The electrode with reaction `:Cr_(2)O_(7)^(2-)(aq)+14H^(o+)(aq)+6e^(-) rarr 2Cr^(3+)(aq)+7H_(2)O` can be represented as

Options

A. `Pt|H^(o+)(aq),Cr_(2)O_(7)^(2-)(aq)`
B. `Pt|H^(o+)(aq),Cr_(2)O_(7)^(2-)(aq),Cr^(3+)(aq)`
C. `Pt_(H2)|H^(o+)(aq),Cr_(2)O_(7)^(2-)`
D. `Pt_(H2)|H^(o+)(aq),Cr_(2)O_(7)^(2-)(aq),Cr^(3+)(aq)`

Explanation

To represent the electrode reaction given by the equation:

\[ \text{Cr}_2\text{O}_7^{2-}(aq) + 14 \text{H}^+(aq) + 6 e^- \rightarrow 2 \text{Cr}^{3+}(aq) + 7 \text{H}_2\text{O} \]

we need to identify the components involved in the half-reaction and determine how to represent this electrochemical cell.

### Step-by-Step Solution:

1. **Identify the Reduction Reaction**:
- The provided reaction shows that the dichromate ion (\(\text{Cr}_2\text{O}_7^{2-}\)) is being reduced to chromium ions (\(\text{Cr}^{3+}\)). This indicates that the chromium is gaining electrons (6 electrons in this case).

2. **Determine the Oxidation State**:
- In the dichromate ion, chromium has an oxidation state of +6, while in the chromium ion (\(\text{Cr}^{3+}\)), it has an oxidation state of +3. This confirms that the chromium is being reduced.

3. **Identify the Cathode**:
- Since reduction occurs at the cathode, the half-reaction represents the cathode process where dichromate ions are reduced to chromium ions.

4. **Identify the Anode Reaction**:
- In an electrochemical cell, oxidation occurs at the anode. In this case, hydrogen gas (\(H_2\)) can be oxidized to \(H^+\) ions. Therefore, the anode reaction can be represented as:
\[ \text{H}_2(g) \rightarrow 2 \text{H}^+(aq) + 2 e^- \]

5. **Construct the Cell Representation**:
- The complete cell representation combines the anode and cathode reactions. The standard representation of an electrochemical cell is:
\[ \text{Anode} \, | \, \text{Electrolyte} \, || \, \text{Electrolyte} \, | \, \text{Cathode} \]
- For our case, the anode is where hydrogen gas is oxidized, and the cathode is where dichromate is reduced. Therefore, the cell can be represented as:
\[ \text{Pt} \, | \, \text{H}_2(g) \, | \, \text{H}^+(aq) \, || \, \text{Cr}_2\text{O}_7^{2-}(aq), \text{Cr}^{3+}(aq) \, | \, \text{H}_2\text{O} \]

6. **Select the Correct Option**:
- Based on the above analysis, the correct representation of the electrochemical cell is option D, which includes the platinum electrode, hydrogen gas, and the dichromate ions.

### Final Answer:
The electrode can be represented as:
\[ \text{Pt} \, | \, \text{H}_2(g) \, | \, \text{H}^+(aq) \, || \, \text{Cr}_2\text{O}_7^{2-}(aq), \text{Cr}^{3+}(aq) \, | \, \text{H}_2\text{O} \]