In acidic medium, only iodide ions (I\(^-\)) can be oxidized by oxygen to form iodine (\( \text{I}_2 \)). The reaction is as follows: \[ 4 \text{I}^- + 4 \text{H}^+ + \text{O}_2 \rightarrow 2 \text{I}_2 (s) + 2 \text{H}_2\text{O} (l). \] Chloride (Cl\(^-\)) and bromide (Br\(^-\)) ions are not oxidized by oxygen in acidic medium because their reduction potentials are not favorable for such oxidation under standard conditions.
Calculate the potential for half-cell containing 0.01 M K\(_2\)Cr\(_2\)O\(_7\)(aq), 0.01 M Cr\(^{3+}\)(aq), and 1.0 x 10\(^{-4}\) M H\(^+\)(aq).
Let \( T_r \) be the \( r^{\text{th}} \) term of an A.P. If for some \( m \), \( T_m = \dfrac{1}{25} \), \( T_{25} = \dfrac{1}{20} \), and \( \displaystyle\sum_{r=1}^{25} T_r = 13 \), then \( 5m \displaystyle\sum_{r=m}^{2m} T_r \) is equal to: