Final answer:
The maximum absorbance peak for the aqua cobalt complex represented by [Ti(H₂O)6]³+ occurs at 499 nm, and the complex appears purple due to the absorption of wavelengths ranging from 450 to 600 nm.
Step-by-step explanation:
The absorbance peak for the aqua cobalt complex indicates the specific wavelength at which the complex absorbs light most strongly. For the octahedral complex [Ti(H₂O)6]³+, this occurs at 499 nm. Using the equation E = hc/λ, where h is Planck's constant (6.626 x 10⁻³´ J s), c is the speed of light (3.00 x 10⁸ m/s), and λ is the wavelength in meters, we can calculate the energy absorbed, Aoct, when the electron transitions from the ground state t2g orbital to the eg orbital.
Since the complex absorbs light ranging from 450 nm (blue) to 600 nm (orange), it will transmit the complementary wavelengths, resulting in the solution appearing purple in color. Therefore, the value of Aoct can be calculated and used to understand the color appearance of the solution.