In liquid \(\mathrm{CCl}_{4}\) which of the following has maximum solubility? (a) \(\mathrm{I}_{2}\) (b) \(\mathrm{Br}_{2}\) (c) \(\mathrm{NaCl}\) (d) \(\mathrm{Cl}_{2}\)

The 'Like dissolves like' principle is foundational in understanding solubility. It signifies that a substance's solubility is influenced by the similarity in polarity between the solvent and the solute. Non-polar solutes tend to dissolve in non-polar solvents, while polar solutes favor polar solvents.

For example, when you attempt to mix oil (non-polar) with water (polar), they do not mix because their polarities are different. On the other hand, if you dissolve table salt (polar) in water, it dissolves readily due to their similar polar nature. This principle is critical in predicting solubility in different media and is instrumental in a wide range of applications, from industrial solvent selection to pharmacological drug design where solubility is key for bioavailability.

Polarity of solutes is a critical concept in chemistry that helps predict how a substance will interact with solvents. The polarity of a molecule is determined by its shape and the distribution of electrical charge. Molecules with uneven charge distribution are polar, as seen in water (H_2O), where the oxygen atom holds a slight negative charge while the hydrogen atoms carry a slight positive charge.

This uneven charge leads to the ability of polar substances to dissolve in polar solvents because they can interact via dipole-dipole attractions. For example, ionic compounds like sodium chloride (NaCl) are highly polar and readily dissolve in polar solvents like water but are less soluble in non-polar solvents such as carbon tetrachloride (CCl_4).

Induced dipole-dipole interactions, also known as London dispersion forces, occur in non-polar molecules when the presence of a molecule with an instantaneous dipole induces a dipole in a neighboring molecule. Although each interaction is weak, collectively, they can have a significant effect on the solubility of larger non-polar molecules.

The strength of induced dipole-dipole interactions increases with the size of the molecule and the number of electrons, leading to higher solubility in non-polar solvents. These interactions are transient and depend on random fluctuations of electron density, which are more pronounced in larger atoms like iodine (I_2) compared to smaller atoms like chlorine (Cl_2).

The size of a molecule can have a substantial impact on its solubility. Larger molecules have more electrons and a greater surface area over which induced dipole-dipole interactions can occur, thereby enhancing solubility in non-polar solvents. This is because larger molecules can induce more substantial temporary dipoles in themselves and nearby molecules.

In the context of the textbook exercise, iodine (I_2) has a higher molecular size compared to bromine (Br_2) and chlorine (Cl_2), leading to stronger induced dipole-dipole interactions and subsequently greater solubility in non-polar solvents such as carbon tetrachloride (CCl_4). This relationship is a key factor when considering solubility in non-polar solvents and has implications in fields such as material science where solubility influences material selection and use.