Question

Compare van't Hoff factor for compounds \(\mathrm{CH}_{3}-\mathrm{CH}_{2} \mathrm{OH}\) and \(\mathrm{Ph}_{3} \mathrm{COH}\) in cold conc. \(\mathrm{H}_{2} \mathrm{SO}_{4}\) determined from measurement of freezing point. (A) \(\mathrm{i}_{\mathrm{ErOH}}>\mathrm{i}_{\mathrm{Ph}_{3} \mathrm{COH}}\) (B) \(\mathrm{i}_{\mathrm{EIOH}}<\mathrm{i}_{\mathrm{Pb}, \mathrm{COH}}\) (C) \(\mathrm{i}_{\text {EIOH }}=\mathrm{i}_{\mathrm{Ph}_{3} \mathrm{COH}}\) (D) \(\mathrm{i}_{\mathrm{E}_{\mathrm{IOH}}}<\mathrm{i}_{\mathrm{Pb}_{\mathrm{y}} \mathrm{COH}}<1\)

Short answer

The correct answer is (A) \(i_{ErOH} > i_{Ph_3COH}\), as Ethanol (ErOH) dissociates in \(\mathrm{H}_{2}\mathrm{SO}_{4}\) while Triphenylmethanol (Ph\(_{3}\)COH) does not.

Step-by-step solution

Identify the degree of dissociation for each compound in \(\mathrm{H}_{2}\mathrm{SO}_{4}\).

Ethanol (ErOH) is a primary alcohol, which reacts with concentrated \(\mathrm{H}_{2}\mathrm{SO}_{4}\) not only as a solvent but also forms an ester in the process. Therefore, ErOH will dissociate in \(\mathrm{H}_{2}\mathrm{SO}_{4}\). Triphenylmethanol (Ph\(_{3}\)COH) is a tertiary alcohol, which does not react with concentrated \(\mathrm{H}_{2}\mathrm{SO}_{4}\). In other words, it remains undissociated in \(\mathrm{H}_{2}\mathrm{SO}_{4}\).

Determine the van't Hoff factors for ErOH and Ph\(_{3}\)COH.

Since Ethanol (ErOH) dissociates in \(\mathrm{H}_{2}\mathrm{SO}_{4}\), its van't Hoff factor (i) is greater than 1: \(i_{ErOH} > 1\). On the other hand, Triphenylmethanol (Ph\(_{3}\)COH) does not dissociate in \(\mathrm{H}_{2}\mathrm{SO}_{4}\), so its van't Hoff factor (i) is equal to 1: \(i_{Ph_3COH} = 1\).

Compare the van't Hoff factors for ErOH and Ph\(_{3}\)COH.

We found that \(i_{ErOH} > 1\) and \(i_{Ph_3COH} = 1\). Therefore, we can compare their van't Hoff factors: \[ i_{ErOH} > i_{Ph_3COH} \] This comparison matches option (A) of the given exercise choices: \(i_{ErOH} > i_{Ph_3COH}\). The correct answer is (A) \(i_{ErOH} > i_{Ph_3COH}\).

Key concepts

Degree of Dissociation

The degree of dissociation refers to the extent to which a compound separates into its ions when dissolved. In the context of the given problem, we compare ethanol, a primary alcohol, with triphenylmethanol, a tertiary alcohol, in concentrated sulfuric acid ( H_2 SO_4 ). This process effectively influences their Van't Hoff factors.
In ethanol ( ErOH ), the reaction in H_2 SO_4 not only incorporates the acid as a solvent but also encourages ester formation, indicating some level of dissociation. Since dissociation leads to more particles in solution, ethanol will typically have a Van't Hoff factor above 1, suggesting that it does dissociate to a certain degree.
Conversely, triphenylmethanol ( Ph_3COH ), being a tertiary alcohol, does not exhibit the same behavior. It remains largely undissociated in H_2 SO_4 due to its steric hindrance and structural stability, keeping its Van't Hoff factor at 1. This comparison highlights how molecular structure and properties like the degree of dissociation directly influence the calculated Van't Hoff factor.

Freezing Point Depression

Freezing point depression is a colligative property that demonstrates how the addition of solutes can lower the freezing point of a solvent. When a substance dissolves, it alters the balance between the liquid and solid phase, causing the solvent to freeze at a lower temperature. This effect is linked to the solution's Van't Hoff factor.
For ethanol ( ErOH ) and triphenylmethanol ( Ph_3COH ) in H_2 SO_4 , their different Van't Hoff factors mean their effect on the freezing point will differ. Ethanol, with its greater degree of dissociation and a Van't Hoff factor greater than 1, will cause a greater depression in freezing point than triphenylmethanol whose factor is 1.
Thus, when comparing these two substances, the degree of freezing point depression illustrates how dissociative properties relate to the Van't Hoff factor, highlighting why erOH depresses the freezing point more substantially than Ph_3COH .

Primary vs Tertiary Alcohols

Alcohols are classified based on the carbon atom to which the hydroxyl group ( -OH ) is attached. Primary alcohols have the -OH group attached to a carbon atom that is only connected to one other carbon atom, while tertiary alcohols attach to a carbon connected to three other carbons.
This structural difference influences how these alcohols behave in different chemical environments. Primary alcohols like ethanol ( ErOH ) can participate in reactions like esterification with H_2 SO_4 , which leads to greater dissociation and a higher Van't Hoff factor.
In contrast, tertiary alcohols such as triphenylmethanol ( Ph_3COH ) are mostly inert in similar reactions due to steric hindrance and the stability associated with their structure. This makes them less reactive and results in a lower degree of dissociation, thus influencing properties like melting and boiling points. This structural and reactive variance showcases why ErOH dissociates and Ph_3COH remains relatively stable in H_2 SO_4 .