## Prediction Or Preparatory Problems Practice IChO 2020 Istanbul Turkey Type 1 (Part 1)

Below we provide training materials to face the 52

^{nd}International Chemistry Olympiad (IChO) of 2020 which will be held in Istanbul Turkey.

**Problem 1. A frog in a well**

The energy levels of an electron in a one-dimensional box are given by:

in which

*h*is the Planck’s constant,*m*is the mass of the electron, and L is the length of the box.**1)**The π electrons in a linear conjugated neutral molecule are treated as individual particles in a one-dimensional box. Assume that the π electrons are delocalized in the molecular length with the total number of N π electrons and their arrangement is governed by the principles of quantum mechanics.

**a.**Derive the general expression for ∆E

_{LUMO–HOMO }when an electron is excited from the HOMO to the LUMO.

**b.**Determine the wavelength λ of the absorption from the HOMO to the LUMO.

**2)**Apply the model of π electrons in a one-dimensional box for three dye molecules with the following structures (see the structural formula). Assume that the π electrons are delocalized in the space between the two phenyl groups with the length L is approximately equal to (2k+1)(0.140) nm, in which

*k*is the number of the double bonds

**a.**Calculate the box length L (Å) for each of the dyes.

**b.**Determine the wavelength λ (nm) of the absorption for the molecules of the investigated dyes.

**3)**Recalculate the box length L (Å) for the three dye molecules, assuming that the π electrons are delocalized over the linear conjugated chain which is presented as a line plotted between the two phenyl groups (see the structural formula). The bond angle C–C–C is 120

^{o}and the average length of C–C bond is 0.140 nm.

**4)**Give the following experimental data on the wavelength λ of absorption.

**a.**Determine the box length L (Å) of the linear conjugated chain for each of the three investigated dyes.

**b.**Tabulate the values of the box length L for the dyes calculated above by the three different methods, denoted as

**1**,

**2**, and

**3**. Choose the method which is the most fit to the experimental data.