A solution contaning `4.5 mM` of `Cr_(2)O_(7)^(2-)` and `15 mM` of `Cr^(3+)` shows a `pH` of `2.0`. Calculater the potential of half reaction. (Standard potential of the reaciton
`Cr_(2)O_(7)^(2-) rarr Cr^(3+)` is `1.33V`)

Explanation

To calculate the potential of the half-reaction for the conversion of \( \text{Cr}_2\text{O}_7^{2-} \) to \( \text{Cr}^{3+} \) in a solution with given concentrations and pH, we will use the Nernst equation.

### Step 1: Write the half-reaction
The half-reaction for the reduction of dichromate ion to chromium ion is:
\[ \text{Cr}_2\text{O}_7^{2-} + 14 \text{H}^+ + 6 \text{e}^- \rightarrow 2 \text{Cr}^{3+} + 7 \text{H}_2\text{O} \]

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