Iodine Color Change in Solvents

Molecular iodine ($\text{I}_2$) appears violet in the gaseous state and as a solid. This color is due to electronic transitions within the $\text{I}_2$ molecule that absorb light in the yellow-green region of the visible spectrum, allowing violet light to be transmitted or reflected.

However, when $\text{I}_2$ is dissolved in certain polar solvents like acetone or ethanol, its color changes from violet to brown. This indicates that the electronic transitions responsible for the color are affected by the solvent environment. Let's analyze the given statements regarding this color change:

Statement (a): Dissociation of $\text{I}_2$ in atomic state

This statement suggests that $\text{I}_2$ molecules break apart into individual iodine atoms ($\text{I}$). While dissociation can occur under certain conditions (like high temperature or UV light), it is not the primary reason for the color change of $\text{I}_2$ when simply dissolved in polar solvents like acetone or ethanol at room temperature. The brown color is characteristic of molecular iodine interacting with the solvent, not isolated iodine atoms.

Statement (b): Interaction of low-lying $\sigma^*$-orbital of iodine with lone pair of O (solvent)

Acetone and ethanol are polar solvents containing oxygen atoms with lone pairs of electrons. $\text{I}_2$ has relatively low-lying antibonding molecular orbitals, specifically the $\sigma^*$ orbital. This $\sigma^*$ orbital can act as an electron acceptor. The lone pairs on the oxygen atom of the solvent can act as electron donors. An interaction occurs between the electron-rich solvent molecule (donor) and the electron-deficient $\text{I}_2$ molecule (acceptor). This interaction forms a new complex.

Statement (c): Formation of a charge-transfer complex

The interaction described in statement (b) is precisely the formation of a charge-transfer complex (also known as a donor-acceptor complex). In this complex, there is a partial transfer of electron density from the solvent molecule (the donor, via the oxygen lone pair) to the $\text{I}_2$ molecule (the acceptor, into the $\sigma^*$ orbital). This charge-transfer interaction creates new electronic energy levels and a new absorption band in the visible spectrum, typically shifting the absorption towards longer wavelengths (lower energy) compared to free $\text{I}_2$. This new absorption band is responsible for the brown color observed in these solutions.

Therefore, the color change from violet to brown is attributed to the formation of a charge-transfer complex between $\text{I}_2$ and the solvent, which involves the interaction of the solvent's lone pair electrons with the $\sigma^*$ antibonding orbital of iodine.

Based on this analysis, statements (b) and (c) correctly describe the reasons for the color change of iodine in acetone or ethanol.