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The information below describes a redox reaction:

[tex]\[
\begin{array}{l}
Cr^{3+}(aq) + 2 Cl^{-}(aq) \longrightarrow Cr(s) + Cl_2(g) \\
2 Cl^{-}(aq) \longrightarrow Cl_2(g) + 2 e^{-} \\
Cr^{3+}(aq) + 3 e^{-} \longrightarrow Cr(s)
\end{array}
\][/tex]

What is the final, balanced equation for this reaction?

A. [tex]\(2 Cr^{3+}(aq) + 6 Cl^{-}(aq) \longrightarrow 2 Cr(s) + 3 Cl_2(g)\)[/tex]

B. [tex]\(2 Cr^{3+}(aq) + 2 Cl^{-}(aq) + 6 e^{-} \longrightarrow Cl_2(g) + 2 Cr(s)\)[/tex]

C. [tex]\(Cr^{3+}(aq) + 6 Cl^{-}(aq) + 3 e^{-} \longrightarrow 2 Cr(s) + 3 Cl_2(g)\)[/tex]

D. [tex]\(Cr^{3+}(aq) + 2 Cl^{-}(aq) \longrightarrow Cr(s) + Cl_2(g)\)[/tex]

Sagot :

GinnyAnswer
To find the balanced redox reaction, we need to balance the given half-reactions for both the reduction and oxidation processes and then combine them.

Step-by-step solution:

1. Identify the given half-reactions:
- Oxidation half-reaction:
[tex]\[ 2 Cl^- (aq) \rightarrow Cl_2 (g) + 2 e^- \][/tex]
- Reduction half-reaction:
[tex]\[ Cr^{3+} (aq) + 3 e^- \rightarrow Cr (s) \][/tex]

2. Balance the electrons in each half-reaction:
- The oxidation half-reaction produces 2 electrons. To balance this with the reduction half-reaction (which requires 3 electrons), we need a common multiple of electrons. Therefore:

- Multiply the oxidation half-reaction by 3:
[tex]\[ 3 \times \left(2 Cl^- (aq) \rightarrow Cl_2 (g) + 2 e^- \right) \][/tex]
This gives us:
[tex]\[ 6 Cl^- (aq) \rightarrow 3 Cl_2 (g) + 6 e^- \][/tex]

- Multiply the reduction half-reaction by 2:
[tex]\[ 2 \times \left(Cr^{3+} (aq) + 3 e^- \rightarrow Cr (s)\right) \][/tex]
This gives us:
[tex]\[ 2 Cr^{3+} (aq) + 6 e^- \rightarrow 2 Cr (s) \][/tex]

3. Combine the balanced half-reactions:
- When we add these two balanced half-reactions, the electrons on both sides will cancel out:
[tex]\[ \left(6 Cl^- (aq) \rightarrow 3 Cl_2 (g) + 6 e^- \right) + \left(2 Cr^{3+} (aq) + 6 e^- \rightarrow 2 Cr (s)\right) \][/tex]
This results in:
[tex]\[ 2 Cr^{3+} (aq) + 6 Cl^- (aq) \rightarrow 2 Cr (s) + 3 Cl_2 (g) \][/tex]

Thus, the final balanced equation for the given redox reaction is:
[tex]\[ 2 Cr^{3+}(aq) + 6 Cl^{-}(aq) \rightarrow 2 Cr(s) + 3 Cl_2(g) \][/tex]
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