1. Statement I: Tropolone is an aromatic compound with a conjugated ring system containing 8 \(\pi\) electrons: - 6 \(\pi\) electrons are endocyclic (within the ring). - 2 \(\pi\) electrons from the \(>\text{C}=\text{O}\) group are exocyclic (outside the ring). Hence, tropolone satisfies the conditions of aromaticity. Therefore, Statement I is correct.
2. Statement II: The \(\pi\) electrons of the \(>\text{C}=\text{O}\) group are not involved in the aromaticity of the compound, as they are exocyclic and do not contribute to the conjugated system of the ring. Therefore, Statement II is incorrect. ### Diagram: \[ \text{Tropolone: Aromatic compound with 6 \(\pi\) endocyclic electrons} \] \[ \text{Structure:} \] \[ \text{OH} \quad \text{C}=\text{O} \]
Conclusion: Statement I is true, but Statement II is false.
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: