can be simplified to:
[tex]\[ 3\text{Ag}^{+} (aq) + 3e^{-} \rightarrow 3\text{Ag (s)} \][/tex]

Now, we can combine the oxidation and reduction half-reactions:
[tex]\[ \text{Al (s)} \rightarrow \text{Al}^{3+} (aq) + 3e^{-} \][/tex]
[tex]\[ 3\text{Ag}^{+} (aq) + 3e^{-} \rightarrow 3\text{Ag (s)} \][/tex]

By adding the two half-reactions together, the electrons cancel out:
[tex]\[ \text{Al (s)} + 3\text{Ag}^{+} (aq) \rightarrow \text{Al}^{3+} (aq) + 3\text{Ag (s)} \][/tex]

Therefore, the balanced equation is:
[tex]\[ \text{Al (s)} + 3\text{Ag}^{+} (aq) \rightarrow \text{Al}^{3+} (aq) + 3\text{Ag (s)} \][/tex]

The coefficient of silver (Ag) in the balanced equation is 3.