Determine the standard reduction potential for the half reaction :
`Cl_2+2e^- to Cl^-`
Given `Pt^2+2Cl^- to Pt+Cl_2`
`E_("cell")^0=0.15V Pt^(2+)+2e^- toPt E^0=1.20V`

Answer

To determine the standard reduction potential for the half-reaction \( \text{Cl}_2 + 2e^- \rightarrow 2\text{Cl}^- \), we can use the provided information about the cell reaction and the standard reduction potentials of the other half-reactions.

### Step-by-Step Solution:

1. **Identify the Given Reactions and Their Potentials:**
- The overall cell reaction is:
\[ \text{Pt}^{2+} + 2\text{Cl}^- \rightarrow \text{Pt} + \text{Cl}_2 \]
with a standard cell potential \( E^\circ_{\text{cell}} = 0.15 \, \text{V} \).
- The reduction half-reaction for platinum is:
\[ \text{Pt}^{2+} + 2e^- \rightarrow \text{Pt} \]
with a standard reduction potential \( E^\circ_{\text{Pt}} = 1.20 \, \text{V} \).

2. **Write the Half-Reaction for Chlorine:**
- The half-reaction we need to find is:
\[ \text{Cl}_2 + 2e^- \rightarrow 2\text{Cl}^- \]
- Let the standard reduction potential for this half-reaction be \( E^\circ_{\text{Cl}} = x \).

3. **Reverse the Chlorine Half-Reaction:**
- Since the cell reaction shows \( \text{Cl}_2 \) on the product side, we need to reverse the chlorine half-reaction:
\[ 2\text{Cl}^- \rightarrow \text{Cl}_2 + 2e^- \]
- The standard reduction potential for the reversed reaction will be \( -x \).

4. **Set Up the Equation Using the Cell Potential:**
- The overall cell potential can be expressed as:
\[ E^\circ_{\text{cell}} = E^\circ_{\text{Pt}} + E^\circ_{\text{Cl}}' \]
- Substituting the known values:
\[ 0.15 \, \text{V} = 1.20 \, \text{V} + (-x) \]

5. **Solve for \( x \):**
- Rearranging the equation gives:
\[ -x = 0.15 \, \text{V} - 1.20 \, \text{V} \]
\[ -x = -1.05 \, \text{V} \]
\[ x = 1.05 \, \text{V} \]

6. **Conclusion:**
- The standard reduction potential for the half-reaction \( \text{Cl}_2 + 2e^- \rightarrow 2\text{Cl}^- \) is:
\[ E^\circ_{\text{Cl}} = 1.05 \, \text{V} \]