Benzoic acid undergoes dimerization in benzene solution, the van't Hoff factor 'i' is related to the degree of association ' \(\mathrm{x}\) ' of to the acid as: (a) \(\mathrm{i}=(1+\mathrm{x})\) (b) \(\mathrm{i}=(1-\mathrm{x})\) (c) \(\mathrm{i}=(1-\mathrm{x} / 2)\) (d) \(\mathrm{i}=(1+\mathrm{x} / 2)\)

Understanding the degree of association is crucial in the study of solutions where molecules may associate or dissociate. The degree of association, often denoted as \(x\), refers to the ratio of molecules that combine to form a new entity in a solution. For instance, when discussing benzoic acid in benzene, \(x\) tells us the fraction of total benzoic acid molecules that have paired up to create dimers.

To conceptualize it, imagine starting with 100 molecules; if the degree of association is 0.3, it means 30 of those original molecules have paired up, leaving 70 as individual benzoic acid molecules. This concept is pivotal in calculating the actual number of particles in a solution after association has taken place, which influences various solution properties like freezing point depression or vapor pressure reduction.

When we discuss benzoic acid dimerization, we're looking at a special type of association where benzoic acid molecules tend to pair up in certain solvents. In a nonpolar solvent like benzene, these acid molecules prefer to stick together in pairs, forming what's known as 'dimers'.

Dimerization occurs because benzoic acid molecules can form hydrogen bonds with each other, which are energetically favorable in a nonpolar environment. This process reduces the total number of particles in the solution since two molecules of benzoic acid become one single dimer. The understanding of this dimerization process is essential for calculating the van't Hoff factor, which will tell us how the physical properties of the solution are altered.

Colligative properties are the physical properties of solutions that depend on the number of dissolved particles but not on their identity. Examples include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure. These properties are widely used to determine molecular masses and the degree of ionization or association of solutes in solutions.

When benzoic acid dimerizes in benzene, it affects these properties because the number of free particles in the solution decreases. The van't Hoff factor, \(i\), plays a critical role; it's adjusted to reflect the reduced particle count due to dimerization. As \(i\) is less than one for benzoic acid dimerizing in benzene, the solution exhibits smaller changes in its colligative properties compared to what would be expected if the solute did not associate. This conceptually ties in how molecular interactions within a solution can lead to observable changes in its physical characteristics.