13. The standard reduction potential of several half-cell reactions are shown below. $$ \mathrm{Ag}^{+}(\mathrm{aq})+ $$ é $$ \rightarrow \mathrm{Ag}(\mathrm{s}) \quad \mathrm{E}^{\circ} \mathrm{Ag}^{+} / \mathrm{Ag}= $$ +0.80 V $$ \mathrm{Cu}^{2+}(\mathrm{aq})+2 \mathrm{e} \rightarrow \mathrm{Cu}(\mathrm{s}) \quad \mathrm{E}^{\circ} \mathrm{Cu}^{2+} / \mathrm{Cu}= $$ +0.34 V $$ \mathrm{Cl}_{2}(\mathrm{~g})+2 \mathrm{e} \rightarrow 2 \mathrm{Cl}-(\mathrm{aq}) \quad \mathrm{E}^{\circ} \mathrm{Cl}_{2} / \mathrm{Cl}^{-}=+ $$ 1.36 V $$ \mathrm{Au}^{3+}(\mathrm{aq})+3 \mathrm{é} \rightarrow \mathrm{Au}(\mathrm{s}) \quad \mathrm{E}^{\circ} \mathrm{Au}^{3+} / \mathrm{Au}= $$ +1.50 V

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Hello! It looks like you've provided the standard reduction potentials for several half-cell reactions:

1. **Silver Reaction:**
   $$
   \mathrm{Ag}^{+}(\mathrm{aq}) + \mathrm{e}^{-} \rightarrow \mathrm{Ag}(\mathrm{s}) \quad \mathrm{E}^{\circ}_{\mathrm{Ag}^{+}/\mathrm{Ag}} = +0.80\, \text{V}
   $$

2. **Copper Reaction:**
   $$
   \mathrm{Cu}^{2+}(\mathrm{aq}) + 2\, \mathrm{e}^{-} \rightarrow \mathrm{Cu}(\mathrm{s}) \quad \mathrm{E}^{\circ}_{\mathrm{Cu}^{2+}/\mathrm{Cu}} = +0.34\, \text{V}
   $$

3. **Chlorine Reaction:**
   $$
   \mathrm{Cl}_{2}(\mathrm{g}) + 2\, \mathrm{e}^{-} \rightarrow 2\, \mathrm{Cl}^{-}(\mathrm{aq}) \quad \mathrm{E}^{\circ}_{\mathrm{Cl}_{2}/\mathrm{Cl}^{-}} = +1.36\, \text{V}
   $$

4. **Gold Reaction:**
   $$
   \mathrm{Au}^{3+}(\mathrm{aq}) + 3\, \mathrm{e}^{-} \rightarrow \mathrm{Au}(\mathrm{s}) \quad \mathrm{E}^{\circ}_{\mathrm{Au}^{3+}/\mathrm{Au}} = +1.50\, \text{V}
   $$

If you have a specific question or problem related to these standard reduction potentials—such as calculating the overall cell potential for a reaction, determining spontaneity, or identifying oxidizing/reducing agents—please provide the details, and I'd be happy to help you solve it!

---

**Example Problem and Solution:**

*Suppose you want to determine whether the reaction between silver ions and gold metal will occur spontaneously. The reaction can be written as:*

$$
\mathrm{Ag}^{+}(\mathrm{aq}) + \mathrm{Au}(\mathrm{s}) \rightarrow \mathrm{Ag}(\mathrm{s}) + \mathrm{Au}^{3+}(\mathrm{aq})
$$

**Solution:**

1. **Identify the Half-Reactions and Their Potentials:**

- **Reduction (Ag⁺ to Ag):**
     $$
     \mathrm{Ag}^{+} + \mathrm{e}^{-} \rightarrow \mathrm{Ag} \quad \mathrm{E}^{\circ} = +0.80\, \text{V}
     $$
   
   - **Oxidation (Au to Au³⁺):**
     $$
     \mathrm{Au} \rightarrow \mathrm{Au}^{3+} + 3\, \mathrm{e}^{-} \quad \mathrm{E}^{\circ} = -1.50\, \text{V} \quad (\text{Reverse of reduction potential})
     $$

2. **Calculate the Standard Cell Potential (ΔE°):**

$$
   \Delta E^{\circ} = \mathrm{E}^{\circ}_{\text{cathode}} - \mathrm{E}^{\circ}_{\text{anode}} = (+0.80\, \text{V}) - (-1.50\, \text{V}) = +2.30\, \text{V}
   $$

3. **Determine Spontaneity:**

Since ΔE° is positive (+2.30 V), the reaction is **spontaneous** under standard conditions.

4. **Identify Oxidizing and Reducing Agents:**

- **Oxidizing Agent:** Ag⁺ (it gets reduced)
   - **Reducing Agent:** Au (it gets oxidized)

Feel free to ask if you need clarification on this example or have another question in mind!
The standard reduction potentials for the given half-cell reactions are: 1. **Silver:** $$ \mathrm{Ag}^{+} + \mathrm{e}^{-} \rightarrow \mathrm{Ag} $$ with $$ \mathrm{E}^{\circ} = +0.80\, \text{V} $$ 2. **Copper:** $$ \mathrm{Cu}^{2+} + 2\, \mathrm{e}^{-} \rightarrow \mathrm{Cu} $$ with $$ \mathrm{E}^{\circ} = +0.34\, \text{V} $$ 3. **Chlorine:** $$ \mathrm{Cl}_{2} + 2\, \mathrm{e}^{-} \rightarrow 2\, \mathrm{Cl}^{-} $$ with $$ \mathrm{E}^{\circ} = +1.36\, \text{V} $$ 4. **Gold:** $$ \mathrm{Au}^{3+} + 3\, \mathrm{e}^{-} \rightarrow \mathrm{Au} $$ with $$ \mathrm{E}^{\circ} = +1.50\, \text{V} $$ If you have a specific question or need help with a problem related to these potentials, feel free to ask!

The standard reduction potential of
several half-cell reactions are shown
below.
é
+0.80 V

+0.34 V

1.36 V
$é$
+1.50 V

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The standard reduction potential of several half-cell reactions are shown below. é +0.80 V +0.34 V 1.36 V é +1.50 V