To determine the correct shorthand notation for the given galvanic cell reaction involving [tex]\( Sn^{2+}(aq) + F_2(g) \rightarrow Sn^{3+}(aq) + 2F^-(aq) \)[/tex], we need to carefully analyze the oxidation and reduction half-reactions, and understand how to represent the galvanic cell in cell notation.
### Step-by-Step Solution:
1. Identify the Oxidation and Reduction Half-Reactions:
- The species [tex]\( Sn^{2+} \)[/tex] is oxidized to [tex]\( Sn^{3+} \)[/tex]:
[tex]\[
Sn^{2+}(aq) \rightarrow Sn^{3+}(aq) + e^-
\][/tex]
- The species [tex]\( F_2 \)[/tex] is reduced to [tex]\( F^- \)[/tex]:
[tex]\[
F_2(g) + 2e^- \rightarrow 2F^-(aq)
\][/tex]
2. Assign Anode and Cathode:
- Oxidation occurs at the anode, so [tex]\( Sn^{2+} \)[/tex] [tex]\( \rightarrow Sn^{3+} \)[/tex] is the anode half-reaction.
- Reduction occurs at the cathode, so [tex]\( F_2 \rightarrow 2F^- \)[/tex] is the cathode half-reaction.
3. Determine the Phases and Interfaces:
- Anode: [tex]\( Sn^{2+}(aq) \rightarrow Sn^{3+}(aq) \)[/tex]
- Cathode: [tex]\( F_2(g) \rightarrow F^-(aq) \)[/tex]
- The electrode for the anode and cathode reactions are typically inert materials such as Platinum (Pt) since neither Sn nor F are solid metals involved in the electrode directly.
4. Constructing the Cell Notation:
- Anode is placed on the left, and the cathode on the right.
- Different phases are separated by a vertical line (|) and a salt bridge represented by double vertical lines (||).
- When different oxidation states of the same element are involved in the same phase, they are separated by a comma (,).
5. Correct Cell Notation:
- Anode (Oxidation): [tex]\( Pt(s) | Sn^{2+}(aq), Sn^{3+}(aq) \)[/tex]
- Salt Bridge (Phase Boundary): [tex]\( || \)[/tex]
- Cathode (Reduction): [tex]\( F_2(g) | F^-(aq) \)[/tex]
Bringing it all together, the shorthand notation that correctly represents the galvanic cell for the reaction [tex]\( Sn^{2+}(aq) + F_2(g) \rightarrow Sn^{3+}(aq) + 2F^-(aq) \)[/tex] is:
[tex]\[
\text{Pt(s)} \mid \text{Sn}^{2+}(\text{aq}), \text{Sn}^{3+}(\text{aq}) \parallel \text{F}_2(\text{g}) \mid \text{F}^-(\text{aq})
\][/tex]
Thus, the correct shorthand notation is:
[tex]\[
\boxed{\text{Pt(s)} \mid \text{Sn}^{2+}(\text{aq}), \text{Sn}^{3+}(\text{aq}) \parallel \text{F}_2(\text{g}) \mid \text{F}^-(\text{aq})}
\][/tex]
